OK with your idea I came up with this:

#!/usr/bin/perl

#program will generate all unique combinations of 4 from a pool of pla
+yers
#without repeating any pair of players

use strict;
use  Math::Combinatorics;

my $count;
my %seen;

sub trackSeen{
    my @players = @{$_[0]};
    #For each set of 4 players the following positions are ones we do 
+not want to see again
    my @pairs = ($players[0].$players[1], #0,1 
                $players[0].$players[2], #0,2 
                $players[0].$players[3], #0,3 
                $players[1].$players[2], #1,2 
                $players[1].$players[3], #1,3 
                $players[2].$players[3]  #2,3
    ); 
    foreach my $pair (@pairs){
        $seen{$pair} = 1;
    }
}

sub notSeen{
    my @players = @{$_[0]};
    my @pairs = ($players[0].$players[1], #0,1 
                $players[0].$players[2], #0,2 
                $players[0].$players[3], #0,3 
                $players[1].$players[2], #1,2 
                $players[1].$players[3], #1,3 
                $players[2].$players[3]  #2,3
    );
    foreach my $pair (@pairs){
        if (scalar grep /$pair/, keys(%seen) ){
            return 0;
        }
    }
    return 1;
}

my @n = 'A'..'X';
my $comboObj = Math::Combinatorics->new(count => 4, data => [@n]);
print "combinations of 4 from: " . join(" ", @n)."\n";
print "-----------------------------" . ("----" x scalar(@n))."\n";
while ( my @combo = $comboObj->next_combination){
    if ( notSeen(\@combo)  == 1) {
        print join(', ', @combo) . "\n";
        $count++;
        trackSeen(\@combo);
    } 
}

print "$count combinations\n";
[download]

The magic number for 24 players seems to be 35. I am sure this is not the most efficient way of doing it, but it works. Thanks. Output:

A, B, C, D
A, E, F, G
A, H, I, J
A, K, L, M
A, N, O, P
A, Q, R, S
A, T, U, V
B, E, H, K
B, F, I, L
B, G, J, M
B, N, Q, T
B, O, R, U
B, P, S, V
C, E, I, M
C, F, H, N
C, G, K, O
C, J, L, P
C, Q, U, W
C, R, T, X
D, E, J, N
D, F, K, P
D, G, H, L
D, I, O, Q
D, M, R, V
D, S, T, W
E, L, O, S
E, P, Q, X
F, J, O, T
F, M, S, U
F, V, W, X
G, I, N, R
H, M, O, W
I, K, S, X
J, K, Q, V
L, N, U, X
35 combinations
[download]

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