# Birthdays, logic and honesty

A friend recently sent me the fun Singapore maths olympiad problem in which Albert and Bernard attempt to discover Cheryl's birthday. As well as being full of mathematical knowledge, this implies some philosophical assumptions about knowledge and truthfulness. Here's a slightly expanded version I made up, incorporating the question of honesty:

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

• April 3, April 29, April 30,
• August 10, August 11, August 12
• September 3, September 29
• December 3, December 10, December 12

Cheryl then tells Albert and Bernard separately the month and 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 didn't know when Cheryl's birthday is, but I know now.
• Albert: Then I also know when Cheryl's birthday is.

(pause)

• Bernard: Actually, I was bluffing when I said "I know now". It wasn't true.
• Albert: Well now that Bernard's admitted that, to be honest, I was lying in the first place when I said that I knew that Bernard didn't know too... I didn't know that.
• Bernard: Outrageous! Well, at least we both know when it is now (assuming we've been perfectly honest since the pause)
• Cheryl: I can see I was wise not to tell you my birthday in the first place, you dishonest scoundrels. But to be perfectly honest, I don't know when my birthday is, and this was all a test...
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