'How old are your three daughters' Fred asks a friend one day. 'The product of their ages is 36,' replied his friend. 'You are not giving me enough information,' protested Fred. 'The sum of their ages is the age of your oldest son.' 'I still need more information.' 'All right, then. I can tell you that the oldest daughter, who is at least a year older than the other two, is a very fine pianist.' 'Ah! Now I know how old your daughters are.' What are the ages of Fred's friend's daughters?

Senior Moments

There has to be one girl older than the other two. The fact that she is a fine pianist is a red herring. If the friend has a 10 year old son then the girls are 4,3 and 3. If the son is 13 years old the girls are 9, 2 and 2. Oct 30 02, 5:45 PM

maybe not

that the oldest is a very fine pianist indicates the oldest is 9 years old, not 4 years old. not quite a red herring. 9,2,2. Oct 30 02, 6:36 PM

Gnomon

The first answer that the friend gives leaves all sorts of possibilities, such as 18, 2, 1. Since Fred knows the age of his own son, but doesn't know the daughters after the second answer, there must be two different possibilities that add up to Fred's son's age. The only possibilities that fit the bill are 9+2+2 = 13 and 6+6+1 = 13. If it was any other set of ages, there would be a unique total so Fred would know the solution. The third answer just tells us that the eldest is more than a year older than the 2nd eldest, so we know it can't be 6+6+1. The fact that she is a pianist is irrelevant. It must therefore be 9+2+2. The answer of 4+3+3 is not possible because it adds up to 10 and is the only such possibility that adds up to 10. Fred would have known immediately when he heard the second answer in this case. Oct 31 02, 12:24 AM

Fred	WAY TO GO MY MAN GNOMON!!! Oct 31 02, 5:06 AM

Senior Moments

Thankyou Gnomon. I had forgotten about the fact that the reference to Fred's son still left him in doubt so I agree that 9,2 and 2 has to be the answer. Oct 31 02, 8:22 AM

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