MP93
Problem for February 2010

The eleven members of the local football team gather at the pub after each game. Afterwards, they roll a pair of dice to determine who picks up the tab. Happily, the numbers on their jerseys run from 2 to 12, so the player whose jersey number matches the sum that shows on the dice pays the bill. But even a football player realizes that the eleven sums are not equally likely. Your task this month is to help make the process fair:

Describe how to load a pair of dice, one red, one green, so that every sum from 2 to 12 is equally likely, or prove that it is impossible.

Please note that in a solution to any math problem the explanation is all-important — every claim must be supported by some mathematical truth. 

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Solvers who submit their solutions by the 21^st of the month will have their names listed on the solutions page along with the best of the submitted solutions.

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