Enigmas and puzzles

December 22, 2007

"Is that chocolate? It has a funny shape," said Twindledum.

"It's a new kind of chocolate bar," replied Twindledee. "It's called a T-bar because it's shaped a bit like a letter T. [See a] And you don't just eat it—you play a game with it."

"Mum always said not to play with our food."

"Yes, and we never took any notice," said Twindledee. "Each square of chocolate has a different flavour. And one of them, at the junction of the upright and the arms of the T, is really nasty. The rules are that we take turns breaking off a piece, which we then have to eat. The break has to be along one of the dividing lines between squares, but you don't have to break off only one square at a time." [See b, a possible move]

"And the point of the game is?" asked Twindledum.

"Not to be the one forced to eat the nasty square, when there's nothing else left."

"So who goes first?"

"We'll toss a coin," said Twindledee. "Whoever wins the toss can choose whether they go first or second."

Twindledum won the toss. To avoid eating the nasty square, should she go first or second, and what are her other moves?



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The answer

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Twindledum should play first and snap off the entire upright.  Then the two remaining arms are symmetric. So whatever move Twindledee makes, Twindledum can copy it on the other arm. This way, Twindledum always has a "safe' move, until finally Twindledee is left with the nasty square.

The winner was Rob Hull, London EC1