Question I'm interested in

Assuming you have 1024 possibilities, if you divide half of the possibilites at each step it takes 10 steps to finish.

What about if you remove 1/4 of the possibilites

1/8 of the possibilites etc

How much longer does it take mathematically?  What is the formula/principle behind this?

2^10 = 1024
4^5 = 1024
8^(10/3) = 1024

10,5,3.33, etc

Number of divisions: N
Number of steps: S
Number of possibilites: P

N^S = P
S*Ln(N) = Ln(P)
S = Ln(P)/Ln(N)