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PutnamSuperchallengeIntegrals I: Feynman's Trick

Integrals I: Feynman's Trick · Superchallenge problem

The numbers 1,2,…,201, 2, \ldots, 20 are written on a board. A move erases two numbers a,ba, b and writes a+b+aba + b + ab. After 1919 moves one number remains. What is it?