## Self-descriptive Numbers

This post is part of a series on Mohammad Anwar’s excellent Perl Weekly Challenge, where Perl and Raku hackers submit solutions to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

Challenge #2 this week (43) is to generate Self-descriptive Numbers in arbitrary bases. A self-descriptive number, as described by Wikipedia, is an integer m that in a given base b is b digits long in which each digit d at position n (the most significant digit being at position 0 and the least significant at position b – 1) counts how many instances of digit n are in m.

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## Olympic Rings

This post is part of a series on Mohammad Anwar’s excellent Perl Weekly Challenge, where Perl and Raku hackers submit solutions to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

Challenge #1 this week (43) is a number puzzle. In short, the task is to fill in the numbers 1, 2, 3, 4, and 6 into the spaces within the intersecting Olympic rings, so that the numbers in each ring sum to 11. Some of the spaces are already filled in (given). Here is the starting point:

I was able to solve this just by staring at it for a few seconds, so I knew this wasn’t going to be a computationally intensive task. And so instead I wrote a console program that draws the rings and animates every step of the recursive backtracking algorithm I used, because why not.

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## Balanced Parentheses

This post is part of a series on Mohammad Anwar’s excellent Perl Weekly Challenge, where Perl and Raku hackers submit solutions to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

The second challenge this week is another old chestnut:

Write a script to generate a string with random number of ( and ) brackets. Then make the script validate the string if it has balanced brackets.

The question has two parts:

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## Octal Representation

This post is part of a series on Mohammad Anwar’s excellent Perl Weekly Challenge, where Perl and Raku hackers submit solutions to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

Challenge 1 this week is an easy one:

Write a script to print decimal number 0 to 50 in [the] Octal Number System.

## Perl and Raku

We can solve this with the following polyglot (runs in both languages at once):

printf "Decimal %2d = Octal %2o\n", $_,$_ for 0..50;


Still, in Raku, we can do the following:

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## Leonardo Numbers

This post is part of a series on Mohammad Anwar’s excellent Perl Weekly Challenge, where Perl and Raku hackers submit solutions to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

Happy new year! We are on Week 41, and this is Challenge #2.

The Leonardo Numbers (A001595) are a simple recursively defined sequence:

$$L(n) = \begin{cases} 1 & \text{if } n \lt 2 \\ 1 + L(n – 1) + L(n – 2) & \text{if } n \geq 2 \end{cases}$$

The sequence starts: 1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, …

You’ll note this sequence is very similar to the well-known Fibonacci sequence, which differs only in that the Fibonacci sequence does not have the + 1 term, and starts at F(0) = 0.

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## Attractive Numbers

This post is part of a series on Mohammad Anwar’s excellent Perl Weekly Challenge, where Perl and Raku hackers submit solutions to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

This week, Mohammad asks us to output a list of all Attractive Numbers between 1 and 50. Attractive numbers, as described by the Online Encyclopedia of Integer Sequences (OEIS) are:

Numbers with a prime number of prime divisors (counted with multiplicity)

OEIS Sequence A063989

The first numbers are 4, 6, 8, 9, 10, 12, 14, 15, 18, 20, 21, 22, 25, 26, 27, 28, 30, 32, 33, 34, 35, 38, 39, 42, 44, 45, 46, 48, 49, 50, …

This is a straightforward problem, but I’m not going to let that stop me from finding an interesting way to solve it. If I were looking for a sensible way to solve it, I’d do something like this:

use Math::Prime::Util ':all';
say for grep { is_prime( factor(\$_) ) } 1..50;

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## Zip6

This post is part of a series on Mohammad Anwar’s excellent Perl Weekly Challenge, where Perl and Raku hackers submit solutions to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)

The zip6 function has long been a staple of the List::MoreUtils CPAN module. The Week 40 challenge #1 describes it very well. But even more succinctly: zip6 takes an array of arrays (AoA) and returns another AoA of all the 1st elements, then the 2nd, and so on.

It’s not a difficult algorithm by any stretch. In fact, the description more or less tells you how to do it. Simply iterate through all of the arrays in parallel, building up the resulting array as you go.

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## Reverse Polish Notation

This is my first blog post regarding the Perl Weekly Challenge tirelessly maintained by Mohammad Anwar. Although I’ve been doing the challenge for a while now, I haven’t maintained my blog for years. Let’s change that!

This week’s challenge #2 from the Perl Weekly Challenge is a computer science classic: create a Reverse Polish Notation (RPN) calculator. This brings back fond memories.

## Basic Algorithm

My Perl 5 and Raku solutions will both use the same basic algorithm. First, we tokenize the input into numbers and operators. Then, we loop through every token. For each token, we either:

1. If the token is a number, we add it to the stack
2. Otherwise, it’s an operator:
1. Pull zero or more items off the stack depending on the operator
2. Perform the required operation (e.g., addition, subtraction, etc.)
3. Push the result onto the stack
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