Explanation:

Let’s break it down:

- You’ve got numbers paired like this: 12 : 136, ? : 188, 24 : 568. The goal is to spot the pattern connecting each pair.

- First, what links 12 to 136?

Try multiplying 12?×?12 = 144. But that's too high.

Try 12?×?11 = 132. Add 4 to that, and you get 136. That's promising.

- Next, let’s test that on the last pair: 24 : 568

24 × 23 = 552. Add 16, you get 568. Okay, so there’s a pattern:

The second number = First number × (First number - 1) + (First number × First number) / 36

Testing that theory:

12 × 11 = 132;

132 + (12 × 12) / 36 = 132 + 4 = 136.

24 × 23 = 552;

552 + (24 × 24) / 36 = 552 + 16 = 568.

Now, to find ? : 188:

Let’s backtrack: ? × (? - 1) + (? × ?) / 36 = 188

Try the options:

- Option 1: 14 × 13 + (14 × 14)/36 = 182 + 5.44 = 187.44 (not 188)

- Option 2: 26 × 25 + (26 × 26)/36 = 650 + 18.78 = 668.78 (way off)

- Option 3: 32 × 31 + (32 × 32)/36 = 992 + 28.44 = 1020.44 (way off)

- Option 4: 41 × 40 + (41 × 41)/36 = 1640 + 46.69 = 1686.69 (way off)

Alright, so obviously, that little addition trick doesn’t quite pan out. Let’s try another angle:

12 : 136 = 12 × 12 - 8 = 144 - 8 = 136

24 : 568 = 24 × 24 - 8 = 576 - 8 = 568

So each time, the right number is square the first, minus 8.

So for ? : 188:

x × x - 8 = 188 ? x × x = 196 ? x = 14

So the missing number is 14.

- Option 1: 14 is the answer.

- Option 2: 26^2 - 8 = 676 - 8 = 668

- Option 3: 32^2 - 8 = 1024 - 8 = 1016

- Option 4: 41^2 - 8 = 1681 - 8 = 1673

The right answer is 1. 14