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Sending scouts into the desert

Everybody knows the leap-frog jump in the game of checkers. There is an interesting problem about checker-jumping on the lattice points of a plane. One begins by arranging a number of men in the starting zone, which consists of the half-plane of lattice points on and below the x-axis. The object is to get a man as far as possible above the x-axis by checker-jumps in the directions of the lattice lines (diagonal jumps are not allowed). You can think of this as sending scouts into the enemy territory (desert). The problem is to determine the least number of men in the starting zone which permits one scout to reach a prescribed penetration depth.

Here is a Java applet to assist you in solving the problem. The desert lies above the horizontal line. Your army is located below. X and Y determine the size of the army. Level is your goal - how far you plan to go into the desert. Try solving the problem for a few first levels before reading further.

  <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>


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