Kata

You have n dices each one having s sides numbered from 1 to s. How many outcomes add up to a specified number k?

For example if we roll four normal six-sided dices we have four outcomes that add up to 5.

(1, 1, 1, 2) (1, 1, 2, 1) (1, 2, 1, 1) (2, 1, 1, 1)

There are 100 random tests with:

• 0 <= n <= 10
• 1 <= s <= 20
• 0 <= k <= n * s

Notes:

• there is always exactly 1 case to reach k = 0 regardless of the number of dice you have
• without any dice, it's not possible to reach any positive k