### Teddy Town

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

### Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

### Nine Colours

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

# Conway's Chequerboard Army

##### Stage: 3 Challenge Level:

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?