We have 2 math puzzles from Perl Weekly Challenge 089 this time around. Their solution look rather naive.
TASK #1 › GCD Sum
Submitted by: Mohammad S Anwar
You are given a positive integer $N.
Write a script to sum GCD of all possible unique pairs between 1 and $N.
Example 1:
Input: 3
Output: 3
gcd(1,2) + gcd(1,3) + gcd(2,3)
Example 2:
Input: 4
Output: 7
gcd(1,2) + gcd(1,3) + gcd(1,4) + gcd(2,3) + gcd(2,4) + gcd(3,4)
Quite literally, we could translate the question to Raku code and get a naive solution:
(1..$N).combinations(2).map(-> ($a, $b) { $a gcd $b }).sum() TASK #2 › Magical Matrix
Submitted by: Mohammad S Anwar
Write a script to display matrix as below with numbers 1 - 9. Please make sure numbers
are used once.
[ a b c ] [ d e f ] [ g h i ] So that it satisfies the following:
a + b + c = 15 d + e + f = 15 g + h + i = 15 a + d + g = 15 b + e + h = 15 c + f + i = 15 a + e + i = 15 c + e + g = 15 Without doing any prior analysis of 3x3 magic square, a brute-force searching apporach would db to generate all permutations of the list of 1..9, then remove those that violates the 8 conditions above:
(1..9).permutations.grep( -> ($a, $b, $c, $d, $e, $f, $g, $h, $i) { all( $a + $b + $c == 15, $d + $e + $f == 15, $g + $h + $i == 15, $a + $d + $g == 15, $b + $e + $h == 15, $c + $f + $i == 15, $a + $e + $i == 15, $c + $e + $g == 15, ) } ) The .permutations subroutine produce an iterator that give us all possible permutations, and since we are permutating 9 numbers, we let the grep afterward takes 9 separate parameters, which then makes it easier to just copy those conditions from the body of the question.
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