Question

I snap my fingers now. in one second, i snap them again. I wait two seconds and snap them a third time. I wait four seconds before snapping them again. then i wait eight seconds, then sixteen, and the pattern continues on. the interval between snaps doubles each time How many times will i snap my fingers during the next year?

Answer 1

seconds in a year = 31,536,000
After n snaps, Sn = 2^n - 1 seconds have passed.

So, what is log₂31536000?
That is 24.9

So, there will be 24 snaps in the year.
25 snaps would require 2^25 = 33554432 seconds.

Answer 2

Actually, that does not count the snap that starts the events. So, add 1, making 25 snaps.

Answer 3

Belay that prior comment
snaps seconds
1 0
2 1
3 3
4 7
5 15
n 2^(n-1) - 1

So, 2^(n-1) = 31536001
n-1 = log₂

so, there will be 25 snaps, but for a different reason.

Answer 4

thanks steve