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.
Sam not knowing any numbers from the sum just trims off the few unique sum solutions from the possible set.
Pat knowing one reduces the set to 64 possible combinations that have only one common number for a given product.
Sam's next statement means that the sum is 29 because it is the only possibility that has two and only two common numbers.
Pat then knows the answer because his product differentiates between the two possible solutions with the same sum
2 8 9 10 and
4 6 9 10
My attempt (I'll look at PCs later)
