DEV Community: 刘西川

Griductive vs. Sudoku: Two Different Theories of What a Logic Puzzle Is

刘西川 — Wed, 25 Mar 2026 04:58:46 +0000

I built Griductive. People often compare it to Sudoku — and the comparison is natural. Both are daily logic puzzles. Both guarantee one unique solution. Both reward careful, methodical reasoning over guessing.

But they are genuinely different kinds of puzzles, built on different design philosophies. This article is about what those differences actually are.

What Sudoku Is

Most people know Sudoku as a number puzzle. That description is misleading in an important way: Sudoku has nothing to do with numbers.

The digits 1–9 are arbitrary symbols. You could replace them with colors, letters, or emoji and the puzzle would be mathematically identical. What Sudoku is about is uniqueness in groups: place exactly one instance of each symbol in each row, each column, and each of the nine 3×3 boxes. Three constraint types, one elegant grid structure, and every puzzle ever made is a variation on those same three rules.

That simplicity is a genuine strength. Sudoku was invented by American architect Howard Garns in 1979, popularized in Japan by Nikoli in 1984 under the name 数独 (Sūdoku), and went global in 2004 when a New Zealand-born retired Hong Kong judge named Wayne Gould pitched his algorithmically-generated puzzles to The Times of London. The key insight Gould had — that algorithmic generation could supply newspapers with infinite fresh puzzles — is the same insight that underlies Griductive's generation pipeline.

What Griductive Is

Griductive is a daily deductive classification puzzle. You're given a grid of characters, each of whom is either a Suspect or an Innocent. Some characters carry logical clues; some start pre-revealed. Your goal is to classify every character correctly using those clues alone.

The clues are natural-language logical statements. Not digits. Not visual patterns. Sentences like:

"There are exactly 3 suspects in row 2."
"Every suspect in column C is connected — they form a continuous chain."
"Row 1 has more suspects than column A."
"Julia is the only person in row 1 with exactly 1 suspect neighbor."
"The two suspects in column C are exactly 2 cells apart."

Over 26 clue types span counting, comparison, spatial arrangement, identity, uniqueness, connectivity, and distance. Four grid sizes — 3×3 through 5×5 — offer different levels of challenge. Every puzzle is verified by a constraint solver before it reaches a player.

The Core Design Difference

Sudoku and Griductive are both constraint satisfaction problems, but they're solving different types of constraints.

Sudoku asks: where does each value go? The constraints are structural and implicit — you learn them once, and they never change. Mastery means building a deep vocabulary of techniques and learning to recognize the patterns those techniques apply to.

Griductive asks: what is each cell? The answer is binary — Suspect or Innocent. The constraints are explicit and linguistic — you read and interpret each clue individually, every puzzle. You're not building fluency with a fixed technique set; you're reasoning through a fresh set of logical relationships each time.

Neither mode is superior. They engage different things. Sudoku rewards visual-spatial pattern recognition built up through practice. Griductive rewards reading and interpreting new logical statements on each puzzle.

A Closer Look at Sudoku's Solving Techniques

With both games in view, it's worth going deeper on what Sudoku mastery actually looks like — because it shapes how the two games feel different over time.

Sudoku technique is hierarchical. Beginners use Naked Singles (only one digit fits a cell) and Hidden Singles (only one cell in a region can take a digit). Most easy puzzles yield entirely to these two techniques.

The intermediate layer introduces Naked/Hidden Pairs and Triples, Pointing Pairs, and Box-Line Reduction — techniques that work by constraining candidate sets across intersecting regions.

The advanced layer is where Sudoku starts to feel like a different game: X-Wing, Swordfish, XY-Wing, and chain-based techniques like Skyscraper and Alternating Inference Chains. X-Wing is a good example of what makes this level satisfying — a digit confined to exactly two cells in each of two rows, sharing columns, forces eliminations across the whole grid. It's genuinely elegant.

At the extreme end sits bifurcation — pick a candidate, assume it's true, trace the consequences, and backtrack when a contradiction appears. The Sudoku community has a genuine philosophical divide about this. One camp holds that with sufficiently advanced techniques, any valid puzzle can be resolved without bifurcation; it's just a shortcut for solvers who haven't learned the deeper chains yet. The other camp argues that exploring hypothetical branches and pruning failures is exhaustive search under a different name. I'm personally in the second camp, which influenced how I designed Griductive — but it's a contested question, not a settled one.

The modern variant Sudoku world deserves mention here. Channels like Cracking the Cryptic have pushed the format into remarkable creative territory: Thermo constraints, Sandwich sums, Anti-Knight movement, Fog of War, Whisper lines — entirely new constraint types invented and layered onto the classic rules every week. The classic 9×9 and the variant Sudoku community are genuinely different experiences.

