Dice Throw Problem

This algorithm finds the number of ways to get summation of values on each face when all the dice are thrown.

									function FindWays($faces, $dice, $sum)
{
	$table = array();
	Fill2DArray($table, $dice + 1, $sum + 1, 0);
	
	for ($i = 1; $i <= $faces && $i <= $sum; ++$i)
		$table[1][$i] = 1;

	for ($i = 2; $i <= $dice; ++$i)
	{
		for ($j = 1; $j <= $sum; ++$j)
		{
			for ($k = 1; $k <= $faces && $k < $j; ++$k)
			{
				$table[$i][$j] += $table[$i - 1][$j - $k];
			}
		}
	}

	return $table[$dice][$sum];
}

function Fill2DArray(&$arr, $rowCount, $colCount, $value)
{
	for ($i = 0; $i < $rowCount; ++$i)
		for ($j = 0; $j < $colCount; ++$j)
			$arr[$i][$j] = $value;
}

Example

									$result = FindWays(4, 3, 5);

Dice Throw Problem

Example

Output