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Conway's Chequerboard Army

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

There are two stages to this challenge. First position some counters below a fixed horizontal line in a square grid. Here is an example:

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The aim of the second stage is to advance one of the counters as far as possible beyond the horizontal line. The counters are only allowed to move in a certain way. They can only move by jumping horizontally or vertically over a neighbouring counter. If one counter jumps over another, then the static counter underneath the jump is removed. Diagonal jumps are disallowed. Also, the counters cannot jump over two neighbours.

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Given an unlimited supply of counters, and freedom to position the counters below the horizontal line in any way that you choose, how far beyond the horizontal line can the counters be advanced? Can you reach target D?

Experiment with the animation below. Click on an empty square to add or remove a counter. Click on "begin attack" to test your strategy.

If you need help understanding the animation, click on 'demo A' and 'demo B' to see how to reach targets A and B.

Full Screen Version
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What is the least number of moves it takes to reach targets C and D?
Can you describe them?

Is it possible to position the counters such that you advance beyond D?