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2 2 9 and using ALL three clues

Well as you all may know.
Clue one tells us 8 probabilities like the below
1 1 36(I know this one doesn't make sense, but.. math doesn't include common sense!)
1 2 18
1 3 12
1 4 9
1 6 6
2 2 9
2 3 6
3 3 4
Now we could think "Damn it, I'm stuck!", but the second clue is actually the best clue of the three!
The salesman knew the total of the children's age by seeing the other houses number.
BUT the important thing is he didn't know, after that clue.
Let's say 1 1 36 was the answer, and the number was 38.
Then when the salesman jotted down the 8 figures he could easily find out which combination was right!
So.. if the sum only made right a particular value. He could know!
In other words, the fact that he didn't know means there were more than two combinations who had the same total.
That gives us only 2 left.
2 2 9 and 1 6 6 (they sum up to 13)
But, the third clue tells us that there is an Elder one, which means there is only one which is the biggest,
and finally the problem is solved with an elegant answer
2 2 9

Jay Kim
12 years old(I'm not joking, I really am a 12 years old Korean boy)
Korea Yong-in
jaysarang20@naver.com

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