What should come in place of question mark (?) in the following ?
22
The missing number is 22 — option 1. Two independent rules in these figures both give it, which is the safest way to answer a missing-number diagram.
Rule 1 — the left pair and the right pair have equal sums. Read each figure as a left wing and a right wing:
| Figure | Left pair | Right pair |
|---|---|---|
| 1 | 16 + 15 = 31 | 21 + 10 = 31 |
| 2 | 7 + 13 = 20 | 10 + 10 = 20 |
| 3 | 15 + 21 = 36 | ? + 14 = 36 |
From the third row, ? = 36 − 14 = 22.
Rule 2 — the centre is a perfect square, and its root is one more than the common difference. Notice that in each figure the two upper numbers differ by the same amount as the two lower numbers:
| Figure | Upper difference | Lower difference | Centre |
|---|---|---|---|
| 1 | 21 − 16 = 5 | 15 − 10 = 5 | (5 + 1)2 = 36 |
| 2 | 10 − 7 = 3 | 13 − 10 = 3 | (3 + 1)2 = 16 |
| 3 | ? − 15 = 7 | 21 − 14 = 7 | (7 + 1)2 = 64 |
Working backwards in the third figure, the centre 64 is 82, so the common difference is 8 − 1 = 7. The lower pair confirms it, since 21 − 14 = 7. The upper pair must therefore also differ by 7, giving ? = 15 + 7 = 22.
Why the other options fail. With 18 the left and right sums become 36 and 32, and the upper difference is 3 against a lower difference of 7. With 20 the sums are 36 and 34. With 36 the right sum jumps to 50 and the difference to 21, which would demand a centre of 484. Only 22 satisfies both patterns at once.
Hence, the answer is 22.
Important Questions from Missing Number in Diagram
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
Study the given pattern carefully and select the number that can replace the question mark (?) in it:
13 108 11 26 55 9 ? 157 14 Study the given pattern carefully and select the number that can replace the question mark (?) in it :
7
4
6
927
?
349
1474
149
947
In the given square, which option will replace the question mark?
4A
6C
2E
6P
13R
7T
8N
10P
?
What is the value of the missing number?