Griductive's Design Choices

Verified Pure Deduction

Every Griductive puzzle is verified — before publication — by the same constraint solver that generated it. The check confirms not just that a unique solution exists, but that the deduction engine can reach it through forward logical inference alone, without backtracking. If a puzzle can't be resolved that way, it's discarded. This is a hard guarantee built into the generation pipeline, not a quality target.

Evidence Analysis

When you classify a character incorrectly, Griductive doesn't just tell you you're wrong — it shows you why. The Evidence Analysis system assumes your incorrect guess as a hypothesis, propagates it through all relevant clues, finds the exact contradiction it produces, and walks you through the chain step by step: hypothesis in blue, clue anchors in orange, the final conflict in red.

You see exactly which clue chain produced the contradiction and what the correct path of reasoning should have been. Over time, this turns every mistake into a micro-lesson.

The better dedicated Sudoku apps — Sudoku Coach, Logic-Wiz, the Cracking the Cryptic apps — do offer sophisticated step-by-step hint systems that explain technique application in detail. What distinguishes Evidence Analysis is that it starts from your specific wrong move and traces the contradiction it produces, rather than explaining what to do next. That's a different kind of feedback.

The Logic Graph

Pro subscribers have access to the Logic Graph — a visualization of the full deduction structure of a puzzle as a directed acyclic graph. Each node is a character; each edge is a deductive dependency. Characters are organized by solving depth, so you can see which clues are entry points, which require long reasoning chains, and why harder puzzles are harder.

Clue Variety

Griductive's 26+ clue types mean the composition of each puzzle shapes its character: a puzzle built around spatial connectivity feels different from one centered on counting and comparison, which feels different from one relying on identity and uniqueness constraints. The difficulty scaling runs across both grid size and clue complexity simultaneously.

The Daily Ritual

Both games are designed around a daily solving habit.

Daily Sudoku is ubiquitous — every major news site has one, and the NYT's Sudoku section is a cultural institution. No signup, no install, playable anywhere including on paper.

Griductive offers four puzzles daily across four grid sizes, from the quick 3×3 Grid Lite to the demanding 5×5 Deep Dive. Puzzles are algorithmically generated with a unique daily seed, so they're fresh worldwide every day. The archive extends backward indefinitely — Pro subscribers can solve any past puzzle, with no repetition, because puzzles are generated rather than drawn from a fixed pool.

What Sudoku Does Particularly Well

Universal accessibility. No language comprehension required. Playable anywhere, on paper, in any language, with nothing to install.

Cultural depth. Sudoku has World Championships, dedicated communities, and YouTube channels with millions of subscribers. The community infrastructure built around it over 40+ years is genuinely remarkable.

Technique elegance. Intermediate Sudoku techniques — Naked Pairs, X-Wing, Hidden Triples — have a beautiful geometric logic. Understanding why X-Wing works is a genuine intellectual pleasure.

Variant Sudoku. The modern variant community has pushed the format into extraordinary creative territory. Thermos, Sandwich sums, Anti-Knight, Fog of War, Whisper lines — constraint invention every week. If you think Sudoku has a fixed constraint space, you haven't explored this corner of it.

Zero friction. Open any newspaper.

What Makes Griductive Distinct

Verified pure deduction. Every puzzle is mathematically guaranteed to be solvable through logical inference alone. Not a goal — a hard constraint on generation.

Evidence Analysis. When you guess wrong, the game traces your hypothesis to the exact contradiction it produces. Every mistake becomes a lesson.

Natural-language clues. You read, interpret, and reason through fresh logical statements each puzzle — a different cognitive mode from pattern recognition against a fixed technique set.

Logic Graph. A full visualization of each puzzle's deduction structure: entry points, dependency chains, solving depth.

Four grid sizes daily. A quick 3×3 warm-up or a demanding 5×5 — structurally distinct complexity at each level.

Who Should Play Which?

Play Sudoku if:

You want a universal format with no language barrier and a massive global community
You enjoy building a deep technique vocabulary and recognizing patterns fluently
You play on paper, or want zero-friction access with nothing to install

Play Griductive if:

You want to reason through fresh logical statements rather than recognize familiar patterns
You care that every puzzle is guaranteed to be solvable through pure deduction
You want a feedback system that explains your specific mistakes from first principles
You want four difficulty tracks daily and a deduction graph to study puzzle structure

Closing Thought

Sudoku is a masterpiece of constraint design. It deserves its status as one of the great puzzle formats, and the variant Sudoku community has shown that its creative space is nowhere near exhausted. I have genuine respect for it — the insight that algorithmic generation could scale a puzzle format to millions of daily players is one I borrowed directly.

