**From New Scientist #2745, 30th January 2010** [link]

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 of the three to Addy. I explained all this to them and our conversation then 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?

[enigma1580]

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The following Python program runs in 37ms.

Solution:The numbers are 2, 3 and 4.