In the following question, select the number which can be placed at the sign…

Concept: in a grid-style number-pattern puzzle, each row hides one fixed arithmetic rule linking its first three numbers to the row's last number. The same rule must reproduce every row whose last number is already known before it can be extended to find the missing entry.

1. Row 1 test: sum of the first three numbers = 3 + 4 + 2 = 9; multiplying by 3 gives 9 × 3 = 27, which matches the row's given last number.

2. Row 2 test: sum of the first three numbers = 6 + 5 + 1 = 12; multiplying by 3 gives 12 × 3 = 36, which matches the row's given last number.

3. Confirmed rule: the last number of a row equals 3 × (sum of the row's first three numbers).

4. Apply the confirmed rule to Row 3: sum of the first three numbers = 9 + 1 + 2 = 12; 3 × 12 = 36.

Cross-check: an alternative rule — (product of the three numbers) + (the first number) — also reproduces Row 1 (3 × 4 × 2 + 3 = 27) and Row 2 (6 × 5 × 1 + 6 = 36), but extending it to Row 3 gives 9 × 1 × 2 + 9 = 27, a value that is not among the four options offered. Since a well-formed puzzle's intended rule must lead to one of the given choices, this cross-check rules out the product-based rule and confirms the sum-based rule.

Result: the missing number is 36.