Category: Fun stuff
Author/Contact Info Juerd
Description: This module creates magic squares. A magic square is a square in which all numbers are differet and the sums of all rows, all columns and the two diagonals are equal.

(To be uploaded to CPAN soon)
package Math::MagicSquare::Generator;
use strict;
use Carp;
use vars qw($VERSION);

$VERSION = '0.01';

sub _sum {
    my $sum = 0;
    $sum += $_ for @_;
    return $sum

sub new {
    my ($class, %opt) = @_;
    $opt{size}  ||= 5;
    $opt{start} ||= 1;
    $opt{step}  ||= 1;
    croak "Size needs to be a positive, odd integer"
        unless $opt{size} > 0 and
               $opt{size} % 2 and
               $opt{size} == int($opt{size});
    my $self = [
        map {
            [ (undef) x $opt{size} ]
        } 1..$opt{size}
    my $value = $opt{start};
    my $halv = int(@$self / 2);
    for my $start_x (-$halv..$halv) {
        my $x = $start_x - 1;
        my $y = $x + @$self + 1;
        for (1 .. @$self) {
            $x = $x - @$self if ++$x > $#$self;
            $y = $y - @$self if --$y > $#$self;
            $self->[$y][$x] = $value;
            $value += $opt{step};
    return bless $self, $class;

sub hflip {
    my ($self) = @_;
    my $clone;
    push @$clone, [ reverse @$_ ] for @$self;
    return bless $clone, ref $self;

sub vflip {
    my ($self) = @_;
    my $clone;
    push @$clone, [ @$_ ] for reverse @$self;
    return bless $clone, ref $self;

sub sum {
    my ($self) = @_;
    return _sum( @{ $self->[0] } );

sub check {
    my ($self) = @_;
    my $sum = $self->sum;
    # Horizontals
    for (@$self[1..$#$self]) {
        return undef if @$_ > @$self; # undef if not square
        return undef if _sum(@$_) != $sum;
    # Verticals
    for my $x (0..$#$self) {
        return undef if _sum(map $self->[$_][$x], 0..$#$self) != $sum;
    # Diagonals
    return undef if _sum(map $self->[$_][$_],           0..$#$self) !=
+ $sum;
    return undef if _sum(map $self->[$#$self - $_][$_], 0..$#$self) !=
+ $sum;
    # Duplicates
    my %seen;
    $seen{$_}++ for map @$_, @$self;
    return undef if _sum(values %seen) != keys %seen;
    # Passed all tests!
    return $sum;

sub as_string {
    my ($self) = @_;
    my $max = 0;
    length > $max and $max = length for map @$_, @$self;
    return map { join(' ', map {' 'x($max - length) . $_} @$_) . "\n" 
+} @$self;

sub as_html {
    my ($self) = @_;
    return "<table>\n" . join("\n",
        map { '<tr><td>' . join('</td><td>', @$_) . '</td></tr>' } @$s
+elf) .

sub as_csv {
    my ($self) = @_;
    return join("\n", map { join ',', @$_ } @$self) . "\n";



=head1 NAME

Math::MagicSquare::Generator - Magic Square Generator


    use Math::MagicSquare::Generator

    my $square = Math::MagicSquare::Generator->new(size => 5,
                                                   step => 3,
                                                   start=> 6);
    for ($square, $square->vflip, $square->hflip) {
        print $_->as_string;
        print "-----\n";

    $square->[0][0] = -15; # Break magic :)
    print $square->check ? "Magic square\n" : "Just a square\n";

    print '<html><body>';
    print Math::MagicSquare::Generator->new->hflip->vflip->as_html;
    print '</body></html>';


This module creates magic squares. A magic square is a square in which
all numbers are different and the sums of all rows, all columns and
the two diagonals are equal.
Math::MagicSquare::Generator cannot create panmagic squares, or square
that have an even size. (A panmagic square is magic square where the
"wrapped" diagonals are also equal.)

=head1 EXAMPLE

     3 16  9 22 15  This square is the output of
    20  8 21 14  2  print Math::MagicSquare::Generator->new->as_string
     7 25 13  1 19
    24 12  5 18  6
    11  4 17 10 23

    The sums of the rows are 65.
    The sums of the columns are 65.
    The sums of the diagonals are 65.

=head1 METHODS

=over 10

=item new

The constructor that generates the square immediately. It
creates an object using the given named arguments. Valid arguments are
C<size>, C<step> and C<start>. C<size> has to be positive, odd and

=item check

A checker - returns the common sum if the square is magic, or undef if
it's not. Because the sum can never be 0, you can use this as a boolea
value. (Well, the sum in a 1x1 square can be 0, if the single number i
0.) You can use this method to check if the square has been tampered w

=item sum

Returns the common sum of the rows, columns and diagonals.

=item vflip, hflip

These methods return a vertically or horizontally flipped clone of the
square. The clone is a Math::MagicSquare::Generator, so stacking these
methods is possible.

=item as_string, as_html, as_csv

DWYM - return the square as a formatted string, piece of html or in
CSV format.


=head1 THIS MODULE AND Math::MagicSquare

Math::MagicSquare is a module that checks if a square is magical. It
takes a list in its C<new> method, so you'll have to dereference the
generated square:

    use Math::MagicSquare;
    use Math::MagicSquare::Generator;

    my $square = Math::MagicSquare::Generator->new;
    print Math::MagicSquare->new( @$square )->check, "\n"; # 2

Its C<check> will always return 2 for squares generated using this
module (or 3 if it's a 1x1 square.


None yet.

=head1 AUTHOR

Juerd <>

Replies are listed 'Best First'.
Re: Math::MagicSquare::Generator
by merlyn (Sage) on Jan 27, 2002 at 21:34 UTC
    (To be uploaded to CPAN soon)
    Did you miss Math::MagicSquare, already in the cpan? How is yours different? Can you just send patches to the original author or take it over instead? I don't see why we need two Magic Square generators in the CPAN!

    -- Randal L. Schwartz, Perl hacker

    Update: Argh. I could swear that when I first looked at Math::MagicSquare, that it was both a generator and a checker, because I noted it for potential material for a column. My mistake.
      I made Math::MagicSquare::Generator last night, just because I couldn't sleep and couldn't stop thinking about magic squares. Years ago, we had an assignment at school to create a simple 3x3 magic square. That hounted me for weeks. After several weeks, I gave my teacher a piece of paper with an 11x11 magic square and he was impressed. Last night, I created a 5x5 magic square in my head, with no paper. While doing that, I realised I was thinking in terms of Perl code. I then wrote a module called Math::MagicSquare (on my laptop - no Internet connection (yes, the same laptop that has a 802.11b connection, but the Internet connection was down :)) in one go. The next morning, I checked CPAN to see if there already was a module. And there was - Just like you did, I thought it could generate and check, and I was kind of disappointed that I had re-invented a wheel. Its source was a mess, so I decided to not read, but use the code. Reading the documentation gave me the answer: it was just a checker. I chose to name my module after what it does, hoping the difference would be obvious - I renamed it to Math::MagicSquare::Generator, added documentation and uploaded it to CPAN after checking thoroughly if a module already existed.

      We both made the same mistake, and perhaps Math::MagicSquare::Checker would have been a better name for the existing Math::MagicSquare module, but it's too late for that now.

      2;0 juerd@ouranos:~$ perl -e'undef christmas' Segmentation fault 2;139 juerd@ouranos:~$