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.

The four numbers are either (4,6,9,10) or,  (2,8,9,10).

Posted by K Sengupta on 2008-03-19 11:23:44