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Message: <blockquote data-quote="Pielorinho" data-source="post: 1343248" data-attributes="member: 259">Vyper, trial and error gives me 2 and 9 as the numbers.  Here's my thinking: A knows that however you divide the total of the number he's given, you get two numbers whose product can be reached in multiple ways.  A number whose product can only be reached in one way keeps B from knowing the solution. For example, if A was given the number 8, that could be the total of the villain's secret numbers 5 and 3.  But if that were the case, then their product would be 15, and if B were given 15, then B would know the villain's numbers were 5 and three.   A knows that B can't know the answer, which tells us that the number A was given can't be the sum of any two such numbers. Eleven, however, can be broken down into 2 and 9 (product 18, reachable also by numbers 3 and 6); 3 and 8 (product 24, reachable also by numbers 4 and 6); 4 and 7 (product 28, reachable also by numbers 2 and 14); and 5 and 6 (product 30, reachable also by numbers 2 and 15).  So if A were given the sum of 11, he would know that B couldn't possibly solve the problem. B has to work from that:  once he finds out that A knows he couldn't solve it, then he has to look at the sums of the different factor-pairs he was given.  We know that he was given either 18, 24, 28, or 30; now we have to see which of numbers can be factored in a way as to tell A that the problem is intractable. ...and here I'm getting stuck to explain the rest of my reasoning.  Am I on the right track, at least? Daniel</blockquote>

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