Rule #1 - Name Stuff.

n = total number of steps.

Phase 1: On Step (n+1)/2

That fact that there IS a middle step suggests an odd number of steps.

Phase 2: +8

Phase 3: -12

Phase 4: +1

Phase 5: + 27 on Step (n+1)/2 + 24 Since this is the top of the stairs.

(n+1)/2 + 24 = n

Solve for n.

This whole problem hinges on that clear and consice definitions up front. We can then focus on the clues without wondering what it is we are talking about.