Tuesday, November 17, 2009

House Kids

At a party you overhear another guest asking the age of the hosts' 3 children. The host tells the guest that the product of his kids' ages is 72 and the sum of their ages is the same as the guest's house number.

Now, the other guest obviously knows her own house number but, after thinking for a bit, she is forced to ask the host for additional information. The host then says that his oldest child likes strawberry ice cream and the other guest is able to say their ages.

Even though you don't know the guest's house number, you have enough information.

1. The kids are 8, 3, and 3.

Those multiply to 72, and the sum is 14. The other possibility would be 6, 6, and 2, but once you know the oldest is not a twin, you know the ages.

Now there's always a chance of Irish twins where one is almost 7 and one just turned 6, or multiple mothers, but I'm ignoring that :)

2. Dang it, Andy, beat me to the punch. Great explanation.

3. I got 6 and 4 and 3. Because I think most people stop eating strawberry icecream after 1st grade.

But it could also be 6 and 6 and 2, if the oldest are twins.
If I am wrong about the strawbrry icecream, another possibility would be 12 and 3 and 2.
Or 12 and 6 and 1
Or 9 and 8 and 1
Or 9 and 4 and 2
Or 8 and 3 year old twins...

4. I think Andy got it.

If we assume that the host could have figured out the ages of the children if there weren't multiple options that summed to their house number, we must have that the host lives at number 14 (all other sums are unique) - which tells us the children are 6, 6 and 2 or 8, 3 and 3. And since they tell us that there is an eldest the only solution is that the children are 8, 3 and 3.

5. Andy got it right. The trick is two-fold. The solution is possible based on the information and the 'eldest' child. If we interpret 'eldest' to say the oldest children are not twins, then you're left with 8, 3 and 3.

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