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Problem of the Day #415: Penny Flipping December 27, 2012

Posted by Saketh in : potd , trackback

Yuqing is playing with a triangle of pennies, similar to those shown below.

pennytriangle

The triangle is of unspecified size, but we know that all but one of the pennies is initially heads up (with the last being tails up). He can manipulate the pennies by flipping any entire row, or by rotating the whole triangle $120^{\circ}$.

Yuqing wants to turn all the coins tails up. Determine, for all triangle sizes, all positions for the coin that is initially tails up such that it is possible for him to do so.

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