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Consider 3* 2 + 2 /4*10

With the default precedence for *,+, and / the result is 11.

I am curious what the results would be for all six choices for the precedence of the +,*, and /

I'm also curious what the set of results would be for all parenthetic groupings. (e.g, 3* (2 + 2) /4*10,3* ((2 + 2) /4)*10,etc)

Can anyone see how to do that?

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1 Answer 1

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stripParentheses = Function[, StringReplace["(" | ")" | " " -> ""] @
    ToString[Unevaluated @ #, InputForm], HoldFirst];

stripParentheses[3*2 + 2/4*10]

enter image description here

ops = {"/", "*", "+"};

split = StringSplit[stripParentheses[3*2 + 2/4*10], a : Alternatives @@ ops :> a]

enter image description here

parenthesize = SequenceReplace[#, {a_, #2, b_} :> StringJoin["(",a,#2,b,")"]]&;


Map[{#, ## & @@ {StringJoin @ #, ToExpression @ StringJoin @ #} & @
   Fold[parenthesize, split, #]} &] @ Permutations[ops] // 
 Grid[#, Dividers -> All] &

enter image description here

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  • $\begingroup$ Excellent. I am still spelunking your code. This answers the first part. Thanks. I'm trying to adapt it to also do the second part (e.g.,` (3*2 + 2/4)*10` = 65 $\endgroup$
    – Craig Carter
    Commented Jul 3, 2023 at 8:56

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