sub roundrobin {
  my ($n, $rounds, $bye) = @_;
  if ($n % 2) {
    $rounds = $n; $bye = 1;
    # There will be $rounds rounds with exactly one bye for each team.
  } else {
    $rounds = $n - 1; $bye = 0;
    # There will be $rounds rounds, and every team will quiz every round.
  }

  my $m = $n; ++$m if $n % 2; # $m is the lowest even number greater than or equal to $n
  my %s = (teams => $n, rounds => $rounds, bye => $bye); # The working schedule.

  # Fill in the working schedule with a nice diagonal pattern:
  for my $round (0 .. ($rounds - 1)) {
    for my $i (0 .. ($round-1)) {
      $s{table}->[$round]->[$i] = (($rounds + $round - $i + 1) + $m) % $m;
    }
    for my $i ($round .. ($n-1)) {
      $s{table}->[$round]->[$i] = (($rounds + $round - $i) + $m) % $m;
    }
  }

  use Data::Dumper; print Dumper(+{tentative => \%s});

  # Now, do knight-like moves with the 0 (bye) in the first row.
  # Every time the 0 lands on a number, put that number in the first column:
  my $byeround = 0;
  for my $i (reverse (1 .. ($m - 2))) {
    $byeround = (($byeround - 2) + $rounds) % $rounds;
    $s{table}->[$byeround]->[0] = $s{table}->[$byeround]->[$i] || 'Oopsie';
    $s{table}->[$byeround]->[$i] = 0;
  }

  # If m != n, then remove team n from all the games, and replace with -1 (which means a bye, i.e., the team sits out that round):
  if (not $m == $n) {
    for my $i (0 .. $rounds-1) {
      $s{table}->[$i]->[$i] = -1;
    }
  }
  return \%s;

}