Find the missing number in the following set of figures –

Concept

A figure-pattern rule must reproduce every completed figure before it is applied to the incomplete one.

Compare signed differences of squares on opposite arms: C = (L2 − R2) + (T2 − B2). The signs of both differences must be retained.

Application

1. Completed figure centred at 70: (112 − 82) + (72 − 62) = (121 − 64) + (49 − 36) = 57 + 13 = 70.

2. Completed figure centred at −12: (42 − 52) + (12 − 22) = (16 − 25) + (1 − 4) = −9 − 3 = −12.

3. Incomplete figure: (62 − 22) + (32 − 42) = (36 − 4) + (9 − 16) = 32 − 7 = 25.

Cross-check

Using the equivalent grouping C = (L2 + T2) − (R2 + B2), the incomplete figure gives (36 + 9) − (4 + 16) = 45 − 20 = 25, confirming the same result.

Result

The missing number is 25.