You are here

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.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.

To open this file please click here.

These pdf files are furnished by JSTOR.

Classroom Capsules would not be possible without the contribution of JSTOR.

JSTOR provides online access to pdf copies of 512 journals, including all three print journals of the Mathematical Association of America: The American Mathematical Monthly, College Mathematics Journal, and Mathematics Magazine. We are grateful for JSTOR's cooperation in providing the pdf pages that we are using for Classroom Capsules.

Average: 2.7 (17 votes)