Simon Green

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# Three means and big bases

## Weekly Challenge 157

I'm back after the three week hiatus!

## TASK #1 › Pythagorean Means

You are given a set of integers.

Write a script to compute all three Pythagorean Means i.e Arithmetic Mean, Geometric Mean and Harmonic Mean of the given set of integers.

### My solution

This is a relatively straight forward task. The Wikipedia page provides the necessary formulas and we can use the `sum` `reduce` and `lambda` functions to calculate the required figures. Finally we use the `round` function to print the results to one decimal place.

The Perl code is similar to the Python version, except we use the product() method in List::Utils. Python's math.product is only available for Python 3.8+

One thing to note is if the sum of integers is 0, a division by zero error might occur when calculating the harmonic mean. I'm not catching this and let the error pass to the user.

### Examples

``````\$ ./ch-1.py 1 3 5 6 9
AM = 4.8, GM = 3.8, HM = 2.8

\$ ./ch-1.py 2 4 6 8 10
AM = 6.0, GM = 5.2, HM = 4.4

\$ ./ch-1.py 1 2 3 4 5
AM = 3.0, GM = 2.6, HM = 2.2
``````

## TASK #2 › Brazilian Number

You are given a number `\$n` > 3.

Write a script to find out if the given number is a Brazilian Number. A positive integer number `N` has at least one natural number `B` where `1 < B < N-1` where the representation of `N` in base `B` has [the] same digits.

### My solution

This was an interesting task. We can't convert numbers into a different base simply by using letters and numbers. For example 1282 is 22 in base 640, but how would you express 639 in the same base?

For this task I considered a value having the same digits even if the number itself has different digits. For example, 925 is express as (25)(25) in base 36.

The guts of this task is to convert the number `n` in base 10 to a specified base, which I have called `b`. The function is called `same_digits`. I take the modulus (remainder) of `n` and `b` and make this value `d`. I then do an integer division and repeat this process comparing that `n % b` is `d`. I return `False` if any digit isn't the same, or `True` if they all are.

Then it's just a matter of having a loop from 2 to `n - 2`, and calling the `same_digits` function for each base. If there is a match, I print `1` (and the base), or `0` otherwise.

The Perl code is a transliteration of the Python code.

### Examples

``````\$ ./ch-2.py 6
0

\$ ./ch-2.py 7
1 (base 2)

\$ ./ch-2.py 8
1 (base 3)
``````

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