Counting the number of ways a pentomino can be placed on an 8x8 board with a 2x2 hole in the middle

pentominoes.pl

#! /usr/bin/perl
use 5.010;
use strict;
use warnings;

my $SIZE = 8;

my %pieces = (
    'F1' => <<"EOP",
.XX
XX.
.X.
EOP

    'F2' => <<"EOP",
XX.
.XX
.X.
EOP

    'I' => <<"EOP",
X
X
X
X
X
EOP

    'L1' => <<"EOP",
X.
X.
X.
XX
EOP

    'L2' => <<"EOP",
.X
.X
.X
XX
EOP

    'P1' => <<"EOP",
XX
XX
X.
EOP

    'P2' => <<"EOP",
XX
XX
.X
EOP

    'N1' => <<"EOP",
X..
XXX
..X
EOP

    'N2' => <<"EOP",
..X
XXX
X..
EOP

    'T' => <<"EOP",
XXX
.X.
.X.
EOP

    'U' => <<"EOP",
X.X
XXX
EOP

    'V' => <<"EOP",
X..
X..
XXX
EOP

    'W' => <<"EOP",
X..
XX.
.XX
EOP

    'X' => <<"EOP",
.X.
XXX
.X.
EOP

    'Y1' => <<"EOP",
.X
XX
.X
.X
EOP

    'Y2' => <<"EOP",
X.
XX
X.
X.
EOP

    'Z1' => <<"EOP",
..XX
XXX.
EOP

    'Z2' => <<"EOP",
XX..
.XXX
EOP
);

sub fits {
    my ($piece, $sr, $sc) = @_;
    my @rows = split /\n/, $piece;
    my $width = length($rows[0]);
    return if $sr + @rows - 1 > $SIZE - 1;
    return if $sc + $width - 1 > $SIZE - 1;
    for my $r (0..@rows-1) {
        my $row = $rows[$r];
        for my $c (0..$width-1) {
            if (substr($row, $c, 1) eq "X") {
                return if (3 == $sr + $r || 4 == $sr + $r)
                       && (3 == $sc + $c || 4 == $sc + $c);
            }
        }
    }
    return 1;
}

sub rotate {
    my ($piece, $rotations) = @_;
    for (1..$rotations) {
        my @rows = split /\n/, $piece;
        my $width = length($rows[0]);
        my @new_piece;
        for my $c (reverse 0..$width-1) {
            push @new_piece, join "", map { substr($_, $c, 1) } @rows;
        }
        $piece = join "\n", @new_piece;
    }
    return $piece;
}

my $rows;
for my $name (keys %pieces) {
    my $piece = $pieces{$name};
    chomp $piece;
    my $rotations = 4;
    $rotations = 2 if $name eq "I" || $name eq "N1" || $name eq "N2";
    $rotations = 1 if $name eq "X";
    for my $a (0..$rotations-1) {
        my $rotated_piece = rotate($piece, $a);
        for my $r (0..$SIZE-1) {
            for my $c (0..$SIZE-1) {
                if (fits($rotated_piece, $r, $c)) {
                    $rows++;
                }
            }
        }
    }
}
say $rows;