Cut the knot: learn to enjoy mathematics
A math books store at a unique math study site. Learn to enjoy mathematics.
Google
Web CTK
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

Flipping Items Simultaneously

The applet displays several (N) triangles, all pointing upwards initially. On any move, you can turn over any M of them. (You do that by clicking on M triangles in turn.) The question is, Is it possible to have all N triangles to point downwards?

<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 http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet. </h3> <hr>

The original puzzle [Mathematical Circles, p. 132] stated for N = 7 and M = 4 has negative solution. It is easily seen that, in this case, the number of inverted triangles is always even and, therefore, can't be 7.

The solution begs for a generalization: what can be said about other pairs of M and N?

References

  1. D. Fomin, S. Genkin, I. Itenberg, Mathematical Circles (Russian Experience), AMS, 1996

Copyright © 1996-2008 Alexander Bogomolny



Search:
Keywords: