# Communications of the ACM

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## Puzzled: Tumbling Dice

These puzzles involve computing probabilities associated with dice.

##### navneeth mandavilli

"the number N of different numbers that appear is determined; for example, if the dice show 3,4,1,6,5,6, then N = 5, and if they show 6,2,2,3,6,2, then N = 3"

It's not clear how N is determined in the above example. What precisely is N supposed to represent?

##### Jeremy Hansen

Hi Navneeth:

With the dice showing 3,4,1,6,5,6, the numbers 1, 3, 4, 5, and 6 all appear, with 6 appearing more than once in this case. Because there are 5 different numbers represented, N=5. With 6, 2, 2, 3, 6, 2, only three numbers appear: 2, 3, and 6, so N=3.

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