Algebra puzzle

Faria · 2014-12-11 19:59:37

ABC + DEF = GHIJ
solution is given : 437 + 589 = 1026
or
743 + 859 = 1602
how is this possible ??

bobbym · 2014-12-11 22:16:21

Hi;

Alphametics can have more than 1 solution. This one has 96 solutions!

David · 2014-12-11 22:36:33

Hi;
How do you know it have 96 solutions? Through M? Explain please.

bobbym · 2014-12-11 22:44:46

The fastest way to get an answer to this type problem especially if there are multiple solutions is to use M.

David · 2014-12-11 22:45:26

How do you do that with m?

bobbym · 2014-12-11 22:57:21

Do you program yet?

David · 2014-12-11 22:58:16

No. But I want to

bobbym · 2014-12-11 23:02:59

You have two options to code this:

1) Download someone elses code.

2) Write it yourself.

For 1) I recommend Rashers' code.

David · 2014-12-11 23:03:36

Do you do Java?

bobbym · 2014-12-11 23:06:02

I came from BASIC -> Assembly -> C++ -> M. No room for Java in there.

David · 2014-12-11 23:06:37

Maybe we could learn Java together? I really like Java.

bobbym · 2014-12-11 23:08:57

Nope, I hate it. Do not let that stop you though if you really like it you should do it.

David · 2014-12-11 23:09:45

Why do you hate it?

David · 2014-12-11 23:13:15

Perhaps we could write the program together for m?

bobbym · 2014-12-11 23:14:41

I have it written already, how do you think I got the answers?

phrontister · 2014-12-12 21:34:56

Hi Bobby,

I also got 96 answers, but am having trouble getting M to restrict the output to just those 96. My output includes invalid answers with a leading zero.

Could you please point me in the right direction?

Thanks.

bobbym · 2014-12-12 21:37:18

Sometimes I roll my own or sometimes I just use Rasher's. Want to see his?

phrontister · 2014-12-12 21:42:43

Yes please. You probably saw my comment in the other thread about me going fishing blindly without success...

bobbym · 2014-12-12 21:49:33

ClearAll[a, b, c, d, e, f, g, h, i, j];

(*Define alphabet,terms,and sum*)

vars = {a, b, c, d, e, f, g, h, i, j};
term1 = {a, b, c};
term2 = {d, e, f};
sum = {g, h, i, j};

(*Define Constraints*)
(*minimum and maximun values*)
{min, max} = {0,
    9};

(*must all letters assume differing values?*)
mustDiffer = True;

(*Additional constraints,use {} for none*)

conditions = {a > 0, d > 0, g > 0};

(*Solve It*)

solutions = 
  TableForm[
   Select[vars /. 
     Solve[Join[{FromDigits[term1] + FromDigits[term2] == 
         FromDigits[sum]}, Table[min <= zz <= max, {zz, vars}], 
       conditions], vars, Integers], ! mustDiffer || Unequal @@ # &], 
   TableHeadings -> {None, vars}];

(*Display Results& Checks*)
If[
 solutions[[1]] == vars || 
  solutions[[1]] == {}, "No solutions found for given", 
 Labeled[solutions, {Length[
      solutions[[1]]] "Solutions found for given\n", 
    "\nCheck all ok:" (varSave = SymbolName /@ vars;
      res = 
       And @@ ((ToExpression[
             ToString[varSave] <> "=" <> ToString[#]];
            
            FromDigits[term1] + FromDigits[term2] == 
             FromDigits[sum]) & /@ solutions[[1]]);
      ClearAll @@ varSave; res)}, {Top, Bottom}] // Framed]

This is Rasher's code.

It is not that fast but it is generic.

phrontister · 2014-12-12 21:54:05

Thanks! I've saved it in my M, and am looking at it now...

bobbym · 2014-12-12 22:00:01

It should be easy to adapt it to any of that type.

phrontister · 2014-12-12 22:17:50

It works instantaneously with SEND + MORE = MONEY.

ABC + DEF = GHIJ takes about 18 seconds for a complete solution that excludes answers with leading zeros, whereas my code takes about 22 seconds for answers that don't exclude them.

I haven't tried the code from hummmer98's thread yet (hope I can get the 2-equation thing going).

bobbym · 2014-12-12 22:18:23

hummer98?

phrontister · 2014-12-12 22:29:23

hummmer98's thread ("help me please and fast")

Btw, hummmer98 hasn't come back on board yet, so maybe you were too slow with your answer!

bobbym · 2014-12-12 22:37:18

Yes, he wanted super speed m and got me instead.

Math Is Fun Forum

#1 2014-12-11 19:59:37

Algebra puzzle

#2 2014-12-11 22:16:21

Re: Algebra puzzle

#3 2014-12-11 22:36:33

Re: Algebra puzzle

#4 2014-12-11 22:44:46

Re: Algebra puzzle

#5 2014-12-11 22:45:26

Re: Algebra puzzle

#6 2014-12-11 22:57:21

Re: Algebra puzzle

#7 2014-12-11 22:58:16

Re: Algebra puzzle

#8 2014-12-11 23:02:59

Re: Algebra puzzle

#9 2014-12-11 23:03:36

Re: Algebra puzzle

#10 2014-12-11 23:06:02

Re: Algebra puzzle

#11 2014-12-11 23:06:37

Re: Algebra puzzle

#12 2014-12-11 23:08:57

Re: Algebra puzzle

#13 2014-12-11 23:09:45

Re: Algebra puzzle

#14 2014-12-11 23:13:15

Re: Algebra puzzle

#15 2014-12-11 23:14:41

Re: Algebra puzzle

#16 2014-12-12 21:34:56

Re: Algebra puzzle

#17 2014-12-12 21:37:18

Re: Algebra puzzle

#18 2014-12-12 21:42:43

Re: Algebra puzzle

#19 2014-12-12 21:49:33

Re: Algebra puzzle

#20 2014-12-12 21:54:05

Re: Algebra puzzle

#21 2014-12-12 22:00:01

Re: Algebra puzzle

#22 2014-12-12 22:17:50

Re: Algebra puzzle

#23 2014-12-12 22:18:23

Re: Algebra puzzle

#24 2014-12-12 22:29:23

Re: Algebra puzzle

#25 2014-12-12 22:37:18

Re: Algebra puzzle

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