Fun little problem (if I understand it correctly)

#!/usr/bin/perl

# https://perlmonks.org/?node_id=1233341

use strict;
use warnings;

local $_ = do { local $/; <DATA> };
my $original = $_;
s/.\K  //g;                       # tweaks to make it easier to work w
+ith
my $width = /\n/ && $-[0];
s/.+/sprintf "%-${width}s", $&/ge;
my @squares;
my $g = qr/..{$width}/s;
my $letter = 'A';

while( /x| / )
  {
  my $pos = $-[0];
  my $found = $&;
  my ($x, $y) = ( $pos % ($width + 1), int $pos / ($width + 1) );
  for my $size ( reverse 1 .. $width - 1 )
    {
    my $sm1 = $size - 1;
    pos($_) = $pos;
    if( /\G(?=$found {$sm1})(?:$g(?= {$size})){$sm1}/ ) # try magic
      {
      push @squares, [ $x, $y, $size, $letter ];
      for my $n ( 1 .. $size )
        {
        substr $_, $pos, $size, $letter x $size;
        $pos += $width + 1;
        }
      $letter++;
      length $letter > 1 and chop $letter;
      last;
      }
    }
  }
use Data::Dump 'dd'; dd \@squares;
print $original;
print s/./$&  /gr =~ s/  $//gmr;

__DATA__
0  1  2  3  4  5  6  7  8  9  0  1  2
1
2                             x
3                    x
4        x
5  x
6              x
7                       x  x
8        x
9        x                 x
0        x
1     x                  x
2
[download]

Outputs:

[
  [1, 1, 3, "A"],
  [4, 1, 3, "B"],
  [7, 1, 2, "C"],
  [9, 1, 1, "D"],
  [10, 1, 1, "E"],
  [11, 1, 2, "F"],
  [9, 2, 1, "G"],
  [10, 2, 1, "H"],
  [7, 3, 4, "I"],
  [11, 3, 2, "J"],
  [1, 4, 1, "K"],
  [2, 4, 1, "L"],
  [3, 4, 2, "M"],
  [5, 4, 2, "N"],
  [1, 5, 2, "O"],
  [11, 5, 2, "P"],
  [3, 6, 2, "Q"],
  [5, 6, 2, "R"],
  [1, 7, 2, "S"],
  [7, 7, 1, "T"],
  [8, 7, 1, "U"],
  [9, 7, 2, "V"],
  [11, 7, 2, "W"],
  [3, 8, 1, "X"],
  [4, 8, 5, "Y"],
  [1, 9, 2, "Z"],
  [3, 9, 1, "A"],
  [9, 9, 2, "B"],
  [11, 9, 2, "C"],
  [3, 10, 1, "D"],
  [1, 11, 1, "E"],
  [2, 11, 2, "F"],
  [9, 11, 2, "G"],
  [11, 11, 2, "H"],
  [1, 12, 1, "I"],
]
0  1  2  3  4  5  6  7  8  9  0  1  2
1
2                             x
3                    x
4        x
5  x
6              x
7                       x  x
8        x
9        x                 x
0        x
1     x                  x
2
0  1  2  3  4  5  6  7  8  9  0  1  2
1  A  A  A  B  B  B  C  C  D  E  F  F
2  A  A  A  B  B  B  C  C  G  H  F  F
3  A  A  A  B  B  B  I  I  I  I  J  J
4  K  L  M  M  N  N  I  I  I  I  J  J
5  O  O  M  M  N  N  I  I  I  I  P  P
6  O  O  Q  Q  R  R  I  I  I  I  P  P
7  S  S  Q  Q  R  R  T  U  V  V  W  W
8  S  S  X  Y  Y  Y  Y  Y  V  V  W  W
9  Z  Z  A  Y  Y  Y  Y  Y  B  B  C  C
0  Z  Z  D  Y  Y  Y  Y  Y  B  B  C  C
1  E  F  F  Y  Y  Y  Y  Y  G  G  H  H
2  I  F  F  Y  Y  Y  Y  Y  G  G  H  H
[download]

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