If *n* traditional six-sided dice are tossed, the probability of obtaining a sum of 1994 is greater than zero and is equal to the probability of obtaining a sum of *S*. What is the smallest possible value of *S*?

This problem apparently appeared on the 1994 **AHSME (American High School Mathematics Examination, which has now been replaced with the ****A****MC 10**** **and the **AMC 12**). I have an answer (cube root of 37,259,704; I’m writing it like this so as not to spoil your fun!) but would love to hear someone else’s approach. Please leave a comment or send an e-mail if you have a solution.

Updated: Upon further reflection and consultation with Dr. Hockema and Mr. Thomas (East Jackson High School), I think my original answer is incorrect. Now, I believe the answer is the cube root of 38272753, although I want to think about it some more.

I was amazed to see diagonals of **Pascal’s triangle** appear in my investigation. Very, very cool!

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