**pizer@ecsvax.UUCP** (07/29/84)

I posted a early answer to this problem <ecsvax.2995> and this is just to clarify that my solution is correct. After modifying my program, and letting it run seven and one-half hours, I discovered that my solution must be correct, since I didn't get another possible answer and it makes sense. The problem is as follows, person A thinks of two integers (2-99), gives the product of the two numbers to person P and the sum of the numbers to person S. Then, the following conversation takes place; S: I don't know what the numbers are. P: I don't know what the numbers are, either. S: I knew you didn't know what the numbers are. P: Well, in that case I DO know what the numbers are. S: In that case, so do I. The problem, of course is to find the two numbers. Without explaining how I arrived at the numbers, as I tried before, I will simply explain my solution, that the numbers were 4 and 13. With the sum being 17, the first statement is obviously true, since there are 7 possible combinations, (2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9). The second statement is also true, with the product being 56, there are two possible combinations (4,13),(2,26). The next statement, by S, is also true, every possible product of the combinations listed above has more than one possible factor combinations, therefore S knows that whatever the product, P cannot know what the numbers are. The next statement, by P, is more difficult. If the numbers were 2 and 26, the sum would be 28, which has (5,23) as a possible combination; making S' statement false (S wouldn't know for sure that P didn't know). The combination 4 and 13 obviously makes sense since that is what S was talking about. The final statement is the clincher, of all the possilbe sum combination, only (4,13) would allow P to discover the answer from what S said, allowing S to discover the answer also. To be more specific, if S thought the combination was (5,12), he would know the product to be 60; which has both (5,12) and (3,20) as factors. Both of those combinations would make S' earlier statement true, and P would not know which combination the numbers were. You might think that there would be another combination like 4 and 13 less than 100, however, after 7 1/2 hours, I would tend to disagree. Conflicts an criticism accepted. Billy Pizer (pizer@ecsvax)