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    <title>DEV Community: Hayden Mankin</title>
    <description>The latest articles on DEV Community by Hayden Mankin (@dry).</description>
    <link>https://dev.to/dry</link>
    <image>
      <url>https://media2.dev.to/dynamic/image/width=90,height=90,fit=cover,gravity=auto,format=auto/https:%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Fuser%2Fprofile_image%2F403538%2F127dacfb-ed99-48d5-aecc-c339bd918f23.jpeg</url>
      <title>DEV Community: Hayden Mankin</title>
      <link>https://dev.to/dry</link>
    </image>
    <atom:link rel="self" type="application/rss+xml" href="https://dev.to/feed/dry"/>
    <language>en</language>
    <item>
      <title>Screenshot Web Elements Across Browsers in Issue Comments.</title>
      <dc:creator>Hayden Mankin</dc:creator>
      <pubDate>Wed, 01 Dec 2021 04:54:18 +0000</pubDate>
      <link>https://dev.to/dry/screenshot-web-elements-across-devices-in-issue-comments-i4</link>
      <guid>https://dev.to/dry/screenshot-web-elements-across-devices-in-issue-comments-i4</guid>
      <description>&lt;h3&gt;
  
  
  My Workflow
&lt;/h3&gt;


&lt;div class="ltag-github-readme-tag"&gt;
  &lt;div class="readme-overview"&gt;
    &lt;h2&gt;
      &lt;img src="https://res.cloudinary.com/practicaldev/image/fetch/s--566lAguM--/c_limit%2Cf_auto%2Cfl_progressive%2Cq_auto%2Cw_880/https://dev.to/assets/github-logo-5a155e1f9a670af7944dd5e12375bc76ed542ea80224905ecaf878b9157cdefc.svg" alt="GitHub logo"&gt;
      &lt;a href="https://github.com/DryCreations"&gt;
        DryCreations
      &lt;/a&gt; / &lt;a href="https://github.com/DryCreations/screenshot-workflow"&gt;
        screenshot-workflow
      &lt;/a&gt;
    &lt;/h2&gt;
    &lt;h3&gt;
      This workflow will run a local server in a GitHub action, take screenshots using Playwright, upload those screenshots to Imgur, and post them as a comment on an issue or pull request.
    &lt;/h3&gt;
  &lt;/div&gt;
  &lt;div class="ltag-github-body"&gt;
    
&lt;div id="readme" class="md"&gt;
&lt;h1&gt;
Screenshot Workflow&lt;/h1&gt;
&lt;p&gt;This workflow will run a local server in a github action, take screenshots using Playwright, upload those screenshots to imgur, and post them as a comment on an issue or pull request.&lt;/p&gt;
&lt;h2&gt;
Instructions&lt;/h2&gt;
&lt;p&gt;To activate this workflow all you need to do is leave a comment in this format:&lt;/p&gt;
&lt;div class="snippet-clipboard-content position-relative overflow-auto"&gt;&lt;pre&gt;&lt;code&gt;/screenshot browser path {selector}
&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;
&lt;p&gt;Your comment can contain as many of these commands as you want, the workflow will post all of the screenshots in the same comment.&lt;/p&gt;
&lt;p&gt;&lt;code&gt;browser&lt;/code&gt;: Represents the browser being run by playwright, try using &lt;code&gt;webkit&lt;/code&gt; or &lt;code&gt;chromium&lt;/code&gt;.&lt;/p&gt;
&lt;p&gt;&lt;code&gt;path&lt;/code&gt;: Represents the path being screenshotted by playwright, this demo project only has a root path &lt;code&gt;/&lt;/code&gt;.&lt;/p&gt;
&lt;p&gt;&lt;code&gt;selector&lt;/code&gt;: An optional flag representing a query selector of an element to screenshot instead of a whole page.&lt;/p&gt;
&lt;p&gt;These options allow contributors and maintainers to screenshot various new features, or compare issues across browser easily by…&lt;/p&gt;
&lt;/div&gt;
  &lt;/div&gt;
  &lt;div class="gh-btn-container"&gt;&lt;a class="gh-btn" href="https://github.com/DryCreations/screenshot-workflow"&gt;View on GitHub&lt;/a&gt;&lt;/div&gt;
&lt;/div&gt;


&lt;p&gt;This workflow will run a local server in a Github action, take screenshots using Playwright, upload those screenshots to Imgur, and post them as a comment on an issue or pull request.&lt;/p&gt;

&lt;h3&gt;
  
  
  Submission Category:
&lt;/h3&gt;

&lt;p&gt;Maintainer Must-Haves&lt;/p&gt;

&lt;h3&gt;
  
  
  Yaml File or Link to Code
&lt;/h3&gt;

&lt;p&gt;Demo Repository: &lt;a href="https://github.com/DryCreations/screenshot-workflow"&gt;https://github.com/DryCreations/screenshot-workflow&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;Workflow:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight yaml"&gt;&lt;code&gt;&lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;Screenshot&lt;/span&gt;
&lt;span class="na"&gt;on&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; 
  &lt;span class="na"&gt;issue_comment&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
    &lt;span class="na"&gt;types&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; 
      &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="s"&gt;created&lt;/span&gt;

