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.
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.
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.
The pattern of intervals can be summarized as follows:
1 second, 2 seconds, 4 seconds, 8 seconds, 16 seconds, and so on, with each interval doubling each time.
Let's break down the intervals in terms of seconds:
First snap: 1 second
Second snap: 1 + 2 = 3 seconds
Third snap: 3 + 4 = 7 seconds
Fourth snap: 7 + 8 = 15 seconds
Fifth snap: 15 + 16 = 31 seconds
From this pattern, we can observe that the time between snaps in each doubling interval can be calculated using the formula: (2^n) - 1, where 'n' represents the number of the interval (starting from 0).
Now, let's calculate the total number of snaps in a year, assuming a year has 365 days:
Total snaps = (2^0 - 1) + (2^1 - 1) + (2^2 - 1) + ... + (2^(n-1) - 1)
Since the intervals double each time, we need to find 'n' such that (2^(n-1)) - 1 is less than or equal to 365 days. We can solve this by finding the maximum value of 'n' that satisfies the inequality:
2^(n-1) - 1 ≤ 365
By substituting different values of 'n', we find that n = 9 is the first value that satisfies the inequality.
Therefore, we need to calculate the total number of snaps for the first 9 intervals:
Total snaps = (2^0 - 1) + (2^1 - 1) + ... + (2^8 - 1)
Using the formula for the sum of a geometric series, the total number of snaps is given by:
Total snaps = (2^9 - 1) - 1 = 511
Hence, you will snap your fingers 511 times during the next year, following the given pattern.