Griductive is something different: binary classification instead of symbol placement, natural-language clues instead of implicit structural rules, a feedback system built around your specific wrong move. The two games share a daily ritual and a uniqueness guarantee. Beyond that, they're doing different things.

The best reason to try Griductive isn't that it fixes something broken — it's that it's a different kind of puzzle experience that some solvers will find genuinely engaging.

Start with the free tier at griductive.com. No download, no credit card required.

Happy solving.

— Shawn, builder of Griductive

What is Griductive and how the puzzles are made

刘西川 — Mon, 23 Mar 2026 05:31:59 +0000

Griductive is a daily deductive logic puzzle game where you play as a detective and determine who is innocent and who is a suspect using pure logic. Some people on the grid may or may not carry a clue — all of them remain logically consistent with it and everyone speaks the truth!

No guessing. No luck. Just pure deduction.

how the puzzles are made

Every Griductive puzzle makes a bold promise: you will never need to guess. Every cell can be determined through logic alone, and every puzzle has exactly one correct answer.

That's not a design goal — it's a mathematical guarantee, enforced by the same class of solver used in operations research and chip verification. This post explains how.

Why Uniqueness Matters

If a puzzle has two valid solutions, there must be at least one cell where both Suspect and Innocent satisfy all the clues. At that cell, no amount of reasoning can tell you which is correct — you'd have to guess. Guessing violates the core contract of a deduction puzzle.

So the generator doesn't just produce puzzles that happen to have one solution. It proves that no second solution exists before a puzzle is ever published.

The Five-Phase Pipeline

Each Griductive puzzle is built through a five-phase pipeline. Here's what happens at each stage.

Phase 1: Generate a Random Solution

The generator starts by creating a valid solution grid — a random assignment of Suspect and Innocent to every cell. This is the ground truth that the player will eventually deduce.

At this point, no clues exist yet. The board is just a random configuration that satisfies basic structural constraints (grid dimensions, suspect count within valid ranges).

Phase 2: Build the Clue Pool

Next, the generator exhaustively enumerates every possible clue that is true on the solution board.

Griductive has over 26 distinct clue types — counting, comparison, spatial, existential, uniqueness, connectivity, and more. For each type, the generator tests every valid parameterization against the board. A 4×4 grid can produce thousands of candidate clues. Only clues that evaluate to true on the solution are kept.

This is the raw material the generator works with: a massive pool of true statements, most of which are redundant.

Phase 3: Select a Minimal Clue Set (the Hard Part)

This is where the real work happens. The generator needs to choose a small subset of clues from the pool such that:

The clues are sufficient — together, they constrain the solution space to exactly one valid board.
No clue is redundant — removing any single clue would allow multiple solutions.

The generator uses a greedy constraint satisfaction approach:

Start with no clues selected. The solution space is wide open — many boards could be valid.
Score every candidate clue by how much it narrows the solution space. A clue that eliminates 80% of remaining possibilities scores higher than one that eliminates 10%.
Select the highest-scoring clue and add it to the set.
Re-solve the constraint model with the updated clue set.
Repeat until the solver confirms that only one solution remains.
Prune: walk through the final set and remove any clue that isn't necessary for uniqueness. This keeps the puzzle clean and avoids giving the player free information.

The result is a tight, fair clue set — enough to solve the puzzle completely, with no wasted clues.

Phase 4: Score Difficulty

With the clue set locked in, the generator scores the puzzle's difficulty on a 0–100 scale. Four factors contribute:

Simple clue ratio (35%) — How many clues are direct counting or identity statements. More simple clues means an easier puzzle.
Complex clue ratio (30%) — How many clues require multi-step or spatial reasoning. These demand deeper deduction chains.
Information scarcity (20%) — How few clues are given relative to grid size. Fewer clues means less to work with.
Grid scale (15%) — Larger grids are inherently harder to track. A 5×5 puzzle has nearly three times the cells of a 3×3.

Each clue type also has an intrinsic complexity rating based on the reasoning it demands. A clue like "Julia is a suspect" is about as simple as it gets. A clue like "Julia is the only person in row 3 with exactly 1 suspect neighbor" requires cross-referencing multiple cells and is scored much higher.

Phase 5: Generate Hints and Format Output

Finally, the generator builds the hint sequence — a recommended solving order that guides stuck players through the puzzle one logical step at a time. Hints are ordered by dependency depth: cells that can be deduced immediately come first, and cells that require long chains of prior deductions come last.