&lt;span class="na"&gt;jobs&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
  &lt;span class="na"&gt;screenshot&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
    &lt;span class="na"&gt;runs-on&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;ubuntu-latest&lt;/span&gt;
    &lt;span class="na"&gt;container&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;mcr.microsoft.com/playwright:focal&lt;/span&gt;
    &lt;span class="na"&gt;if&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;contains(github.event.comment.body, '/screenshot')&lt;/span&gt;
    &lt;span class="na"&gt;steps&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
    &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;Checkout Main&lt;/span&gt;
      &lt;span class="na"&gt;if&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;${{ !github.event.issue.pull_request }}&lt;/span&gt;
      &lt;span class="na"&gt;uses&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;actions/checkout@v2&lt;/span&gt;
    &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;Get Branch for Pull Request&lt;/span&gt;
      &lt;span class="na"&gt;if&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;${{ github.event.issue.pull_request }}&lt;/span&gt;
      &lt;span class="na"&gt;uses&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;xt0rted/pull-request-comment-branch@v1&lt;/span&gt;
      &lt;span class="na"&gt;id&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;comment-branch&lt;/span&gt;
    &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;Checkout Branch&lt;/span&gt;
      &lt;span class="na"&gt;if&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;${{ github.event.issue.pull_request }}&lt;/span&gt;
      &lt;span class="na"&gt;uses&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;actions/checkout@v2&lt;/span&gt;
      &lt;span class="na"&gt;with&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
        &lt;span class="na"&gt;ref&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;${{ steps.comment-branch.outputs.head_ref }}&lt;/span&gt;
    &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;Cache NPM Dependencies&lt;/span&gt;
      &lt;span class="na"&gt;uses&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;actions/cache@v2&lt;/span&gt;
      &lt;span class="na"&gt;with&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
        &lt;span class="na"&gt;path&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;~/.npm&lt;/span&gt;
        &lt;span class="na"&gt;key&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;${{ runner.OS }}-npm-cache-${{ hashFiles('**/package-lock.json') }}&lt;/span&gt;
        &lt;span class="na"&gt;restore-keys&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="pi"&gt;|&lt;/span&gt;
          &lt;span class="s"&gt;${{ runner.OS }}-npm-cache-&lt;/span&gt;
    &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;Install Playwright&lt;/span&gt;
      &lt;span class="na"&gt;run&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="pi"&gt;|&lt;/span&gt;
        &lt;span class="s"&gt;npm install playwright&lt;/span&gt;
    &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;Run Server&lt;/span&gt;
      &lt;span class="na"&gt;run&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="pi"&gt;|&lt;/span&gt;
        &lt;span class="s"&gt;npm run start &amp;amp; &lt;/span&gt;
        &lt;span class="s"&gt;npx wait-on http://127.0.0.1:3000/&lt;/span&gt;
    &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;Screenshot Images&lt;/span&gt;
      &lt;span class="na"&gt;id&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;sc_step&lt;/span&gt;
      &lt;span class="na"&gt;uses&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;actions/github-script@v5&lt;/span&gt;
      &lt;span class="na"&gt;with&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
        &lt;span class="na"&gt;github-token&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;${{secrets.GITHUB_TOKEN}}&lt;/span&gt;
        &lt;span class="na"&gt;script&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="pi"&gt;|&lt;/span&gt;
          &lt;span class="s"&gt;const { webkit, firefox, chromium } = require('playwright');&lt;/span&gt;

          &lt;span class="s"&gt;let browsers = {&lt;/span&gt;
            &lt;span class="s"&gt;"webkit": webkit,&lt;/span&gt;
            &lt;span class="s"&gt;"firefox": firefox,&lt;/span&gt;
            &lt;span class="s"&gt;"chromium": chromium&lt;/span&gt;
          &lt;span class="s"&gt;}&lt;/span&gt;
          &lt;span class="s"&gt;let comment_body = context.payload.comment.body;&lt;/span&gt;

          &lt;span class="s"&gt;let matches = comment_body.matchAll(/\/screenshot (?&amp;lt;browser&amp;gt;.+?) (?&amp;lt;path&amp;gt;.+?)(\s{(?&amp;lt;selector&amp;gt;.+)})?/gm);&lt;/span&gt;
          &lt;span class="s"&gt;let img_ctr = 0;&lt;/span&gt;

          &lt;span class="s"&gt;for (const { groups: { browser, path, selector } } of matches) {&lt;/span&gt;
            &lt;span class="s"&gt;console.log(browser, path, selector);&lt;/span&gt;
            &lt;span class="s"&gt;let img_id = img_ctr++;&lt;/span&gt;
            &lt;span class="s"&gt;(async () =&amp;gt; {&lt;/span&gt;
              &lt;span class="s"&gt;const b = await browsers[browser].launch();&lt;/span&gt;
              &lt;span class="s"&gt;const page = await b.newPage();&lt;/span&gt;
              &lt;span class="s"&gt;await page.goto(`http://127.0.0.1:3000${path}`, { waitUntil: 'domcontentloaded' });&lt;/span&gt;
              &lt;span class="s"&gt;const element = selector ? await page.$(selector) : page;&lt;/span&gt;
              &lt;span class="s"&gt;await element.screenshot({ path: `image-uploads/${img_id}.png` });&lt;/span&gt;
              &lt;span class="s"&gt;await b.close();&lt;/span&gt;
            &lt;span class="s"&gt;})()&lt;/span&gt;
          &lt;span class="s"&gt;}&lt;/span&gt;
    &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;Upload to Imgur&lt;/span&gt;
      &lt;span class="na"&gt;id&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;imgur_step&lt;/span&gt;
      &lt;span class="na"&gt;uses&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;devicons/public-upload-to-imgur@v2.2.1&lt;/span&gt;
      &lt;span class="na"&gt;with&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
        &lt;span class="na"&gt;path&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;image-uploads/&lt;/span&gt; &lt;span class="c1"&gt;# or path/to/images&lt;/span&gt;
        &lt;span class="na"&gt;client_id&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;${{secrets.IMGUR_CLIENT_ID}}&lt;/span&gt;
    &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;Comment Images&lt;/span&gt;
      &lt;span class="na"&gt;uses&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;actions/github-script@v5&lt;/span&gt;
      &lt;span class="na"&gt;env&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
        &lt;span class="na"&gt;IMG_URLS&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;${{ steps.imgur_step.outputs.imgur_urls }}&lt;/span&gt;
      &lt;span class="na"&gt;with&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
        &lt;span class="na"&gt;github-token&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;${{secrets.GITHUB_TOKEN}}&lt;/span&gt;
        &lt;span class="na"&gt;script&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="pi"&gt;|&lt;/span&gt;
          &lt;span class="s"&gt;const { IMG_URLS } = process.env&lt;/span&gt;
          &lt;span class="s"&gt;let img_urls = JSON.parse(IMG_URLS)&lt;/span&gt;
          &lt;span class="s"&gt;console.log(img_urls)&lt;/span&gt;
          &lt;span class="s"&gt;console.log(img_urls[0])&lt;/span&gt;

