for my $row (1 .. $row_size) {
    for my $column (1 .. $column_size) {
        ...
    }
}

##</code><code>##

use List::Util qw{ shuffle };

# ...

for my $row (shuffle(1 .. $row_size)) {
    for my $column (shuffle(1 .. $column_size)) {
        ...
    }
}

##</code><code>##

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

local $SIG{ALRM} = sub { system killall => '1a1.pl'; die };

for my $r (2 .. 20) {
  SIZE:
    for my $c (2 .. 20) {
        open my $OUT, '>', 'x1' or die $!;
        say {$OUT} 1;
        say {$OUT} "$r $c";
        close $OUT;

        for my $rand (1 .. 100) {
            print "$r $c $rand\n";
            eval {
                alarm 1;
                0 == system '1a1.pl', $rand, 'x1';
            } and do {
                print "$r $c $rand\n";
                next SIZE
            };
        }
        say "NOT FOUND";
    }
}

##</code><code>##

my %srand = ('3 16' => 2,
             '4 10' => 2,
             '4 17' => 3,
             '4 19' => 3,
             '5 15' => 5,
             # ...
);

##</code><code>##

srand ($srand{"$rows $columns"} || 1);
$grid = solve($rows, $columns);