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Dentist — Series 2. Thu 15 Mar Fri 13 Apr Sat 21 Apr Thu 15 Nov Ariel, Balthazar and Chastity are great mates, genius logicians and they always tell the truth. Interestingly, that was the longest conversation like that we could have possibly had before both figuring it out. There are 12 months in the year. Since the day of the birthday is at most the number of the month of the birthday, the maximum number for the day must also be In other words, both Ariel and Balthazar are whispered a number between 1 and We are told that the day of the birthday is at most the number of the month.
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This is the same as saying that the day can be any number less than or equal to the month. Ariel knows the day of the birthday, Balthazar the month. The only way for Balthazar to also know the day would be if the month is January, since then he could deduce that her birthday was January 1.
But for Ariel to be able to say that Balthazar cannot not know the birthday, he must know that Balthazar does not have January. How does he know that?
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Well, he must have a number bigger than 1. Since if he had a 1, he would be able to deduce nothing about what Balthazar has. But if he had anything bigger than 1, Balthazar cannot have January since the day is always less than the month. So, we can eliminate 1 for Ariel, and 1 January for Balthazar. Now to the next statement.
The only way for Ariel to know the month of the birthday would be if he had been told 12, since he would be able to deduce that the month would also be 12, or December.