          &lt;span class="s"&gt;let comment_body = context.payload.comment.body;&lt;/span&gt;
          &lt;span class="s"&gt;let matches = comment_body.matchAll(/\/screenshot (?&amp;lt;params&amp;gt;.+? .+?(\s{.+})?)/gm);&lt;/span&gt;
          &lt;span class="s"&gt;let params = Array.from(matches, m =&amp;gt; m.groups.params);&lt;/span&gt;

          &lt;span class="s"&gt;let body = img_urls.map((url, idx) =&amp;gt; `# ${params[idx]}\n![Image](${url})`).join('\n\n')&lt;/span&gt;

          &lt;span class="s"&gt;github.rest.issues.createComment({&lt;/span&gt;
            &lt;span class="s"&gt;issue_number: context.issue.number,&lt;/span&gt;
            &lt;span class="s"&gt;owner: context.repo.owner,&lt;/span&gt;
            &lt;span class="s"&gt;repo: context.repo.repo,&lt;/span&gt;
            &lt;span class="s"&gt;body: body&lt;/span&gt;
          &lt;span class="s"&gt;})&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Additional Resources / Info
&lt;/h3&gt;

&lt;p&gt;Relies on the following actions:&lt;/p&gt;

&lt;p&gt;&lt;a href="https://github.com/marketplace/actions/checkout"&gt;https://github.com/marketplace/actions/checkout&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;&lt;a href="https://github.com/marketplace/actions/cache"&gt;https://github.com/marketplace/actions/cache&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;&lt;a href="https://github.com/marketplace/actions/github-script"&gt;https://github.com/marketplace/actions/github-script&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;&lt;a href="https://github.com/marketplace/actions/publish-on-imgur"&gt;https://github.com/marketplace/actions/publish-on-imgur&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;Important Notes:&lt;/p&gt;

&lt;p&gt;If you plan on using this in your own project, you may want to play attention to line 37. Currently the project runs the following command:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;npm run start
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;And expects a server to start at &lt;code&gt;http://127.0.0.1:3000/&lt;/code&gt;&lt;/p&gt;

&lt;p&gt;If your project acts differently, or has another run command, update the command on line 37 as needed.&lt;/p&gt;

</description>
      <category>actionshackathon21</category>
      <category>opensource</category>
      <category>github</category>
    </item>
    <item>
      <title>Coins on a Chessboard</title>
      <dc:creator>Hayden Mankin</dc:creator>
      <pubDate>Thu, 09 Jul 2020 03:44:19 +0000</pubDate>
      <link>https://dev.to/dry/coins-on-a-chessboard-4gif</link>
      <guid>https://dev.to/dry/coins-on-a-chessboard-4gif</guid>
      <description>&lt;h1&gt;
  
  
  Introduction
&lt;/h1&gt;

&lt;p&gt;Recently I've discovered the concept of error detecting/correcting codes and have been fascinated. Specifically I read an article here about the &lt;a href="https://en.wikipedia.org/wiki/Luhn_algorithm" rel="noopener noreferrer"&gt;Luhn algorithm&lt;/a&gt; the other day. &lt;/p&gt;


&lt;div class="ltag__link"&gt;
  &lt;a href="/divyajyotiuk" class="ltag__link__link"&gt;
    &lt;div class="ltag__link__pic"&gt;
      &lt;img src="https://media.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Fuser%2Fprofile_image%2F383310%2Fc273b2be-b09e-4824-8370-f30ea603330c.jpg" alt="divyajyotiuk"&gt;
    &lt;/div&gt;
  &lt;/a&gt;
  &lt;a href="/divyajyotiuk/credit-card-number-check-4cf8" class="ltag__link__link"&gt;
    &lt;div class="ltag__link__content"&gt;
      &lt;h2&gt;Credit card number check&lt;/h2&gt;
      &lt;h3&gt;Divyajyoti Ukirde ・ Jul 5 '20&lt;/h3&gt;
      &lt;div class="ltag__link__taglist"&gt;
        &lt;span class="ltag__link__tag"&gt;#javascript&lt;/span&gt;
        &lt;span class="ltag__link__tag"&gt;#algorithms&lt;/span&gt;
        &lt;span class="ltag__link__tag"&gt;#tutorial&lt;/span&gt;
      &lt;/div&gt;
    &lt;/div&gt;
  &lt;/a&gt;
&lt;/div&gt;


