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Ok, for those that want to work it out, here is a hint:
Spoiler: The key to the puzzle is to realize that after recieving two clues, he was still unable to work it out. That is important
And the full solution is here:
Spoiler: First, we know that their ages when multiplied together give 72. So we write out all of the "triplet-factors" of 72.
1 3 36
1 3 24
1 4 18
1 6 12
1 8 9
2 2 18
2 3 12
2 4 9
2 6 6
3 3 8
3 4 6
Next we know that they all add up to give the number next door. So we add them up:
1 + 3 + 36 = 39
1 + 3 + 24 = 28
1 + 4 + 18 = 23
1 + 6 + 12 = 19
1 + 8 + 9 = 18
2 + 2 + 18 = 32
2 + 3 + 12 = 17
2 + 4 + 9 = 15
2 + 6 + 6 = 14
3 + 3 + 8 = 14
3 + 4 + 6 = 13
We now have another piece of information: The fact that the census taker was unable to solve the problem with this information. He what the sum of their ages was (the house number) but was still unable to solve it. So we know that the sum must not be unique. We look through the list to find non-unique sums:
2 + 6 + 6 = 14
3 + 3 + 8 = 14
We know that it must have been one of these two. The lady tells the census taker that the eldest likes chocloate pudding. The choclate pudding is irrelevant. The point is that we know there is an eldest
It has to be 3,3 and 8.
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