You're kidding!
A and B have the following conversation:
A: How old are your three kids?
B: The product of their ages is 36.
A: I still don't know their ages.
B: The sum of their ages is the same as your house number.
A: I still don't know their ages.
B: The oldest one has red hair.
A: Ah, now I know their ages.
How old are the kids?
Assume the kids ages are an exact number of years.
A: How old are your three kids?
B: The product of their ages is 36.
A: I still don't know their ages.
B: The sum of their ages is the same as your house number.
A: I still don't know their ages.
B: The oldest one has red hair.
A: Ah, now I know their ages.
How old are the kids?
Assume the kids ages are an exact number of years.
Labels: logic, mathemagic
posted by Chris at
6:24 AM
7 Comments:
A * B * C = 36
A + B + C = House Number
im not sure here in that...
factors of 36 Sum of Factors
1 1 36 38
2 2 9 13 --this one
1 2 18 21
1 3 12 16
1 4 9 14
1 6 6 13 -- and this one both are 13
2 3 6 11
3 3 4 10
I would imagine that those 2 are suspect (the 13's)
2 2 9 13
1 6 6 13
since he said THE oldest meaning one... that must be 2 2 and 9
since the other group would have 2 oldest..
i think?
phreebsd, well done.
Because the sums of the ages are unique, except the pair that add to 13, A's house number must be 13 - that's why he didn't know which of the pair to choose. Otherwise a perfect answer.
Why must the house number be 13? It seems kinda arbitrary to select 13 over a different sum, such as 21. Just because there are two combinations whose sum is 13 does not make it more special.
Please explain why this is so.
I worked out that the twins are 2 and the oldest is 9. Phreebsd beat me too it, but it was pretty much the same logic.
Out of all the factors of 36, only 2 had the same sum. If none had the same sum (or his house# wasn't 13 in this case), then B would have known the ages after the first two responses. Since he didn't, then it could only be 2,2,9 or 6,6,1. The last response about the oldest means the twins were younger.
Nice puzzle, took me a few minutes.
Thanks EB. Anonymous, does that explain it for you?
hehehe, liked that one =)
Hi t:b:H, I found it somewhere on the www. As soon as I read it (and before seeing the answer), I decided that it absolutely had to be posted here.
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