&lt;p&gt;And even more fascinating to me was this video from &lt;a href="https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw" rel="noopener noreferrer"&gt;3blue1brown&lt;/a&gt;.&lt;/p&gt;

&lt;p&gt;&lt;iframe width="710" height="399" src="https://www.youtube.com/embed/wTJI_WuZSwE"&gt;
&lt;/iframe&gt;
&lt;/p&gt;

&lt;p&gt;This problem is fascinating to me for so many reasons, especially how it can be rewritten as a graph theory problem. I won't be diving into the many different ways to write or solve this problem, but I encourage you to watch his video if you're interested.&lt;/p&gt;

&lt;h1&gt;
  
  
  The Chessboard Problem
&lt;/h1&gt;

&lt;p&gt;In case you don't wanna watch the whole video, I'll summarize the problem posed.&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;There are 3 people involved in this scenario two prisoners and a warden.&lt;/li&gt;
&lt;li&gt;The warden takes prisoner 1 to a room with a chessboard, the chessboard has a coin on every square.&lt;/li&gt;
&lt;li&gt;The warden is able to flip any coins he wants over, and hide a key under one coin.&lt;/li&gt;
&lt;li&gt;Prisoner 1, knowing where the key is, is allowed to flip over one coin in an attempt to relay the keys position to prisoner 2.&lt;/li&gt;
&lt;li&gt;No other information or hints may be left by prisoner 1, he is escorted out of the room and prisoner 2 enters.&lt;/li&gt;
&lt;li&gt;Prisoner 2 is allowed to pick up one coin to find the key, if he finds the key their freedom is assured, if not they are stuck in prison.&lt;/li&gt;
&lt;li&gt;If the prisoners are allowed to strategize before attempting the puzzle, is it possible to relay the position of the key to the other prisoner?&lt;/li&gt;
&lt;/ul&gt;

&lt;h1&gt;
  
  
  The Solution
&lt;/h1&gt;

&lt;p&gt;While it would be tricky to do by hand (entirely feasible, but tedious), writing a program to find a solution is fairly simple. I thought I would share my implementation and how I worked through it.&lt;/p&gt;

&lt;p&gt;To solve this problem I'm going to start with an example of a 2x2 chessboard, every position on the checkerboard is going to be assigned a unique index.&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;0&lt;/td&gt;
&lt;td&gt;1&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;2&lt;/td&gt;
&lt;td&gt;3&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;The problem doesn't actually need a 2D grid to be solved, we can just as easily work it out if we flatten the above array:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;0&lt;/td&gt;
&lt;td&gt;1&lt;/td&gt;
&lt;td&gt;2&lt;/td&gt;
&lt;td&gt;3&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;For the sake of matching the original problem, I will mostly display the table in 2d format.&lt;/p&gt;

&lt;p&gt;It's also important to note that all of these numbers can be written in binary.&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;00&lt;/td&gt;
&lt;td&gt;01&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;10&lt;/td&gt;
&lt;td&gt;11&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;Next we can represent the board state in terms of heads and tails, or true and false.&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Heads&lt;/td&gt;
&lt;td&gt;Heads&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Heads&lt;/td&gt;
&lt;td&gt;Tails&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;For our notation the above layout will match the following representation.&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;Before we can find a way to send information by flipping a coin, we need a way to turn our board state into a message for the other prisoner. If we look at all the spots on the board that are heads up, we get the positions &lt;code&gt;{00, 01, 10}&lt;/code&gt; while &lt;code&gt;{11}&lt;/code&gt; is tails. If we XOR all of the positions in the heads up positions we get &lt;code&gt;00 XOR 01 XOR 10 -&amp;gt; 11&lt;/code&gt; meaning the message prisoner 2 would receive is position 11.&lt;/p&gt;

&lt;p&gt;We now need a way to send a specific message, let's say the warden hides the key position &lt;code&gt;10&lt;/code&gt;.  We need to flip one and only one coin to change the message from &lt;code&gt;11&lt;/code&gt; to &lt;code&gt;10&lt;/code&gt;, to do this we find the differing bits &lt;code&gt;11 XOR 10 -&amp;gt; 01&lt;/code&gt; and flip the resulting coin.&lt;/p&gt;

&lt;p&gt;So our board state goes from:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;&lt;strong&gt;True&lt;/strong&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;em&gt;True&lt;/em&gt;&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;To:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;&lt;strong&gt;False&lt;/strong&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;After flipping the coin prisoner 1 can leave and allow prisoner to decode the message using the previously described method. &lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;The heads up coins are in positions &lt;code&gt;{00, 10}&lt;/code&gt; &lt;/li&gt;
&lt;li&gt;XOR all heads up coins: &lt;code&gt;00 XOR 10 -&amp;gt; 10&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;Look under the resulting coin (&lt;code&gt;10 -&amp;gt; 3&lt;/code&gt;) to find the key&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;This method extends to larger boards, with some caveats I will explain later.&lt;/p&gt;

