Friday, 1 August 2014

She chooses her moves

The numbers from 1 to 100 are written in order around a circle. On each move Ana chooses
an even number, y, on the circle, erases it along with its two neighbors, x and z, and replaces
the three numbers with the sum of the two neighbors, x + z. She continues to make moves
until either all the remaining numbers are odd or there are fewer than 3 numbers remaining.
Prove that no matter how she chooses her moves, she will end up with 2 even numbers.

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