The Birthday
Catherine and Belinda just became friends with Mary, and they want to know when her birthday is. Mary gives them a list of 10 possible dates:
January 15, January 16, January 19 February 17, February 18 March 14, March 16 April 14, April 15, April 17
Mary then tells Catherine and Belinda separately the month and day of her birthday, respectively.
Catherine: I don't know when Mary's birthday is, but I know that Belinda doesn't know. Belinda: At first I don't know when Mary's birthday is, but now I know. Catherine: Then, I also know when Mary's birthday is.
So when is Mary's birthday?
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1 solution
This is more of a critical thinking problem. Now, we have the dates, so we mainly need to focus on how the conversation between Catherine and Belinda was coordinated so that they could understand each other.
When Catherine got the month, she immediately said that Belinda didn't know. What this signifies is that the month that Catherine has in her mind cannot be a month with a unique number in it. The unique numbers here are 18and 19. Therefore, if the number was truly 18 or 19, Belinda would immediately know the corresponding month, since it is only repeated once. Now, for Catherine to say for certain that Belinda doesn't know what the birthday is, the month needs to be March or April. We have knocked out half of the dates.
Next, we need to determine the meaning behind Belinda's response. When Belinda said she knew immediately, it meant that March and April 14 can't be the date, because they repeat. From there, Belinda knew the date, because she had the number. This isn't enough information. However, if Catherine knew the date when Belinda said she knew, this would have been her process of thinking: if Belinda knows that the month is either March or April, and she knows that it can't be March or April 14. She knows the date now, and Catherine knows the month. Catherine would then immediately know the date is March 16, because there is only ONE March date, while there are TWO April dates. For Catherine to know, the date would have to be March 16.
I hope that wasn't confusing..... This was my reasoning when i was introduced to this problem.