&lt;p&gt;We will expand to a 4x4 for another example. The positions are going to be assigned as follows:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;0000&lt;/td&gt;
&lt;td&gt;0001&lt;/td&gt;
&lt;td&gt;0010&lt;/td&gt;
&lt;td&gt;0011&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;0100&lt;/td&gt;
&lt;td&gt;0101&lt;/td&gt;
&lt;td&gt;0110&lt;/td&gt;
&lt;td&gt;0111&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;1000&lt;/td&gt;
&lt;td&gt;1001&lt;/td&gt;
&lt;td&gt;1010&lt;/td&gt;
&lt;td&gt;1011&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;1100&lt;/td&gt;
&lt;td&gt;1101&lt;/td&gt;
&lt;td&gt;1110&lt;/td&gt;
&lt;td&gt;1111&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;The warden flips coins to give this board:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;&lt;em&gt;False&lt;/em&gt;&lt;/td&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;Then the warden hides the key in position &lt;code&gt;0010&lt;/code&gt;.&lt;/p&gt;

&lt;p&gt;Prisoner 1 takes the following steps to flip a coin over:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Find all positions that are heads up: &lt;code&gt;{0011, 0101, 1000, 1010, 1100}&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;XOR all positions: &lt;code&gt;0011 XOR 0101 XOR 1000 XOR 1010 XOR 1100 -&amp;gt; 1000&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;Find different bits between the keys position and the current message: &lt;code&gt;0010 XOR 1000 -&amp;gt; 1010&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;Flip the coin at position &lt;code&gt;1010&lt;/code&gt;
&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;The new board state is:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;th&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;&lt;em&gt;False&lt;/em&gt;&lt;/td&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;&lt;strong&gt;False&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;True&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;td&gt;False&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;Prisoner 2 takes the following steps to decode the message:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Find all positions that are heads up: &lt;code&gt;{0011, 0101, 1000, 1100}&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;XOR all positions: &lt;code&gt;0011 XOR 0101 XOR 1000 XOR 1100 -&amp;gt; 0010&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;Look under the coin in position &lt;code&gt;0010&lt;/code&gt;
&lt;/li&gt;
&lt;/ol&gt;

&lt;h1&gt;
  
  
  The Implementation
&lt;/h1&gt;

&lt;p&gt;To implement, there are 5 individual functions we will implement:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;randomBoard(n)&lt;/code&gt;

&lt;ul&gt;
&lt;li&gt;returns randomized &lt;code&gt;n&lt;/code&gt; x &lt;code&gt;n&lt;/code&gt; board of coins&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;
&lt;code&gt;randomPosition(board)&lt;/code&gt;

&lt;ul&gt;
&lt;li&gt;returns random position on &lt;code&gt;board&lt;/code&gt; in the format &lt;code&gt;{i: int, j: int}&lt;/code&gt;
&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;
&lt;code&gt;decodeBoard(board, target=0)&lt;/code&gt;

&lt;ul&gt;
&lt;li&gt;returns result of XOR operations on all true values on &lt;code&gt;board&lt;/code&gt; as well as the &lt;code&gt;target&lt;/code&gt; parameter&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;
&lt;code&gt;whatCoinToFlip(board, target)&lt;/code&gt;

&lt;ul&gt;
&lt;li&gt;returns position of coin to flip to encode &lt;code&gt;target&lt;/code&gt; on the &lt;code&gt;board&lt;/code&gt; in the form &lt;code&gt;{i: int, j: int}&lt;/code&gt;
&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;
&lt;code&gt;flipCoin(board, target)&lt;/code&gt;

&lt;ul&gt;
&lt;li&gt;return a deep copy of &lt;code&gt;board&lt;/code&gt; where the coin at &lt;code&gt;target&lt;/code&gt; is flipped&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;
&lt;code&gt;findKey(board)&lt;/code&gt;

&lt;ul&gt;
&lt;li&gt;return position in the form &lt;code&gt;{i: int, j: int}&lt;/code&gt; of key given a &lt;code&gt;board&lt;/code&gt; that has the proper message encoded.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;/ul&gt;

&lt;h2&gt;
  
  
  randomBoard(n)
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[];&lt;/span&gt;
    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;([]);&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;All this function does is initialize an array, push &lt;code&gt;n&lt;/code&gt; arrays into it then push &lt;code&gt;n&lt;/code&gt; random boolean values into all of those.&lt;/p&gt;

&lt;p&gt;We can also test it using &lt;code&gt;console.table(board)&lt;/code&gt; which will allow us to view our board in a very attractive way.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;┌─────────┬──────┬───────┬───────┬───────┐
│ (index) │  0   │   1   │   2   │   3   │
├─────────┼──────┼───────┼───────┼───────┤
│    0    │ true │ false │ true  │ true  │
│    1    │ true │ true  │ false │ true  │
│    2    │ true │ true  │ true  │ false │
│    3    │ true │ true  │ false │ false │
└─────────┴──────┴───────┴───────┴───────┘
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  randomPosition(board)
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;randomPosition&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="na"&gt;i&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
        &lt;span class="na"&gt;j&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;max&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt;  &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;max&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Javascript doesn't have a built in random function that takes a range, so I just wrote a small random function to make it more readable to me. Our indexes i and j line up with the boards row and column respectively. Simply returning two random numbers constrained to the boards length is enough.&lt;/p&gt;

&lt;p&gt;Also, rather than calling board.length, it's easier to destructure the object and just get length in the function parameters.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomPosition&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;key:  { i: 3, j: 2 }
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  decodeBoard(board, target=0);
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;decodeBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;flat&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="nf"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;cum&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;val&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;cum&lt;/span&gt; &lt;span class="o"&gt;^&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;val&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;First I'm going to flatten the array because 1D arrays are easier to iterate over, from here we can proceed with reduce. Using javascript reduce to XOR all elements of an array is pretty trivial, the trick here is &lt;code&gt;val * idx&lt;/code&gt; will be 0 whenever &lt;code&gt;val&lt;/code&gt; is false. Because when it tries to do multiplication the &lt;code&gt;True&lt;/code&gt; value will act is if it is &lt;code&gt;1&lt;/code&gt; and &lt;code&gt;False&lt;/code&gt; will act as if it is a &lt;code&gt;0&lt;/code&gt;. I can see how this might be viewed as bad practice, however I think it makes the code look pretty nice in this case.&lt;/p&gt;

