1994 AHSME Problems/Problem 30
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
Since the sum of dice is , there are at least dice. Now consider the following numbers and . They both have the same probability of occurring because negated by switching it to and is negated by switching it to . So we have obtained an upper bound over which is . Only smaller numbers to consider are , , , . As it turns out, none of these work.