Answer to: How Old Are Your Kids?

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Two men standing in the street talking:

Mr. Jones -- I've got 3 wonderful kids.

Mr. Smith -- How old are they?

Mr. Jones -- Well, the product of their ages equals 36.

So they could be any combination of ages that equal 36, or:

Child #1	Child #2	Child #3
36	1	1
18	2	1
12	3	1
9	4	1
6	6	1
9	2	2
6	3	2
4	3	3

Mr. Smith -- What else can you tell me?

Mr. Jones -- Well, the sum of their ages equals the address of that house over there.

So lets add the sum of their ages to the table:

Child #1	Child #2	Child #3	Sum
36	1	1	38
18	2	1	21
12	3	1	16
9	4	1	14
6	6	1	13
9	2	2	13
6	3	2	11
4	3	3	10

So the address of the house must have been 13. If it was any of the other numbers in the table, Mr. Jones would have known the ages of the each child because every other number has only a single solution.

Mr. Smith -- Is there anything else can you tell me?

Mr. Jones -- The oldest got new shoes this week.

Mr. Smith -- Oh, their ages are 9, 2 and 2.

The only other option is 6, 6 and 1. But then there isn't an "oldest", both twins are older than the 1 year old. So the answer is 9, 2 and 2!

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