## Wednesday 15 April 2015

### Cheryl's Birthday

Imagine my delight when I found out last night that loads of people on the internet were talking about a maths puzzle! Some people are even saying #Cheryl'sBirthday was the new #TheDress. Not being a Twitter user (is it OK that I just don't get it?) I arrived a bit late to this party but I hope you don't mind.

So, this puzzle comes from a Singapore Maths competition which I think is probably comparable to the UKMT Intermediate Maths Challenge follow-up round (the Pink Kangaroo) which means it is supposed to be challenging. Can I just take this opportunity to brag and say I got the answer right in about three minutes? Please, if you haven't already, pause and work out the answer for yourself.

There are lots of explanations of the solution out there on the internet, but I'm a maths teacher and I can't help myself, I love explaining stuff!

Statement one:

Albert knows the month. This means he can't know when the birthday is, as there are no months with just one possible date.

However, Albert has deduced that Bernard cannot know either. The only way Bernard would be able to know is if the number he was told was 19th or 18th because they are the only dates with one possible month. So for Albert to know that Bernard does not know, these two options must not be possible. Albert only knows the month, so for him to know these are not possible, the months of these must not be correct. Therefore it is not May or June.

Statement two:

Now that Albert has said that, Bernard has deduced that it is not May or June, just like we have. This information is enough for him to know the correct date. This means it can't be the 14th because there are two months with the 14th. So it must be 16th July, 15th August, or 17th August. .Bernard knows which one of these it is because he knows the number. We do not know.

Statement 3:

Albert has deduced the same as us, and narrowed it down to those three dates. But Albert knows the month, and by knowing this, he knows the answer. So it must be July, as if it was August he still wouldn't know.

Therefore the answer is 16th July.

What a wonderful question!

This question is similar to those questions where nobody knows anything but by saying "I don't know" enough times everyone suddenly knows everything. Do you know the kind of question I'm talking about? My favourite is probably the one with the island full of brown eyed and blue eyed people: The Blue Eyes Logic Puzzle. This is so difficult to wrap your head round it but once you do, you feel like you have understood the secrets of the universe and your brain suddenly enters this state of ultimate clarity. Unfortunately this only lasts for a few minutes and then you stop understanding it again. I have read about this puzzle so many times now I can hold onto this state for a whole evening. I always wake up ignorant again.

Maybe I will do a full post on the Island puzzle one day when I'm feeling brave and I have a large supply of stimulants to hand.

Let me leave you with a link to my favourite place to find logic puzzles. These are great for teaching the Logic chapter in D2. They are also nice and short so you can do one at the beginning of every maths faculty meeting just to get everyone's brains warmed up.

And also, a maths joke: Three logicians walk into a bar. The barman asks “does everyone want a drink?” The first logician says, “I don’t know”. The second logician says, “I don’t know”. The third logician says, “Yes”.

Ha ha ha ha ha ha!

Emma x x x