square mystics

Consider a 3 × 3 square where each small square 1 × 1 is written one of the integers 1,2,3 or square 4.This is called Mystic the sum of the numbers in each row and each column is a multiple of 4. How many squares are mystics?

Note by Vander Nemitz
4 years, 9 months ago

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There are 256 3x3 mystic squares, because given the upper-left 2x2 square of a 3x3 mystic square, you can uniquely reconstruct the mystic square, and every 2x2 square is the upper-left 2x2 square of a 3x3 mystic square.

Colby Wolfe - 4 years, 9 months ago

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Colby, you can explain how to get the answer 256?

Vander Nemitz - 4 years, 9 months ago

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The number of 3x3 mystic squares is equal to the number of 2x2 normal squares as per the reasoning above, and there are 256 normal 2x2 squares because you have 4 spots to fill with 4 numbers and 444*4 = 256.

Colby Wolfe - 4 years, 9 months ago

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