I feel so dumb. I thought this was a tough one to figure out. So anyway, I went ahead and wrote a script that generates nice PDF bingo cards:

#!/usr/bin/perl -w
use strict;
use PDFLib;

my @words = <DATA>;
chomp @words;

warn("got @words\n");

my $cards = shift @ARGV || die "Must supply number of cards\n";

print "Making $cards bingo cards\n";

my $pdf = PDFLib->new(
    filename => "bingo.pdf",
    papersize => "a4",
    creator => "Matt Sergeant",
    author => "Heather Sergeant",
    title => "Bingo!",
);

foreach my $i (1..$cards) {
    my %seen;

    print "Card $i\n";
    
    $pdf->start_page;
    
    $pdf->set_font(face => "Helvetica", size => 30, bold => 1);

    $pdf->print_boxed("Bingo!", mode => "center", x => 0, y => 740, w 
+=> 595, h => 50);
    
    $pdf->rect(x => 100, y => 200, w => 400, h => 400);
    $pdf->stroke;

    $pdf->set_font(face => "Helvetica", size => 20, bold => 0);

    for my $x (1..4) {
        for my $y (1..4) {
            my $word;
            while (1) {
                my $index = rand(@words);
                $word = $words[$index];
                if (!$seen{$word}) {
                    $seen{$word}++;
                    last;
                }
            }
            $pdf->print_boxed($word, mode => "center", x => (100 + (($
+x - 1) * 100)), y => (160 + (($y - 1) * 100)), w => 100, h => 100);
            if ($y != 1) {
                $pdf->move_to( 100, (200 + (($y - 1) * 100)) );
                $pdf->line_to( 500, (200 + (($y - 1) * 100)) );
                $pdf->stroke;
            }
        }
        if ($x != 1) {
            $pdf->move_to( (100 + (($x - 1) * 100)), 200 );
            $pdf->line_to( (100 + (($x - 1) * 100)), 600 );
            $pdf->stroke;
        }
    }
}

$pdf->finish;

1;
__DATA__
WORDS HERE
[download]

Fill the DATA section with the things you want on the bingo card (maybe it's just numbers, in my case it was words). Remember to include at least 16 or you end up in an infinite loop ;-)