Find the missing number, if same rule is followed in all the three figures.
2024
Find the missing number, if same rule is followed in all the three figures.

- A.
28
- B.
25
- C.
21
- D.
60
Attempted by 7 students.
Show answer & explanation
Correct answer: A
Concept: In each figure the number inside the central triangle is half the sum of the squares of the three corner values (the top circle and the two bottom circles). In symbols, centre = (top2 + left2 + right2) / 2.
Application: Apply this single rule to every figure.
First figure, corners 7, 2, 3: 72 + 22 + 32 = 49 + 4 + 9 = 62, and 62 / 2 = 31, which matches the centre shown.
Second figure, corners 9, 4, 3: 92 + 42 + 32 = 81 + 16 + 9 = 106, and 106 / 2 = 53, which matches the centre shown.
Third figure, corners 4, 6, 2: 42 + 62 + 22 = 16 + 36 + 4 = 56, and 56 / 2 = 28.
Cross-check: The rule reproduced both given centres (31 and 53) exactly, so the same computation on the third figure is reliable. The missing number is 28.