Which number replaces the question mark?

2024

Which number replaces the question mark?

  1. A.

    15

  2. B.

    10

  3. C.

    7

  4. D.

    5

Show answer & explanation

Correct answer: C

This is a wheel-pattern puzzle: the circle is split into 8 wedges by the two diameters and two diagonals. Each wedge shows two numbers in its outer band and one number in its inner band next to the shaded centre. The rule connecting the wedges is: the inner number of a wedge equals the sum of the two outer numbers of the wedge directly opposite it (the wedge on the other side of the centre).

Checking this rule on the three fully known opposite pairs:

  • Outer numbers 9 and 7 (inner = 8) are opposite outer numbers 4 and 4 (inner = 16): 9 + 7 = 16 and 4 + 4 = 8 — both match.

  • Outer numbers 3 and 3 (inner = 4) are opposite outer numbers 1 and 3 (inner = 6): 3 + 3 = 6 and 1 + 3 = 4 — both match.

  • Outer numbers 3 and 1 (inner = 5) are opposite outer numbers 3 and 2 (inner = 4): 3 + 1 = 4 and 3 + 2 = 5 — both match.

The wedge holding the missing value has a known outer number 2 and inner number 6. The wedge opposite it has outer numbers 1 and 5, with inner number 9. Applying the rule in both directions: the missing wedge's outer sum must equal 9 (the opposite wedge's inner number), so 2 + ? = 9, giving ? = 7. In the other direction, the opposite wedge's outer sum (1 + 5 = 6) must equal the missing wedge's inner number, and indeed 6 = 6 — confirming the rule holds only when the missing number is 7.

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