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.