Unusual dice

January 27, 2011 Leave a comment Go to comments

I heard of this problem from Justin James in his TechRepublic post My First IronRuby Application. He tried this fun problem as a toy example to brush up his skills in ruby:

Roll simultaneously a hundred 100-sided dice, and add the resulting values. The set of possible outcomes is, of course, \{100, 101, \dotsc, 10000\}. Note that there is only one way to obtain the outcome 100—all dice showing a 1. There is also only one way to obtain the outcome 10000—all dice showing 100. For the outcome 101, there are exactly 100 different ways to obtain it: all dice except one show a 1, and one die shows a 2. The follow-up question is:

Write a (fast) script that computes the different ways in which we can obtain each of the possible outcomes.

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