The ages of the children can be 1 1 36, 1 2 18, 1 3 12, 1 4 9, 1 6 6, 2 2 9, 2 3 6, and 3 3 4.
The sum of their ages is respectively 38, 21, 16, 14, 13, 13, 11 and 10. So the number of the house next door is 13, otherwise he would have known their ages. He needs the third clue; there is an eldest one. So the ages of the chidren are 2 2 and 9.

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