Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: notesfiles Path: utzoo!linus!decvax!decwrl!amd!dual!zehntel!hplabs!hp-pcd!hpfcrs!lief From: lief@hpfcrs.UUCP (lief) Newsgroups: net.puzzle Subject: Re: Orphaned Response Message-ID: <15400001@hpfcrs.UUCP> Date: Thu, 18-Oct-84 22:01:00 EDT Article-I.D.: hpfcrs.15400001 Posted: Thu Oct 18 22:01:00 1984 Date-Received: Thu, 18-Oct-84 19:23:18 EDT References: <-83700@ihuxe.UUCP> Lines: 47 Nf-ID: #R:ihuxe:-83700:hpfcrs:15400001:37777777600:1666 Nf-From: hpfcrs!lief Oct 8 18:01:00 1984 In response to the SEND + MORE = MONEY puzzle: SEND + MORE ------ MONEY (1) D + E = 10*C1 + Y (2) C1 + N + R = 10*C2 + E (3) C2 + E + O = 10*C3 + N (4) C3 + S + M = 10*M + O where C1, C2, and C3 are the corresponding carries. These can be rewritten: (4) C3 = 9*M + O - S (5) C2 = 90*M + 9*O - 10*S + N - E (6) C1 = 900*M + 90*O - 100*S + 9*N - 9*E - R (7) D = 9000*M + 900*O - 1000*S + 90*N - 91*E - 10*R + Y (subs for C1 in (1)) assume C3=1, then from (4) M = (S - O - 1)/9 where M,S, and O are integers less than or equal to 9. This equation is impossible for this stipulation so therefore C3=0, and S=9, O=0, and M=1. plug this result into (5) and C2 = N - E. We know that N is not equal to E so therefore C2 must be 1 and E = N -1. plug the above results into (6) and C1 = 9 - R. Since S is already 9, R must be 8 and C1 must be 1. (Of course you agree that C1 can only be either 0 or 1). finally, play with (7) and D - Y = 10 - E. Let's assume that N = 7. Then E = 6 since E = N - 1. Thus we have D - Y = 4. The only integer pairs that can solve this is D,Y = 4,0 5,1 6,2 7,3 8,4 9,5. However, one of the numbers in each pair is already defined so none of these will work. Let's assume that N = 6 and of course E = 5. Then we have to fit D - Y = 5. The possible solutions are D,Y = 5,0 6,1 7,2 8,3 9,4. Note that both 7 and 2 have not been defined yet, so this pair is a solution. O=0 M=1 Y=2 E=5 N=6 D=7 R=8 S=9 9567 +1085 ----- 10652 which is a correct solution (I didn't prove it was unique!) Lief Sorensen