It is a standard exercise in elementary combinatorics to the number of ways of rolling any given value with 2 fair 6-sided dice (by taking the of the two rolls). The below table the number of such ways of rolling a given value :
|# of ways|
A somewhat (un?)natural question is to ask whether or not there are any other ways of re-labeling the faces of the dice with positive integers that these sums with the same frequencies. The surprising answer to this question is that there does indeed exist such a re-labeling, via the labeling
and a pair of dice with this labeling are called a set of crazy dice. It is straight-forward to verify that the various possible occur with the same frequencies as given by the above table.
|Date of creation||2013-03-22 15:01:43|
|Last modified on||2013-03-22 15:01:43|
|Last modified by||mathcam (2727)|