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7 pieces of paper in the hat.

Source: Polish MO Recond Round 1977 p3

September 9, 2024
combinatoricsnumber theory

Problem Statement

There are 7 pieces of paper in the hat. On the n n th piece of paper there is written the number 2n−1 2^n-1 (n=1,2,…,7 n = 1, 2, \ldots, 7 ). We draw cards randomly until the sum exceeds 124. What is the most probable value of this sum?
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