Question

Write a python function to solve the following problem.

Roll N(amount of) fair six-sided dice. The sum of the face values is M. Write a python function to determine how many different ways can you roll the dice given M and N.

For example, if N=2 and M=7 the answer is 6, because you can roll this dice in these 6 different ways: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

Another example: if N = 3 and M = 9 the answer is 25

Another example: if N = 8 and M = 24 the answer is 98813

def roll_dice(N,M):

result = []

return len(result)

Answer 1

def roll_dice(N, M):

  faces = 6

  poss=[[0]*(M+1) for j in range(N+1)]

  for j in range(1,min(faces+1,M+1)):

    poss[1][j]=1

    

  for a in range(2,N+1):

    for b in range(1,M+1):

      for c in range(1,min(faces+1,b)):

        poss[a][b]+=poss[a-1][b-c]

  

  return poss[-1][-1]

print(roll_dice(2,7))

print(roll_dice(3,9))

print(roll_dice(8,24))

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