If 12*9=9, 15*7=6, 17*8=10, then 16*9=?

Concept: In this type of coded-operation puzzle, the symbol used between two numbers (here, "*") does not mean ordinary multiplication as the final answer — it stands for a rule that must be discovered from the solved examples. A common rule combines the two numbers by an arithmetic operation (such as their real product) and then reduces the result to its digit sum.

1. Test the rule on 12*9: the real product of 12 and 9 is 108; the sum of the digits of 108 (1 + 0 + 8) is 9 — this matches the given value 9.

2. Test the rule on 15*7: the real product of 15 and 7 is 105; the sum of the digits of 105 (1 + 0 + 5) is 6 — this matches the given value 6.

3. Test the rule on 17*8: the real product of 17 and 8 is 136; the sum of the digits of 136 (1 + 3 + 6) is 10 — this matches the given value 10.

4. Since the rule (multiply the two numbers, then add the digits of the product) holds for all three given equations, apply the same rule to 16*9: the product of 16 and 9 is 144.

5. Sum the digits of 144: 1 + 4 + 4 = 9.

Cross-check: The rule gives 9 for the first pair (from a digit sum of 108), 6 for the second (from 105), and 10 for the third (from 136) — each consistent with products of similar size, so a value of 9 for 16*9 (from the similarly sized product 144) fits the same pattern without any inconsistency.