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

作者：gugod 發佈於：`#raku`

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.