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 Don't know how to do this with a spreadsheet, but... by Charlie)

In fact, Charlie, the only work you have with a spreadsheet is to list all the 210 possibilities (that is not too difficult).

After creating the sum and product of each quadruple, itīs just a matter of ordering alternately by the sum and by the product, keeping in each step those quadruples which would give the correspondent answer of Sam and Pat.

I took less than 10 minutes.

Cheers.

Posted by pcbouhid on 2006-01-04 04:59:16