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In a square of nine numbers, every row, every column and both diagonals add up to the same total. The top row reads 15, 8, 13 and the middle row reads 10, 12, 14. What number stands in the middle of the bottom row?

Competition practiceReasoning & Mental Ability
  • A11
  • B16
  • C24
  • D9

Step-by-Step Solution

The common total comes straight from a complete row: 15 + 8 + 13 = 36 (and the middle row checks it, since 10 + 12 + 14 = 36 too). The middle column already holds 8 and 12, so the missing entry beneath them is 36 − 8 − 12 = 16. Filling the rest the same way gives a bottom row of 11, 16, 9, and both diagonals then come to 36 as well. The traps: 11 is the bottom-left entry, found by the same method but in the wrong column; 9 is the bottom-right entry; 24 is 36 − 12, with only one of the two known entries in the column taken away.
Answer: B) 16

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