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Two tiles are missing in Panel I. Which one of the options in Panel II is the appropriate choice for the missing tiles?

A 3 by 3 arrangement of tiles, each a 3 by 3 pattern of filled and empty dots, with the two right-hand tiles of the lower rows missing

  • A.Two stacked tiles; filled dot = 1: top tile rows 011, 011, 111; bottom tile rows 000, 001, 001
  • B.Two stacked tiles; filled dot = 1: top tile rows 011, 011, 011; bottom tile rows 000, 001, 001
  • C.Two stacked tiles; filled dot = 1: top tile rows 011, 011, 111; bottom tile rows 001, 001, 001
  • D.Two stacked tiles; filled dot = 1: top tile rows 011, 011, 011; bottom tile rows 001, 001, 011

Answer: A

The missing tiles are option (i).

Count the filled dots in each tile of Panel I. The grid reads:

816
35?
49?

The first row sums to 15, and so do the first two columns (8 + 3 + 4 and 1 + 5 + 9). This is the 3 by 3 magic square, every row and column totalling 15. So the missing tiles must have 15 - 8 = 7 filled dots (middle row) and 15 - 13 = 2 (bottom row), which also makes the last column 6 + 7 + 2 = 15.

Option (i) has 7 filled dots above and 2 below. Option (ii) has 6 and 2, option (iii) 7 and 3, and option (iv) 6 and 4, so none of them completes the square.

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