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

Aliquot Game

Aliquot part is another name for a proper divisor, i.e. any divisor of a given number other than the number itself. A prime number has only one aliquot part - the number 1. 1, 2, 3, 4, 6 are all aliquot parts of 12. The number 1 does not have aliquot parts. In the Aliquot game, players take turns subtracting an aliquot part of the number left by their opponent. The winner is the last player able to perform such a subtraction. The loser is the player left with a number that has no aliquot parts - 1. Thus the objective of the game is to leave your opponent without a move. What is the winning strategy?

<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