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.
If the numbers are 1,3,4
Their product is 12, which is also the product of 1,2,6.
Proddy can't work out what the three numbers are.
The sum of 1+3+4=8, which is the same sum of 1+2+5.
Proddy thinks that Addy won't be able to work out what the numbers are.
Addy knows that the sum is 8. It could be from both (1,3,4) and (1,2,5), but if it were from (1,2,5) Proddy would had directly guess the numbers as 1*2*5=10 is not the product of any other three different digits.
Edited on January 14, 2019, 11:22 am
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Posted by armando
on 2019-01-14 11:19:27 |
Solution?