&lt;p&gt;I'm also using target as the starting point of our accumulator, since &lt;code&gt;target&lt;/code&gt; is 0 by default it will decode the board normally if not given anything. However, if we give it a value it will also XOR that value, this allows us to pass an extra parameter to get the coin we need to flip to get a specific value encoded.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;val&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;decodeBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;val&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;┌─────────┬──────┬───────┬───────┬───────┐
│ (index) │  0   │   1   │   2   │   3   │
├─────────┼──────┼───────┼───────┼───────┤
│    0    │ true │ false │ true  │ true  │
│    1    │ true │ false │ false │ true  │
│    2    │ true │ true  │ true  │ false │
│    3    │ true │ true  │ false │ false │
└─────────┴──────┴───────┴───────┴───────┘
8
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  whatCoinToFlip(board, target)
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;whatCoinToFlip&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;decodeBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="na"&gt;i&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
        &lt;span class="na"&gt;j&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;I'm using the same destructuring trick as earlier (in &lt;code&gt;randomPosition&lt;/code&gt;) to just get i and j from the target passed in. Then we need to convert the row column indexes to our mapping we laid out in the solution part of the post. It will be the same as an index in the flattened array, so we can use &lt;code&gt;i * board.length + j&lt;/code&gt;&lt;/p&gt;

&lt;p&gt;We can then decode the board, passing in the extra parameter to get the specific coin we need to flip.&lt;/p&gt;

&lt;p&gt;We can then convert the index on a 1D array to a position on a 2D array and return it.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomPosition&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;The key is hidden at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;whatCoinToFlip&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;flip over the coin at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;┌─────────┬───────┬───────┬───────┬───────┐
│ (index) │   0   │   1   │   2   │   3   │
├─────────┼───────┼───────┼───────┼───────┤
│    0    │ true  │ false │ true  │ false │
│    1    │ false │ false │ false │ true  │
│    2    │ true  │ false │ true  │ false │
│    3    │ true  │ true  │ true  │ false │
└─────────┴───────┴───────┴───────┴───────┘
The key is hidden at { i: 3, j: 1 }
flip over the coin at { i: 1, j: 1 }
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  flipCoin(board, target)
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;flipCoin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;newBoard&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;map&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;slice&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;
    &lt;span class="nx"&gt;newBoard&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;newBoard&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;newBoard&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;While this may be a somewhat unnecessary addition as I can always just change board itself, I wanted to avoid mutations as much as possible, so I'm returning a new array. The array is also always going to be 2D, so the copy can be made by using map, where every array in the board is mapped to a copy.&lt;/p&gt;

&lt;p&gt;Then, we make the change at position &lt;code&gt;[i][j]&lt;/code&gt; and return the newBoard.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;locationToFlip&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomPosition&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Flipping coin at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;locationToFlip&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;flipCoin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;locationToFlip&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;┌─────────┬───────┬───────┬───────┬───────┐
│ (index) │   0   │   1   │   2   │   3   │
├─────────┼───────┼───────┼───────┼───────┤
│    0    │ false │ false │ false │ false │
│    1    │ true  │ false │ false │ true  │
│    2    │ true  │ true  │ false │ true  │
│    3    │ false │ false │ false │ false │
└─────────┴───────┴───────┴───────┴───────┘
Flipping coin at { i: 2, j: 3 }
┌─────────┬───────┬───────┬───────┬───────┐
│ (index) │   0   │   1   │   2   │   3   │
├─────────┼───────┼───────┼───────┼───────┤
│    0    │ false │ false │ false │ false │
│    1    │ true  │ false │ false │ true  │
│    2    │ true  │ true  │ false │ false │
│    3    │ false │ false │ false │ false │
└─────────┴───────┴───────┴───────┴───────┘
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  findKey(board)
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;findKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;decodeBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="na"&gt;i&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
        &lt;span class="na"&gt;j&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This function is very simple as we only need to decode the board, and then convert the 1D index to a 2D index and return it.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomPosition&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;The key is hidden at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;whatCoinToFlip&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;flip over the coin at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;flipCoin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;decodedKeyLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;findKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;The key is at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;decodedKeyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;┌─────────┬───────┬───────┬───────┬───────┐
│ (index) │   0   │   1   │   2   │   3   │
├─────────┼───────┼───────┼───────┼───────┤
│    0    │ false │ false │ true  │ false │
│    1    │ true  │ false │ true  │ false │
│    2    │ false │ true  │ false │ false │
│    3    │ true  │ false │ true  │ true  │
└─────────┴───────┴───────┴───────┴───────┘
The key is hidden at { i: 1, j: 0 }
flip over the coin at { i: 0, j: 0 }
┌─────────┬───────┬───────┬───────┬───────┐
│ (index) │   0   │   1   │   2   │   3   │
├─────────┼───────┼───────┼───────┼───────┤
│    0    │ true  │ false │ true  │ false │
│    1    │ true  │ false │ true  │ false │
│    2    │ false │ true  │ false │ false │
│    3    │ true  │ false │ true  │ true  │
└─────────┴───────┴───────┴───────┴───────┘
The key is at { i: 1, j: 0 }
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h1&gt;
  
