There is nothing amazing of a computer to fails to solve a problem. There are a number of problem that cannot be solved through the computer. CaptainBlankcan probably tell you better for he claims to be an expert in computability theory (algorithms).

For example, a computer cannot solve a quintic equatin.

-------

The product of the ages is 36 that means it must be:

1,1,36---> SUM=38

1,2,18---> SUM=21

1,3,12---> SUM=16

1,4,9----> SUM=14

1,6,6----> SUM=13

2,2,9----> SUM=13

2,3,6----> SUM=11

3,3,4----> SUM=10

She first says "I do not know" and after she says "I know". This means shemust have known what the house door was. But she cannot decide because each sum is uniqueeach for 13. There are two ways of expressing it. Hence, when she said "The older one...." that gives the hint that she has an older thing. Thus, it cannot be 1,6,6 and must be 2,2,9