Re: Arithmetic Puzzle (so simple it's hard)

*To*: mathgroup at smc.vnet.net*Subject*: [mg71392] Re: Arithmetic Puzzle (so simple it's hard)*From*: "Scout" <Scout at nodomain.com>*Date*: Thu, 16 Nov 2006 00:53:59 -0500 (EST)*References*: <ejc4pv$6nf$1@smc.vnet.net>

Some years ago I wrote a routine that looked for all the solutions to this type of game with the substitution of all the digits and the operators ("*","+","-","/") in the Integers. "Doubly True" is the name of this game If I remember well... A brute approach in this case helps: In[1]:= <<DiscreteMath`Combinatorica` In[2]:= s=ToUpperCase["but*ask==feast"] s2=StringCases[s,LetterCharacter]; unicChs=Union[Flatten[Characters[ToUpperCase[s2]]]]; l=Length[unicChs]; digs=CharacterRange["0","9"]; p=Take[digs,l]; ks=p; Do[ Do[ test=StringReplace[s,Thread[unicChs->p]]; If[ToExpression[test],Print[test]]; p=NextPermutation[p], {l!}]; ks=NextKSubset[digs,ks]; p=ks, {Binomial[10,l]}]; Well formed solutions: 160*283==45280 630*124==78120 670*142==95140 540*128==69120 165*439==72435 Bye, ~Scout~ "Bruce Colletti" <vze269bv at verizon.net> news:ejc4pv$6nf$1 at smc.vnet.net... > How would this problem be solved in Mathematica? > > BUT * ASK = FEAST, where each letter is a 1-digit number, no two letters > may stand for the same number, and the letters are in {0,1,2,4,5,6,7,9}. > > Thankx. > > Bruce >