  
  Conclusion
&lt;/h1&gt;

&lt;p&gt;Now after putting everything together we are left with a fairly concise program that can simulate and solve the puzzle.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[];&lt;/span&gt;
    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;([]);&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;randomPosition&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="na"&gt;i&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
        &lt;span class="na"&gt;j&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;

    &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;max&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt;  &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;max&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;whatCoinToFlip&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;decodeBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="na"&gt;i&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
        &lt;span class="na"&gt;j&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;flipCoin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;newBoard&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;map&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;slice&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;
    &lt;span class="nx"&gt;newBoard&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;newBoard&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;newBoard&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;findKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;decodeBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="na"&gt;i&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
        &lt;span class="na"&gt;j&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;decodeBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;flat&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="nf"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;cum&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;val&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;cum&lt;/span&gt; &lt;span class="o"&gt;^&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;val&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// generate new board&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// generate random position for the key&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomPosition&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;The key is hidden at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// get the coin prisoner 1 should flip&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;whatCoinToFlip&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;flip over the coin at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// flip the specified coin over&lt;/span&gt;
&lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;flipCoin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// have prisoner 2 decode the board and find key.&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;decodedKeyLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;findKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;The key is at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;decodedKeyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;┌─────────┬───────┬───────┬───────┬───────┐
│ (index) │   0   │   1   │   2   │   3   │
├─────────┼───────┼───────┼───────┼───────┤
│    0    │ true  │ false │ true  │ false │
│    1    │ true  │ false │ false │ false │
│    2    │ false │ true  │ false │ false │
│    3    │ true  │ true  │ true  │ true  │
└─────────┴───────┴───────┴───────┴───────┘
The key is hidden at { i: 0, j: 0 }
flip over the coin at { i: 3, j: 3 }
┌─────────┬───────┬───────┬───────┬───────┐
│ (index) │   0   │   1   │   2   │   3   │
├─────────┼───────┼───────┼───────┼───────┤
│    0    │ true  │ false │ true  │ false │
│    1    │ true  │ false │ false │ false │
│    2    │ false │ true  │ false │ false │
│    3    │ true  │ true  │ true  │ false │
└─────────┴───────┴───────┴───────┴───────┘
The key is at { i: 0, j: 0 }
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Pretty cool right? the program also changes pretty easily to larger boards, lets try it with n=8 since the original problem wanted a chessboard.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// generate new board&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// generate random position for the key&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomPosition&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;The key is hidden at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// get the coin prisoner 1 should flip&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;whatCoinToFlip&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;flip over the coin at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// flip the specified coin over&lt;/span&gt;
&lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;flipCoin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// have prisoner 2 decode the board and find key.&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;decodedKeyLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;findKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;The key is at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;decodedKeyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;┌─────────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┐
│ (index) │   0   │   1   │   2   │   3   │   4   │   5   │   6   │   7   │
├─────────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
│    0    │ false │ false │ true  │ true  │ false │ true  │ true  │ false │
│    1    │ false │ true  │ false │ false │ true  │ false │ false │ false │
│    2    │ false │ true  │ true  │ false │ true  │ true  │ true  │ true  │
│    3    │ true  │ false │ true  │ false │ false │ true  │ false │ true  │
│    4    │ true  │ false │ true  │ true  │ true  │ false │ true  │ true  │
│    5    │ false │ true  │ false │ false │ true  │ false │ true  │ false │
│    6    │ false │ true  │ false │ false │ false │ true  │ false │ false │
│    7    │ false │ false │ true  │ false │ false │ true  │ true  │ false │
└─────────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┘
The key is hidden at { i: 5, j: 5 }
flip over the coin at { i: 7, j: 3 }
┌─────────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┐
│ (index) │   0   │   1   │   2   │   3   │   4   │   5   │   6   │   7   │
├─────────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
│    0    │ false │ false │ true  │ true  │ false │ true  │ true  │ false │
│    1    │ false │ true  │ false │ false │ true  │ false │ false │ false │
│    2    │ false │ true  │ true  │ false │ true  │ true  │ true  │ true  │
│    3    │ true  │ false │ true  │ false │ false │ true  │ false │ true  │
│    4    │ true  │ false │ true  │ true  │ true  │ false │ true  │ true  │
│    5    │ false │ true  │ false │ false │ true  │ false │ true  │ false │
│    6    │ false │ true  │ false │ false │ false │ true  │ false │ false │
│    7    │ false │ false │ true  │ true  │ false │ true  │ true  │ false │
└─────────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┘
The key is at { i: 5, j: 5 }
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Lastly I wanted to jump back to something I mentioned briefly, there are some caveats to this scaling up, I was very intentional in using &lt;code&gt;n=2&lt;/code&gt;, &lt;code&gt;n=4&lt;/code&gt; and &lt;code&gt;n=8&lt;/code&gt;. these can all be written in the form of n=2&lt;sup&gt;k&lt;/sup&gt;, since our algorithm is relies on flipping over a specific coin derived from repeated XOR operations there needs to actually be a coin for every possible value using &lt;code&gt;2k&lt;/code&gt; bits. So its impossible to solve a 9 x 9 board as we need 7 bits to represent numbers &lt;code&gt;n &amp;gt; 63&lt;/code&gt;, however there is no coin for any &lt;code&gt;n &amp;gt; 81&lt;/code&gt; such as &lt;code&gt;93 -&amp;gt; 1011101&lt;/code&gt;&lt;/p&gt;

