Interesting problem...
Since it's that time of year...

q(May all your Christmases be white.) =~ s/Christmase/loop/r =~ s/whit
+e/implicit/r
[download]

Inspired by mention of "sliding".

#!/usr/bin/perl

use strict; # https://theweeklychallenge.org/blog/perl-weekly-challeng
+e-248/#TASK2
use warnings;
use List::AllUtils qw( zip_by reduce );
use Data::Dump qw( pp );

sub slide
  {
  my @new;
  reduce { push @new, $a + $b; $b } @_;
  @new;
  }

for ( [ [1,  2,  3,  4],
        [5,  6,  7,  8],
        [9, 10, 11, 12] ],
      [ [1, 0, 0, 0],
        [0, 1, 0, 0],
        [0, 0, 1, 0],
        [0, 0, 0, 1] ],
    )
    {
    print 'Input: $a = ', pp($_), "\n";
    my @new = zip_by { [ @_ ] } map [ slide @$_ ],
      zip_by { [ @_ ] } map [ slide @$_ ], @$_;
    print 'Output: $b = ', pp(\@new), "\n\n";
    }
[download]

Outputs

Input: $a = [[1 .. 4], [5 .. 8], [9 .. 12]]
Output: $b = [[14, 18, 22], [30, 34, 38]]

Input: $a = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
Output: $b = [[2, 1, 0], [1, 2, 1], [0, 1, 2]]
[download]

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