The official solution is as follows:

*This question also requires a knowledge of logarithms. Don’t stress if you don’t understand it yet!*

To solve a problem like this, it is often helpful to draw a diagram and/or table to illustrate what is happening. It then becomes easier to spot a pattern. We will draw a table to compare the number of finger snaps (n) with the total time elapsed in minutes (t):

*Can we find some mathematical expression that will give us the time elapsed for a certain number of finger snaps? Since the time elapsed between finger snaps always doubles, we would expect powers of 2 to be involved in the expression. In fact, we notice that the numbers in the time elapsed column are all 1 less than a power of 2. We could try the expression*

*but this doesn’t quite work. With a little bit of thought, you should realise that *

*is the correct expression. Since we can now calculate the time elapsed for any given number of finger snaps, we can work out how many finger snaps fit into a year. We do this by first finding the number of minutes in a year. *

We could of course look this up on the internet; but we really should be able to work it out for ourselves! One year is 365 days, which is 365 × 24 hours, i.e. 8760 hours. This in turn is 8760 × 60 minutes; so there are 525600 minutes in a year.

Now we ask the question: for which value of n (for how many finger snaps) do we get a value of t that is close to the number of minutes in a year? In other words, we want to solve ,

*which gives*
*Since we can only have a whole number of finger snaps, we have shown that by following the pattern, we would only snap our fingers 20 times in one year.*
I hope this helps!