1994 AHSME Problems/Problem 30
Problem
When standard 6-sided dice are rolled, the probability of obtaining a sum of 1994 is greater than zero and is the same as the probability of obtaining a sum of . The smallest possible value of is
Solution
Given that there are dice, we know that the chance of rolling a sum of is the same as that of rolling a sum of . This is because there exists a bijection between the set of dice rolls that sum to and the set of dice rolls that sum to . In other words, for every ordered n-tuple such that for all valid and that , there is a unique ordered n-tuple where for all valid , whose sum is indeed .
As such, minimizing is the same as minimizing . The minimum value of is . Hence, .
See Also
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