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?

Okay for the case of 1024 possibilites removing 1/4 of them each step

natural log(1024) / natural log(4) = 5 which can't be right.

with 4 on the denominator it gives me 5 which is impossible since it is faster then removing 1/2 each step.

log(1 024) / log(1 / (1 / 4)) = 5  also is wrong


My question wasn't how to get 4^5 = 1024 but given 1024 possibilities and removing 1/4 of them each step, how many steps until 1 or 0 possibilities are left.

I believe it takes 26ish(+-2) steps to leave no possibilities left (used recursive programming).

I'm wondering what formula would allow me to calculate this.