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.

2, 8, 9, and 10, if Pat has 1440.

4, 6, 9, and 10, if Pat has 2160.

In both cases, Sam has 29.

 

Edited to say that I used a spreadsheet, in a hurry.

Edited on January 3, 2006, 4:25 pm

Posted by pcbouhid on 2006-01-03 16:19:54