&lt;p&gt;We can even try this odd board size and see an error occur as the index it tries to find is out of bounds&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;┌─────────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┐
│ (index) │   0   │   1   │   2   │   3   │   4   │   5   │   6   │   7   │   8   │
├─────────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
│    0    │ false │ true  │ false │ false │ false │ false │ true  │ false │ false │
│    1    │ false │ true  │ true  │ true  │ false │ false │ false │ false │ false │
│    2    │ true  │ true  │ true  │ true  │ false │ false │ false │ true  │ true  │
│    3    │ false │ true  │ false │ false │ false │ true  │ false │ true  │ false │
│    4    │ true  │ false │ false │ false │ false │ false │ true  │ true  │ false │
│    5    │ true  │ true  │ false │ false │ true  │ false │ false │ false │ true  │
│    6    │ true  │ false │ false │ false │ false │ true  │ false │ false │ false │
│    7    │ false │ true  │ false │ true  │ false │ true  │ false │ true  │ true  │
│    8    │ true  │ false │ false │ true  │ true  │ true  │ true  │ false │ true  │
└─────────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┘
The key is hidden at { i: 1, j: 3 }
flip over the coin at { i: 12, j: 3 }
TypeError: Cannot read property '3' of undefined
    at flipCoin (/home/runner/ChessBoardProblem/index.js:35:32)
    at /home/runner/ChessBoardProblem/index.js:65:9
    at Script.runInContext (vm.js:131:20)
    at Object.&amp;lt;anonymous&amp;gt; (/run_dir/interp.js:156:20)
    at Module._compile (internal/modules/cjs/loader.js:1133:30)    at Object.Module._extensions..js (internal/modules/cjs/loader.js:1153:10)
    at Module.load (internal/modules/cjs/loader.js:977:32)
    at Function.Module._load (internal/modules/cjs/loader.js:877:14)
    at Function.executeUserEntryPoint [as runMain] (internal/modules/run_main
.js:74:12)
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;It is entirely possible however, for some non-square boards, such as a 2 x 32 which will use all 5 bit numbers or an 8 x 16 board using all 7 bit numbers. As long as the total number of coins can be written in the form &lt;code&gt;n=2^k&lt;/code&gt;&lt;/p&gt;

&lt;p&gt;Rewriting some code we can generalize it for n x m boards.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;m&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[];&lt;/span&gt;
    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;([]);&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;m&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;randomPosition&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="na"&gt;length&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;width&lt;/span&gt;&lt;span class="p"&gt;}})&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="na"&gt;i&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
        &lt;span class="na"&gt;j&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;width&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;

    &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;max&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt;  &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;random&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;max&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;whatCoinToFlip&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;decodeBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="na"&gt;i&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
        &lt;span class="na"&gt;j&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;flipCoin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;newBoard&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;map&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;slice&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;
    &lt;span class="nx"&gt;newBoard&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;newBoard&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;j&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;newBoard&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;findKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;decodeBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="na"&gt;i&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
        &lt;span class="na"&gt;j&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;decodeBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;flat&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="nf"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;cum&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;val&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;cum&lt;/span&gt; &lt;span class="o"&gt;^&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;val&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// generate new board&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomBoard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// generate random position for the key&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;randomPosition&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;The key is hidden at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// get the coin prisoner 1 should flip&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;whatCoinToFlip&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;keyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;flip over the coin at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// flip the specified coin over&lt;/span&gt;
&lt;span class="nx"&gt;board&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;flipCoin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;flipLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// have prisoner 2 decode the board and find key.&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;decodedKeyLocation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;findKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;board&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;The key is at&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;decodedKeyLocation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;┌─────────┬───────┬───────┬──────┬──────┬───────┬───────┬───────┬──────┐
│ (index) │   0   │   1   │  2   │  3   │   4   │   5   │   6   │  7   │
├─────────┼───────┼───────┼──────┼──────┼───────┼───────┼───────┼──────┤
│    0    │ false │ true  │ true │ true │ false │ true  │ false │ true │
│    1    │ false │ false │ true │ true │ true  │ false │ true  │ true │
└─────────┴───────┴───────┴──────┴──────┴───────┴───────┴───────┴──────┘
The key is hidden at { i: 1, j: 4 }
flip over the coin at { i: 0, j: 2 }
┌─────────┬───────┬───────┬───────┬──────┬───────┬───────┬───────┬──────┐
│ (index) │   0   │   1   │   2   │  3   │   4   │   5   │   6   │  7   │
├─────────┼───────┼───────┼───────┼──────┼───────┼───────┼───────┼──────┤
│    0    │ false │ true  │ false │ true │ false │ true  │ false │ true │
│    1    │ false │ false │ true  │ true │ true  │ false │ true  │ true │
└─────────┴───────┴───────┴───────┴──────┴───────┴───────┴───────┴──────┘
The key is at { i: 1, j: 4 }
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;I'll leave it you to read through and find the changes on that one :)&lt;/p&gt;

&lt;p&gt;This was my first post here, I hope you learned something, I thought this was a really cool and wanted to share. If anyone else knows any similar puzzles/algorithms I'd love to dive more into this subject. I know my university offers a course on error correcting codes but it's only offered in the spring semesters so I have a bit until I can take it, so I'd love some resources to dive into the subject on my own.&lt;/p&gt;

&lt;p&gt;Thanks!&lt;/p&gt;

</description>
      <category>javascript</category>
      <category>algorithms</category>
      <category>tutorial</category>
      <category>computerscience</category>
    </item>
  </channel>
</rss>
