Answer: 2, 3 and 4
The winner is Peter Hayes of Moreland, Victoria, Australia. There were 133 entries.
Worked answer
Since Proddy does not know the numbers, the product of which he has been told must be the product of at least two triples.
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So we all know after his first comment that the product is one of those shown in Figure 1, right.
The boldface in the 鈥淪ums鈥� column only occur once. So if Addy had been told one of the boldface sums above, he would now be able to work out the three numbers. Proddy is sure this won鈥檛 happen and so those three rows are ruled out, leaving only the options in column X.
In column X the boldface 9 is the only number which occurs just once, and since Addy can now work out the numbers he must know that the sum is 9 and that the numbers are 2, 3 and 4.