The final puzzle is packaged with all the data the game needs: metadata, clue set, hint sequence, and difficulty score.

The Solver: How Uniqueness Is Proven

At the heart of the pipeline is Google OR-Tools CP-SAT — a constraint programming solver that combines constraint propagation, integer programming, and SAT solving.

How a puzzle becomes a math problem

Each cell on the grid is modeled as a boolean variable: Suspect (1) or Innocent (0). Each clue becomes one or more mathematical constraints over those variables.

For example:

"There are exactly 2 suspects in row 3" becomes: cell[3,0] + cell[3,1] + cell[3,2] + cell[3,3] = 2
"All suspects in column A are connected" becomes: a connectivity constraint ensuring that suspect cells in column A form a contiguous chain with no gaps.
"Row 1 has more suspects than column B" becomes: sum(row_1) > sum(col_B)

How uniqueness is verified

After assembling the clue set, the generator asks CP-SAT a precise question: "Given these constraints, does more than one valid assignment exist?"

CP-SAT doesn't just find a solution — it can enumerate all solutions. If the solver finds exactly one, the puzzle is valid. If it finds two or more, the generator goes back to Phase 3 and adds another clue.

This is a formal proof, not a heuristic. CP-SAT exhaustively explores the entire solution space. If it says there's one solution, there is exactly one — period.

Why not just brute-force it?

A 5×5 grid has 25 cells, each with 2 possible values. That's 2²⁵ = 33 million possible boards. Brute-forcing all of them is slow and doesn't scale.

CP-SAT is dramatically faster because of constraint propagation: when a clue says "row 3 has exactly 2 suspects," the solver immediately reduces the search space for every cell in row 3 without checking each combination individually. Complex clues compound this effect. In practice, CP-SAT proves uniqueness for a 5×5 puzzle in milliseconds.

What Could Go Wrong (and How We Prevent It)

"What if a clue is ambiguous?"

Every clue type has a formal mathematical definition. "Neighbors" always means the up-to-8 surrounding cells including diagonals. "Connected" always means a contiguous chain of adjacent cells. "Between" always means cells in the same row or column, excluding endpoints.

These definitions are built directly into the constraint model — there's no natural language interpretation step where ambiguity could creep in. The in-game Clarifying Details reference shows players exactly what each spatial keyword means.

"What if the solver has a bug?"

The CP-SAT solver is a well-tested, widely-used tool maintained by Google's optimization team. But we don't rely on trust alone. Every generated puzzle is independently verified:

An automated solver attempts to solve every puzzle step-by-step, simulating a human player. If it can't reach a complete solution through logical deduction alone, the puzzle is rejected.
Hint soundness checks verify that each hint in the sequence is logically valid — that the hinted cell is genuinely deducible from the clues and previously revealed cells, not from hidden information.

"What if clue generation misses edge cases?"

Each clue type has a formal evaluation function that is tested against known puzzle configurations. The clue pool generation phase only includes clues that evaluate to true on the actual solution — a clue that's false on the solution can never appear in the puzzle.

The Result

When you open a Griductive puzzle, here's what has already happened:

A random solution was generated.
Thousands of candidate clues were evaluated against it.
A minimal, non-redundant subset was selected.
A formal solver proved that exactly one solution satisfies those clues.
An automated solver independently verified that the puzzle is solvable through pure deduction.
A difficulty score was computed and a hint sequence was generated.

Every puzzle, every day, across all four grid sizes. No exceptions.

The promise holds: if you're stuck, there's a clue you haven't fully used yet. If you think two answers are possible, re-read the clues — the logic will resolve it. And if you want proof, the Logic Graph will show you the exact deduction chain from clues to solution.

What's Next: Clues That Tell a Story

Right now, Griductive's clues read like precise logical statements — clear and unambiguous, but admittedly a bit clinical. "There are exactly 2 suspects in row 3" gets the job done, but it doesn't exactly make you feel like a detective on a case.

We're actively working on changing that. The goal is to diversify how clues are expressed — weaving in thematic flavor while preserving the same underlying logical precision. Imagine clues tied to holiday events, or framed as witness testimony from a specific crime scene. Instead of a sterile formula, you'd read something that feels like an actual piece of evidence from an investigation.

The key constraint hasn't changed: every clue must remain consistent, unambiguous, and formally verifiable. The solver doesn't care whether a clue sounds like a math textbook or a noir detective novel — it only cares about the logical content. That separation is what makes richer expression possible without compromising correctness.

Same guarantees. Same rigor. But puzzles that feel less like equations and more like cases worth cracking.

No guessing. No luck. Mathematically guaranteed.

Play today's puzzle →