# Solving Perl Weekly Challenge 089 -- GCD Sum and the magic square.

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.