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The Fifteen Billiard Balls-A Case Study in Combinatorial Problem Solving

by Solomon W. Golomb (University of Southern California)

This article originally appeared in:
Mathematics Magazine
May, 1985

Subject classification(s): Discrete Mathematics | Combinatorics
Applicable Course(s): 3.7 Discrete Math | 4.4 Combinatorics

In how many orders can you remove billiard balls (numbered 1, 2, ? 15) if, after the first, each ball must be consecutive to a previously-removed ball? The author counts both by brute force and a clever counting argument.


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