Two different integers from 1 to N are chosen. Sam is given the sum and Pat is given the product. Sam and Pat take turns stating whether they can determine the numbers

Sam: I don't know the numbers.
Pat: I don't know the numbers.
Sam: I don't know the numbers.
Pat: I don't know the numbers.
.
.
.
.
Sam and Pat continue like this until one of them realizes that it is impossible for either of them to determine the numbers. What is the smallest possible N for which this can happen?

Using the same format as last time, (Sum node)-edge-[Product Node], here is such a 3-graph: (The three edges are separate since every node is a 0-node)

(3)-1-2-[2] (4)-1-3-[3] (5)-2-3-[6]

Here is part of a 6-graph:

[4]-1-4-(5)-2-3-[6]-1-6-(7)-2-5-[10]

In this part, [4] and [10] are 0-nodes, (5) and (7) are 1-nodes, and [6] is a 2-node. So 1-4, and 2-5 would take 2 turns, and 2-3 and 1-6 would take 3 turns.

Posted by Gamer on 2007-03-18 17:01:00