# well, you could have an absolute maximum of 5 3s
# 16 1s
# so i'd start off with 5 3s and a 1
# remove 1 3 and add 3 1s
# loop until 16 1's
# for each result, find the total number of possible combinations
# so say the result is [3,3,3,1,1,1,1,1,1,1]
# you'd have to find the total possible number of results without using
# any more or any less than 3 3s
# and 7 1s
# and without repeating a combination
# Therefore:

$max_3s = 5;
$max_1s = 16;

# Define $sum as the sum of the current loop's values.
# If $sum > 16 at any point, or < 16 when loop ends, discard the value.
$sum = 0;

# $sum_3s is the number of 3s in the current loop.
# We don't need 1s; if there are more than 16 1s then
# the limit of sixteen has already been reached.
$sum_3s = 0;

# Define $valid as an array containing all valid strings.
# Will use valid.length to get the total number.
$valid = [];

$startstr = "133333";
$str = $startstr;

# Function to return the next string.
def nextStr(str)
  orig = str;
  str = str.sub('3', '1');
  return (str==orig ? false : str);
end

while true do
  $str.each_byte { |ch|
    $sum += ch.to_i;
    if (ch.to_i == 3) then $sum_3s += 1; end
    if ($sum > 16) or ($sum_3s > $max_3s) then
      $sum=0;
      break;
    end
  }
  if not ($valid.index($str)) then
    $valid.push($str);
  end
  $str = nextStr($str);
  break if not $str;
end
print $valid.length, " values.\n";