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September 2000

Monkey Nut Puzzle

Here's a seemingly simple challenge...

You have a chessboard, which can be as large as you like, and on the bottom left square there is a monkey-nut. All other squares are empty.

At any time, you may remove a monkey-nut, and replace it with two more: one on the square above the removed nut, and one on the square to the right of the removed nut. But only if both these squares are empty to start with.

Can you completely free the six squares in the bottom left hand corner of the playing board from monkey-nut infestation?

If not, can you prove it can't be done?

[APPLET: monkey-nuts on a chessboard]

This is quite a hard problem, so here's a clue: can you see a link between this puzzle and John Webb's article The Solitaire Advance in Mystery Mix in this issue?

You can send your solution by e-mail to <plus@maths.cam.ac.uk>.

You can find other puzzles for ages 15+ at the 15+ Challenges page at NRICH.

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