I think there should be 22 steps.

I worked it out this way:

I had climbed down seven steps when the boy started.

After that, I climb down a few more steps (let this number be "x") when the boy reaches the top.

I have yet to climb down four more steps.

Therefore, the total number of steps is: 7 + x + 4, or 11 + x.

The boy takes two steps at a time. So when I have taken "x" steps, he has climbed up "2x" number of steps and reached the top. Therefore, the total number of steps is 2x; this is because the boy started climbing up when I began climbing down the "x" steps and he had reached the top when I completed the "x" steps.

Thus, 11 + x = 2x.

Thus, x = 11.

The total number of steps is 2x. Substitute x = 11, and we get the total number of steps as 22.

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