I played a little logical game with my two highly intelligent godsons, Proddy and Addy.

I had in mind three different digits chosen from 1 to 8 and I whispered the product of the three to Proddy and the sum to Addy. I explained all this to them and our conversation went as follows:

Me: “Proddy, can you now work out what my three numbers are?”

Proddy: “No.”

Me: “Now do you think that Addy will be able to work out what my numbers are?”

Proddy: “No, he will not be able to work them out.”

Addy: “Now I know what the numbers are.”

What are they?

Credit due to Aunt Susan Denham.

(In reply to

Two possibilities (spoiler?) by Steve Herman)

I think the numbers are either (1,3,4) or (2,3,5). ** Neither!**

**YOU ARE WRONG.**

**1. This is the only hint I provide NOW.**

**2. IMHO it is an excellent puzzle, with one unique answer, achievable by logical reasoning.**

**3. Your low rating of a problem should be applied in the future only towards puzzles solved correctly by you.**

**I'LL PUBLISH THE ANSWER ONLY - A WEEK TODAY- & give you a chance to add the reasoning, and change your evaluation of rating.**