If 27 × 4 = 77 and 31 × 9 = 239, then 21 × 6 = ?

Such pattern-based arithmetic puzzles hide a fixed non-standard rule connecting the two multiplied numbers to the stated result — it is never plain multiplication. The rule must first be inferred by testing simple combinations (sum, difference, product) against both given examples, and only then applied unchanged to the new pair.

Apply this to the given examples to find the rule, then use it on the new pair:

1. Product = 27 × 4 = 108. Sum = 27 + 4 = 31. Product − Sum = 108 − 31 = 77, which matches the given result.

2. Product = 31 × 9 = 279. Sum = 31 + 9 = 40. Product − Sum = 279 − 40 = 239, which again matches the given result, confirming the same rule holds across both examples.

3. Apply the same confirmed rule to 21 × 6: Product = 21 × 6 = 126. Sum = 21 + 6 = 27. Product − Sum = 126 − 27 = 99.

Cross-check: adding the sum back to the result should return the product — 99 + 27 = 126, which equals 21 × 6, confirming the calculation.

Hence, 21 × 6 = 99.