A STUDY OF A DICE PROBLEM

Dice are well-studied objects in combinatorial studies. In this paper, we study the following problem about dice: Given m dice, each of whi ch has n faces, how many arrangements of those dice are there such tha t the sum of their outcomes equals to p? We will give a computer solut ion as well as a combinatorial analysis of this problem. After studyin g the relationship between this dice problem and multinomial coefficie nt, we will further generalize this dice problem to its extreme and pr ovide corresponding solutions.