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Putnam Exam Seminar
Fall 2010
August 30
Exercise 1.
Consider the following game. You are given a pile of at least two marbles and
allowed to divide that pile into two smaller (nonempty) piles of sizes
a
and
b
.
You earn
exactly
ab
points for this move. You perform the same type of move on any of the smaller
piles that have at least two marbles, and earn points for those moves in the same way. You
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Unformatted text preview: continue dividing the resulting piles and earning points until every pile has only a single marble in it, at which point the game ends. In terms of the number of marbles you begin with, what is the highest score you can possibly achieve?...
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- Fall '10
- RyanDaileda
- Marble, Putnam Exam Seminar, exactly ab points
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