You Know I Know
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i dont know
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what u wan us to know?
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Ben is told the month, but you cannot identify the birthday from the month, because each month covers at least two birthdays. This is why Ben cannot identify the birthday initially.
Mark is told the day, and there is a small chance that you can identify the birthday from the day, because the 7 (for June) and 2 (for December) are unique in the list.
Ben insists however that Mark cannot identify the birthday, even though Ben doesn't know what "day" Mark was told! This means that Ben somehow knows that, whatever Mark was told, it was not 7 or 2. This means that Ben knows that the birthday is not in June or December. So he must have been told either March or September.
Mark sees this and announces that he now knows the birthday. So Mark must have been told either 1, 4 or 8, because from 1, he can now deduce September, and from either 4 or 8, he can now deduce March. (The 5 is ruled out because it is ambiguous between March and September.)
Ben sees this and says that he now knows the birthday too. So he must have been told September, because if he was told March, he wouldn't be able to deduce whether Mark was told 4 or 8, whereas if he was told September, he can deduce at once that Mark was told 1.So the answer is 1 September.
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For question 2,
X and Y are prime numbers that are less than 100 and more than 1.
If Sam told Peter that x*y is a prime number eg 247, then 13 x 19 = 247 and so Peter knew that x will be 13 and y will be 19 as a prime number x a prime number = a prime number or 2 x a prime number = an even number ie if x*y = 26, then x will be 2 and y will be 13.
A tedious method known as the sieve method is taught to IP Sec 1 Maths students to find the prime numbers that are less than 100 and more than 1.
So, does this mean that FireIce has a Sec 1 child who is in an IP school now ? :)