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## 'Conway's Chequerboard Army' printed from http://nrich.maths.org/

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?