Find the missing number from the given alternatives.
20172017
Find the missing number from the given alternatives.
- A.
41
- B.
42
- C.
43
- D.
45
Attempted by 12 students.
Show answer & explanation
Correct answer: C
Concept: In a number-in-figure puzzle like this one, the four outer numbers are combined by one fixed arithmetic rule to produce the number written at the centre. The rule is confirmed by testing it on every figure whose centre value is already known, and only then applied to the figure with the missing centre.
Rule for this figure family: the two outer numbers that lie on the same diagonal line through the centre are paired, the two diagonal sums are multiplied, and 2 is subtracted from that product to get the centre number.
Pair the diagonally opposite outer numbers: Top-Right with Bottom-Left, and Top-Left with Bottom-Right.
Add the numbers within each diagonal pair to get two sums.
Multiply the two sums together.
Subtract 2 from the product — the result is the centre number.
Applying this rule to all three figures:
Figure | Top-Right + Bottom-Left | Top-Left + Bottom-Right | Product | Product − 2 (Centre) |
|---|---|---|---|---|
Figure 1 | 6 + 8 = 14 | 2 + 3 = 5 | 14 × 5 = 70 | 70 − 2 = 68 (given, matches) |
Figure 2 | 3 + 7 = 10 | 5 + 4 = 9 | 10 × 9 = 90 | 90 − 2 = 88 (given, matches) |
Figure 3 | 5 + 4 = 9 | 3 + 2 = 5 | 9 × 5 = 45 | 45 − 2 = 43 (missing number) |
Cross-check: the rule reproduces both known centre values (68 and 88) exactly, confirming it is the correct governing rule. Applying it to Figure 3 gives 45 − 2 = 43, so the missing number is 43.