Explanation:

Let's break this down together.

- We're looking for a pattern between the numbers in the sets. You're told: don't split numbers into digits, just whole number operations.

- Take the first set: (23, 25, 16). How are 23 and 25 connected to 16?

- Let's try the difference: 25 - 23 = 2. Doesn't match 16 directly.

- Try addition: 23 + 25 = 48. Not 16.

- Multiplication or division, nothing straightforward.

- But check: what's 23 minus 25? -2. Square it? (-2)² = 4. Not 16.

- How about the difference squared multiplied by something? Seems convoluted.

- Try the second set: (21, 17, 256)

- 21 - 17 = 4. 4 squared = 16. Wait, 256 is 16 squared!

- 256 = (21 - 17)4, because 44 = 256.

- So here's the pattern: the third number is the difference of the first two numbers, raised to the 4th power.

Let’s apply this to each option:

1. (14, 19, 125): 14 - 19 = -5. (-5)4 = 625, not 125.

2. (27, 23, 64): 27 - 23 = 4. 44 = 256, not 64.

3. (18, 15, 81): 18 - 15 = 3. 34 = 81.

- This fits the pattern perfectly.

4. (11, 9, 12): 11 - 9 = 2. 24 = 16, not 12.

So, the set in Option 3 is the only one where the third number equals the difference between the first two numbers raised to the fourth power, just like the original sets.

Option 3: (18, 15, 81) is absolutely the answer you want. Nice job spotting the pattern!