Here is a direct, iterative solution generating the possibilities in reverse lexicographical order (no modules, no waste). 

use strict;
use warnings;

my $base = 1; # minimum of cards per hole

sub first {
  my( $holes, $cards ) = @_;
  my @c = ($base) x $holes;
  $c[0] += $cards - $base * $holes; 
  $c[0] >= $base or die "Not enough cards!\n";
  return \@c;
}

sub next_comp {
  my $c = shift;
  my $i = 0;
  $i++ while $i < @$c and $c->[$i] == $base;
  $i >= @$c-1 and return;
  $c->[$i+1]++;
  $c->[0] = $c->[$i] - 1;
  $c->[$i] = $base if $i > 0;
  return $c;
}

@ARGV == 2 or die print "Usage: $0 holes cards\n";
my $c = first( @ARGV );
my $i = 0;
print ++$i.": @$c\n";
print ++$i.": @$c\n" while $c = next_comp $c;

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This also reminds me of Odometer pattern iterator (in C). (Updated.).

In reply to Re: Combinatorics problem. (Updated with more info.) by hdb
in thread Combinatorics problem. (Updated with more info.) by BrowserUk

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