Yesterday I posed a When is Cheryl’s birthday, which is to find Cheryl’s birthday given just a few basic facts. If you have not read the When is Cheryl’s birthday, please do this first.

Contrary to what I said yesterday about this problem, whereas it create a viral storm on the Internet, it was actually a problem from the Singapore and Asian Mathematics Olympiad for senior secondary students. You can read more about it Mothership if you are interested.

Today we will look at this problem and work towards a solution.

I have developed a structured approach to solving problems, based upon the work “How to Solve It” by Polya (1945), and I will use this approach here.

I call this approach is called APEX, which is a mnemonic for Analyse, Plan, Execute, and Cross(X)check. The APEX approach uses these four steps in addressing any mathematical problem, normally in sequence, and perhaps with backtracking as required.

In this page I will focus on the initial Analysis of this problem and will also explore how to Plan and Execute.

Let us look at the information available in the problem we have been given and to discover what we are required to determine to solve this problem.

Cheryl gave 10 options for possible birthdays, which I repeat here:

May 15 May 16 May 19 June 17 June 18 July 14 July 16 August 14 August 15 August 17

Look at these and see if you can see any patterns in the dates. It does not matter if these patterns are useful or not, since you will not know this at this step of the approach whether the information you find if useful or not. So just look at these dates and try to make some sense of them, and look for some order in the dates provided.

I will let you look at these carefully,and when you are ready then move onto the next page where I will provide the first hint to help you solve this problem.

You will not need pencil and paper for this, but it this will help you then feel free to use it.