Advent Calendar 2021

| Day 16 | Day 17 | Day 18 |

The gift is presented by Walt Mankowski. Today he is talking about his solution to “The Weekly Challenge - 089”. This is re-produced for Advent Calendar 2021 from the original post by Walt Mankoswki.

Task #2: Magical Matrix

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

For this task we need to create a 3 x 3 magic square; i.e. a matrix where each row, column, and diagonal sums to the same value. We’re restricted to the numbers 1-9, so the sums should all be 15.

This is trivial in Matlab and Octave since there’s a built in function to create magic squares, so all we need to do is say

magic(3)

We have to do a bit more work in Perl, but fortunately there’s a simple algorithm for creating these sorts of magic squares called the Siamese method. It works for any m x m magic square where m is odd. Here’s the algorithm:

1. Start with a 1 in the middle column of the top row.

2. For each subsequent number, try to move to the cell to the northeast (1 row up and 1 column right), wrapping around to the left and bottom when we reach the edge.

3. If that cell is occupied, move one 1 down (wrapping around to the top if we’re on the bottom row) instead of moving to the northeast.

This is easy to do in Perl, and we don’t even have to initialize the matrix.

my @m;
my $m = 3;
my $r = 0;
my $c = 1;

# fill in the magic square using the Siamese method
for my $i (1..9) {
    $m[$r][$c] = $i;
    my $r1 = ($r - 1) % $m;
    my $c1 = ($c + 1) % $m;
    if (defined $m[$r1][$c1]) {
        $r = ($r + 1) % $m;
    } else {
        $r = $r1;
        $c = $c1;
    }
}

If you have any suggestion then please do share with us perlweeklychallenge@yahoo.com.

Advent Calendar 2021