Cheryl must be a politician as she can't answer a straight question

There's a little logic puzzle that's been doing the rounds on the internet for the past few days, that probably everyone has already seen by now.  Seemingly it's come from some Singaporean schoolchildren's homework.  It is a rather fiendish puzzle and seems to having been given a lot of adults difficulty.

Here is the question:

"Albert and Bernard just become friends with Cheryl, and they want to know when her birthday is.  Cheryl gives them a list of 10 possible dates.

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

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.
Bernard: At first I don't know when Cheryl's birthday is, but I know now.
Albert: Then I also know when Cheryl's birthday is.
So when is Cheryl's birthday?"

If you want to have a go at figuring this out for yourself and don't want to know the solution stop reading now.


There are loads of solutions to this problem posted all over the internet and in various news outlets now, but having seen a few of them and worked through the problem myself, none of the explanations I've seen seem particularly clear or well explained - the best one I've seen so far has been on the NY Times website.

Here is my attempt to explain the solution:

After giving her list of ten possible dates, Cheryl tells Albert the month and Bernard the day of her birthday.

Albert and Bernard both have more information than we have.  The key to figuring this out is to keep this in mind and to pay very close attention to the statements made by Albert and Bernard and the information that they (inadvertently) reveal.

Albert states that he doesn't know the exact date of Cheryl's birthday, but he knows that Bernard doesn't know it either.  However, Bernard could have known the exact date if it had been May 19 or June 18, as in our range of dates these are the sole occurrences of these specific days (18 & 19), therefore if it had been either of these dates Bernard would have known the exact date right away.  The fact that Albert is so confident that Bernard doesn't know the exact date of Cheryl’s birthday reveals (to us and to Bernard) that Albert knows the month isn't May or June (and therefore must be either July or August).

This leaves us with the following possibilities:

July 14, July 16

August 14, August 15, August 17

Bernard then declares that at first he didn't know, but now (following Albert’s first statement) he’s figured it out.  So, Cheryl’s birthday can’t be on the 14th of the month, otherwise Bernard wouldn't have been able to narrow down whether it was in July or August.

This leaves 3 possibilities:

July 16

August 15, August 17

Albert then claims to have figured it out as well, which means that it can’t be either of the dates in August, otherwise he wouldn’t have been able to narrow down the day.  This leaves July 16 as the only possible date of Cheryl’s birthday.

Fun with Probabilities

This post by Stephen Landsburg on his Big Questions blog has got me thinking about probabilites.

I'd like to post my own (well, plagarised from here) problem to readers:

Three poker chips are in a cup. One is marked with a BLUE dot on each side, another with a RED dot on each side, and the third has a BLUE dot on one side and a RED dot on the other. So there is one blue/blue chip, one red/red chip, and one blue/red chip.

Without looking, you take out one chip, and lay it on the table.

1. Suppose the up-side turns out to be BLUE? What is the chance that the down-side will also be BLUE?

2. What if the up-side is RED? What is the chance that the down-side will also be RED?

3. Before you see how the chip has fallen, what is the chance that it has the same color dot on both sides?

4. Suppose you answered 1/2 in response to Questions 1 & 2. That would mean that whichever the up color of the chip, the chance is 50/50 that the color on the down side is the same. But if at Question 3 you said that chance is 2/3, aren't you contradicting yourself?

If you follow the link to the paper the question comes from you'll get an explanation of the correct answer.  This is essentially a rephrasing of the more familiar Monty Hall problem.

UPDATE: The original link to this problems source no longer appears to be active.  You can try this one instead.