Cut the knot: learn to enjoy mathematics
A math books store at a unique math study site. Learn to enjoy mathematics.
Terms of use
Privacy Policy

More Mathematics
CTK Exchange

Games to Relax
Guest book
Recommend this site

Sites for teachers
Sites for parents

Manifesto: what CTK is about Buying a book is a commitment to learning Things you can find on CTK Email to Cut The Knot Recommend this page

A Sticky Problem

The game presented by a Java applet below was published in 2002 the American Mathematical Monthly as problem #569 (Sung Soo Kim). A solution by Li Zhou appeared in v. 111, n. 4 (April, 2004), pp. 363-364.

A game starts with one stick of length 1 and four sticks of length 4. The two players move alternately. A move consists of breaking a stick of length at least two into two sticks of shorter lengths or removing n sticks of length n for some n{1, 2, 3, 4}. The player who makes the last move wins. Which player can force a win, and how?

The applet allows one to start with different initial configurations, but also with the standard one. At the outset, you can force the computer to make the first move by pressing the "Make move" button. Sticks are represented by a row of small squares that might remind of a chocolate brick. To break a piece click on a square to the right of the desired break line.

<hr> <h3> This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet. </h3> <hr>


Copyright © 1996-2008 Alexander Bogomolny