Monotone Number Sequences

Depending on your selection, there are 9 or 10 numbers at the bottom of the applet below. Above them, there are as many boxes. You are to drag the numbers into the boxes. The numbers snap into position if dropped near the center of a box. The task is to arrange the numbers in the boxes so that no four of them form a monotone, either decreasing or increasing, subsequence.

There is a little theory based on the Pigeonhole, a.k.a. Direchlet's, principle. (Also, the same problem is illustrated with a different applet.)

References

1. M. Aigner, G. Ziegler, Proofs from THE BOOK, Springer, 2000
2. M. Gardner, The Last Recreation, Copernicus, 1997
3. M. Gardner, The Colossal Book of Short Puzzles and Problems, W. W. Norton, 2006, pp. 26-27

Copyright © 1996-2008 Alexander Bogomolny