Re: Playing with numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg50162] Re: Playing with numbers*From*: kzhang at flashmail.com (Kezhao Zhang)*Date*: Wed, 18 Aug 2004 01:20:14 -0400 (EDT)*References*: <cfshq3$9qf$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"Thomas Manz" <thomasmanz at web.de> wrote in message news:<cfshq3$9qf$1 at smc.vnet.net>... > Hello! > > Everyone of you knows number riddles! Here´s an example: > you have five equations: > (1) H - F = I > (2) F x G = C > (3) E / B = F > (4) A + B = H > (5) C - D = A > every variable from A to I stands for a number from 1 to 9, where each number appears only once (no two variables can have the same value)!! > > Solving this problem with a piece of paper and your brain should take not more than 10 minutes. > (I tried it, and also found that 5-4-6-1-8-2-3-9-7 (A-I) is the ONLY solution!) > > But how can I solve it with Mathematica?? > > best regards > Thomas Here is a way to solve it by brute force: p=Permutations[Range[9]]; loc=Position[(And[h - f == i, f g == c, e/b == f, a + b == h, c - d == a] /. Thread[{a, b, c, d, e, f, g, h, i} -> #]) & /@ p, True]; p[[loc[[1,1]]] Indeed, there is only one solution. K. Z.