ags@pucc-k (Seaman) (11/23/83)
Sorry, but you blew it. You said that 23 was one of the possible sums that S might have, such that P could not determine the sum. As you already pointed out, one of the possible products corresponding to 23 is 76. If I am P, and I see that the product is 76, and if I also know that the sum is less than 40, then I can immediately conclude that the sum is 23. How? Because the only admissible factorization of 76 is 4 * 19, and 4 + 19 = 23. Note that 2 * 38 = 76 is NOT an admissible factorization in your version of the puzzle, since the sum is not less than 40. Therefore, when S announces that P does not know the sum, you can conclude (since S does not make mistakes) that his sum is NOT 23. The rest of the analysis is exactly as I posted earlier, and every word of it is correct. The only possible sums are 11 and 17, and there is no way for S to determine the product. Dave Seaman ..!pur-ee!pucc-k!ags
ags%pucc-k@phs.UUCP (Seaman) (11/23/83)
References: <576@alberta.UUCP> Relay-Version:version B 2.10.1 6/24/83; site duke.UUCP Posting-Version:version B 2.10.1 6/24/83; site pucc-k Path:duke!decvax!genrad!grkermit!masscomp!clyde!ihnp4!inuxc!pur-ee!CS-Mordred!Pucc-H:Pucc-I:Pucc-K:ags Message-ID:<119@pucc-k> Date:Wed, 23-Nov-83 09:58:39 EST Organization:Purdue University Computing Center Sorry, but you blew it. You said that 23 was one of the possible sums that S might have, such that P could not determine the sum. As you already pointed out, one of the possible products corresponding to 23 is 76. If I am P, and I see that the product is 76, and if I also know that the sum is less than 40, then I can immediately conclude that the sum is 23. How? Because the only admissible factorization of 76 is 4 * 19, and 4 + 19 = 23. Note that 2 * 38 = 76 is NOT an admissible factorization in your version of the puzzle, since the sum is not less than 40. Therefore, when S announces that P does not know the sum, you can conclude (since S does not make mistakes) that his sum is NOT 23. The rest of the analysis is exactly as I posted earlier, and every word of it is correct. The only possible sums are 11 and 17, and there is no way for S to determine the product. Dave Seaman ..!pur-ee!pucc-k!ags