Cheryl's birthday

I'll give my solution to this logical reasoning problem in my next post, so anyone reading this has the chance to solve it themselves first. This is the problem from a Singapore mathematics test that has apparently 'gone viral'. It was constructed by Dr Joseph Yeo Boon Wool, a mathematics professor at the Singapore National Institute of Education.

So here is the actual problem.

Albert and Bernard want to know the birthday of their new friend Cheryl. She tells them that it is one of the following ten options:

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

She whispers in A's ear the month of her birthday and tells B that she has done this.
She then whispers in B's ear the day of her birthday and tells A that she has done this.

Then A says, 'I do not know C's birthday; but I know for sure that B does not know either.'
B replies: 'At first I did not know C's birthday, but I do now.'
A replies: 'Now I know as well!'

This is an excellent example of a logical reasoning problem that involves making deductions from what people say about what they know or do not know. These puzzles always assume that all the people involved have high powers of deductive reasoning, so you can assume that if something can be deduced they will deduce it!

Here is another example, much easier than finding Cheryl's birthday!

A, B and C are told that in a bag there are 3 red hats and 2 blue hats. B is blindfold, so is unable to see anything. One hat is put on each person's head and they have to work out what colour hat they are wearing. A and C can see the hats on the other two, but none of them can see their own hat.
A says: I do not know what colour my hat is.
C says: Nor do I.
B says: Then I am wearing a red hat.
How did B work that out?

Solutions in my next post.

Logic problem

Here's one my favourite problems requiring simple logic. Only the brightest children I have worked with in Year 6 have ever been able to get this right!

There are four cards on a table. Each card has a letter on one side and a number on the other. The cards are laid out so that we can see two of the letters and two of the numbers:

A B 8 5

Someone makes this assertion: 'If a card has a vowel on one side then it has an even number on the other side.'

Which cards must you turn over to find out whether this assertion is true or not?