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Subdividing a circle into 2 halves with equal number of letters A, B and C in each half Question

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Draw a straight line through the center of the circle below to subdivide it into two halves so that each half will have the same number of occurrences of the letter A. Also each half will have the same number of B's and the same number of C's.

Circle with several A’s, B’s and C’s inside its circumference

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Answer
Solution method First count how many As, Bs, and Cs there are, which is 6 each. That means we are looking for a break that leaves 3 on each side.

There are a total of 18 letters, so 9 different dividing lines that leave whole letters on both sides. That's a small enough solution space to simply search exhaustively.

Surprisingly, that worked. I was expecting it not to work and a "clever" interpretation of the problem statement would be required such that the line would include parts of two letters on either side.

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