Saturday 23 April 2011

Magic square solution

In the previous post I gave this big hint for solving my magic square problem:
The number in the shaded square must be equal to 22 + 14 – 25.

Why is this?

Call the number in the square below the shaded one X. This number occurs in both the middle row and the right-hand column. And the numbers in this row and column have the same totals. Since X occurs in both, then the other two numbers in the middle row and the other two numbers in the right-hand column must add up to the same thing.

So, "number in shaded square" + 25 = 22 + 14.
Hence, number in shaded square = 22 + 14 – 25 (= 11).

You can then use a similar approach to get the number in the top left hand corner (25 + 0 - 22 = 3) and then all the other numbers follow.

The solution, row by row from the top is:

3 28 11
22 14 6
17 0 25

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