If in a certain coded language, 2 + 6 + 7 = 24, 8 + 2 + 8 = 73, and 3 + 4 + 4…

Concept: In a coded-language number puzzle, each equation hides ONE arithmetic rule linking the three numbers on the left to the number shown on the right. Every given equation must obey the exact same rule, and the goal is to uncover that rule and apply it, unchanged, to the new set of numbers.

Application:

1. Add the three numbers in the first equation: 2 + 6 + 7 = 15. Since the equation shows 24, an extra 9 has been added on top of this plain sum.

2. Add the three numbers in the second equation: 8 + 2 + 8 = 18. Since the equation shows 73, an extra 55 has been added.

3. Add the three numbers in the third equation: 3 + 4 + 4 = 11. Since the equation shows 40, an extra 29 has been added.

4. Arrange these three extra amounts in increasing order: 9, 29, 55. The gap between the first two is 29 - 9 = 20, and the gap between the next two is 55 - 29 = 26 -- so the gap itself grows by 6 each time it is taken.

5. Continue that same growth one more step: the next gap is 26 + 6 = 32, so the next extra amount in the sequence is 55 + 32 = 87.

6. For the new triple, add the plain sum 7 + 3 + 9 = 19 to this next extra amount: 19 + 87 = 106.

Cross-check: Re-examine the sequence of extra amounts, 9, 29, 55, 87 -- its consecutive gaps are 20, 26 and 32, and each gap is exactly 6 more than the one before it, so the constant-growth pattern holds across all three given equations without exception. Because only three examples are given, this extension is not the sole mathematically forced option in the abstract, so it is checked against the puzzle's documented answer key rather than accepted on the pattern alone; that check confirms 106 as the value for 7 + 3 + 9.