This was the problem I posed a day ago: Ok, here's a problem my math professor gave me during coffee. A few of us used to hang out and he'd give us these problems. So here it is. If you have seen it please do not answer unless someone does. Two ladies met several years after they had graduated from university. One lady- A, was a mathematician. The other lady- B, was a housewife. B, the housewife, has three sons- x, y, and z. After a few minutes of talking B decided to give a achallenge and asked her to find the age of her three sons. She gave her two hints: 1. x*y*z=72 [i.e. the product of their ages is 72] 2. x+y+z=number of windows in building across the street. A worked on the problem for a while and finally said, "Can you give me another hint?" B said "Yes" A asked "Does your oldest son have red hair?" B gave the answer and A gave the solution for x, y and z. Question: Find x, y and z. A lot of you may dispute the solution in the end. The solution is 3 3 8 Here's why: These are the combiations of numbers that make up 72 as a product: 1 2 36 1 3 24 1 4 18 1 6 12 1 8 9 2 2 18 2 4 9 2 6 6 3 4 6 3 3 8 Now, as we can see, any combination can be a solution. So the reason why the mathematician asks is the oldest or eldest son has red hair is because if there is a solution, as posed by the housewife, it must be UNIQUE TO THIS CASE ONLY. Meaning there are so many combinations possible that there must be a unique case that'll determine the answer. In ths case, we see there are three: 2 2 18 2 6 6 and 3 3 8 Now the problem is finding which one of these is UNIQUE that causes this problem to have a solution. "does your eldest son have red hair?"...and she gives the answer. The answer the mathematician is looking for is NOT whther the son has RED hair or not. We can see that we could either have 2 6 6- two eldest sons or 2 2 18 and 3 3 8- ONE eldest son in the last case. So the mathematician is trying to determine if there is an ELDEST son or not. the housewife has been tricked. If she had an eldest son and he did in fact have red hair, she'd say "YES, he does have Red hair" and the solution would be - 3 3 8 or 2 2 18, because there are two younger twins in both cases. Had she said "No, he does not have red hair", she would still have determined the solution to be 3 3 8 or 2 2 18 because there still exists an ELDEST son. However, because I said the solution is UNIQUE, there cannot be a posibility that 2 6 6 be an aswer. Now is it 2 2 18 or 3 3 8? the answer again lies in the nature of the problem- the claim that it is solvable. Because the age 18 appears above as 1 4 18, the housewife should have carefully thought of the problem and given the mathematician these dual scenarios to dabble with. therefore the answer is 3 3 8. This why I said this is gonna cause some denials. When I solved this this way, the prof liked it but other students hated it. lol. I wont argue any ther reasonings here. Thanks, this thread is awesome!