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'Sliding Puzzle' printed from http://nrich.maths.org/
This puzzle is an old favourite. The aim of the game is to slide the green square from its starting position, in the top right hand corner, to the bottom left hand corner in the least number of moves. You may only slide squares up, down, left or right and not diagonally.
Try first on a small two by two grid and then as you become more confident, alter the size.
Can you find a strategy?
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You may like to have a look at the problem Changing Places
for some helpful hints.