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]:=
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[
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
>

```

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