Solve equation with unknown numeric operators?

Questions
, ,
1

How to solve an equation with unknown numeric operators in Wolfram Alpha?

75 ? 4 ? 10 ? 6 ? 2 ? 2 = 286

? are the basic numeric operators + - * /

With a bash shell, I can use the brace expansion to generate all combinations and use the basic calculator (bc) to evaluate it:

n=0
for i in 75{+,-,*,/}4{+,-,*,/}10{+,-,*,/}6{+,-,*,/}2{+,-,*,/}2; do
    n=$((n+1))
    j=$(echo $i | bc)
    if [ $j -eq 286 ]; then 
        echo "Result is ${i}=${j} (${n} iterations)" | sed -r 's/([=+*\/-])/ \1 /g'
        break
    fi
done

The answer is

75 * 4 + 10 - 6 * 2 * 2 = 286

I understand this could be tricky to implement if you also permute all numbers.

2

Please find below my suggestion about your problem.

buildLeft[randList_, ratorList_] :=  
  Append[Flatten@
    Transpose[{Take[randList, Length@randList - 1], ratorList}] , 
   Last@randList];

leftEqBuilder[randList_, ratorList_] :=  
  StringJoin[
   If[MemberQ[randList, #], ToString@#, #] & /@ 
    buildLeft[randList, ratorList]];

solver[randList_, ratorList_, rhs_] := 
  Module[{ tup = Tuples[ratorList, Length[randList] - 1]},
   leftEqBuilder[randList, 
    SelectFirst[tup, 
     ToExpression[leftEqBuilder[randList, #]] == rhs &]]];

solutionQ[str_, rhs_] := ToExpression@str == rhs;

Tests

solver[{1, 2, 3, 4}, {"+", "-"}, 10]
(*      1+2+3+4                *)


solver[{75, 4, 10, 6, 2, 2}, {"+", "-", "*", "/"}, 286]
(*   75*4+10-6*2*2                                          *)

Check

solutionQ[solver[{1, 2, 3, 4}, {"+", "-"}, 10],10]
(*  True *)
solutionQ[solver[{75, 4, 10, 6, 2, 2}, {"+", "-", "*", "/"}, 286], 286]
(* True *)

Note that the solution provided is quite general: The operands do not have to be numbers. The operators need only to be compatible with the operands.
Thanks,

3

Would it be possible to use an infix like “?” (or something else) as new custom operator and call the above solver function?

The Wolfram Alpha built-in Infix function is not designed to define custom operator right?

(like custom-defined infix operators in Perl 6)

Bottom line it would be nice for Wolfram Alpha to guess that ? is for the missing numeric operators.

in: 1 ? 1 ? 1 = 3
out: 1 + 1 + 1 = 3

Extend the InputForm capabilities to understand the meaning of ? or a create a special sign for this purpose

REFERENCES

4

The answer to you question is YES. You need just to add a on-liner parser to accomplish what you want. I have added such a parser and the new solver. Please find below the updated code.

buildLeft[randList_, ratorList_] :=  
  Append[Flatten@
    Transpose[{Take[randList, Length@randList - 1], ratorList}] , 
   Last@randList];

leftEqBuilder[randList_, ratorList_] :=  
  StringJoin[
   If[MemberQ[randList, #], ToString@#, #] & /@ 
    buildLeft[randList, ratorList]];

solver[randList_, ratorList_, rhs_] := 
  Module[{ tup = Tuples[ratorList, Length[randList] - 1]},
   leftEqBuilder[randList, 
    SelectFirst[tup, 
     ToExpression[leftEqBuilder[randList, #]] == rhs &]]];
solutionQ[str_, rhs_] := ToExpression@str == rhs;
parseExpression[expr_, dum_: "?"] := 
  Module[{s = 
     StringSplit[StringReplace[expr, " " -> ""], "="]}, {StringSplit[
     First@s, dum], Last@s}];
newSolver[strExpr_, ratorList_, dum_: "?"] := 
  Module[{s = parseExpression[strExpr, dum]}, 
   solver[ToExpression@HoldForm /@ First@s, ratorList, 
     ToExpression@Last@s] <> " = " <> Last@s];

Now let’s test it.

newSolver["75*4?10?6?2*2=286", {"+", "-", "*", "/"}]
(*  75*4+10-6*2*2 = 286   *)   
newSolver["1?1?1=3", {"+", "-", "*", "/"}]
(* 1+1+1 = 3 *)

Thanks,