Intelligent Math Puzzle – Challenge 93

Intelligent Math Puzzle – Challenge 93 shows two three-by-three grids of numbers. One is complete, the other is missing its bottom-right entry, and the same relationship holds inside each grid.

Challenge:

The numbers in each set of nine are related in the same way. The first grid reads 3, 8, 9 across the top, 5, 11, 6 across the middle, and 2, 7, 1 across the bottom. The second grid reads 6, 5, 10 across the top, 10, 6, 11 across the middle, and 2, 5, ? across the bottom. What is the value of the question mark?

The Answer

The correct answer is 7.

In each grid the centre number equals the sum of the four edge cells minus the sum of the four corner cells.

First grid — edges 8 + 5 + 6 + 7 = 26, corners 3 + 9 + 2 + 1 = 15, and 26 − 15 = 11, which is the centre. ✓

Second grid — edges 5 + 10 + 11 + 5 = 31, centre 6, so the corners must sum to 31 − 6 = 25. Three corners are known: 6 + 10 + 2 = 18.

The missing corner is 25 − 18 = 7.

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