Four different integers from 1 to 10 are chosen. Sam is given the sum and Pat is given the product. Sam and Pat take turns stating how many of the four numbers they can deduce:

Sam: I don't know any
Pat: I know one
Sam: I now know two
Pat: I now know all four

What could the four numbers be?

Tip: A spreadsheet is very useful in solving this problem.

(In reply to Pardon my dyslexia. by Robert Fulton)

I'm afraid this doesn't work.  The only possible sets of numbers from 84 are 1,3,4,7 or 1,2,6,7.  As such Pat would know two of the numbers (1 and 7) from the beginning, not just one.

Posted by AvalonXQ on 2006-02-18 19:00:16