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.

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.

What if applet does not run?

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.)


  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

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