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Muggles Magic

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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Cogs

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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.

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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?
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.