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This equation is false. Make it true by adding as few operators as possible:

987654321 = 123456789

Only the operators + - × ÷ are allowed. You can change both sides, but not the numbers. APL notation not allowed.

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A note about voting: Please do not just upvote the earliest or the accepted answer, instead try to find the best answer, even if it is not the accepted answer. Please upvote the answer(s) with the fewest operands, and only downvote answers that are invalid - do not downvote simply because an answer uses more operands; it can still be a helpful answer!

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  • $\begingroup$ There is 5 solutions with 4 operands. Time is ticking! $\endgroup$ Commented Jun 6 at 17:56
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    $\begingroup$ The same puzzle but only allowing plus signs: puzzling.stackexchange.com/questions/123600/… $\endgroup$ Commented Jun 6 at 18:41
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    $\begingroup$ Just for the entertainment value: 987654321=⍎⌽⍕123456789 $\endgroup$ Commented Jun 6 at 18:46
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    $\begingroup$ Are brackets allowed (they are not operators) $\endgroup$ Commented Jun 6 at 23:13
  • $\begingroup$ With this website, sha256 is b63a592da7f40f4291f72dcc3fde8fa12327f03ab387a4fd16a3d4edcf18a791 $\endgroup$ Commented Jun 6 at 23:32

2 Answers 2

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Fun question :). I believe these are all the four-operator solutions (I don't think there are any with four operands..):

\begin{alignat*}3 9-8765+4321 &= 1234-5678+9 &&= -4435 \\ 9876-5432+1 &= 1-2345+6789 &&= 4445 \\ 987654\div3\times21 &= 1\times2\times3456789 &&= 6913578 \\ 9876543+2\div1 &= 1234567\times8+9 &&= 9876545 \\ 9876543+2\times1 &= 1234567\times8+9 &&= 9876545 \\ \end{alignat*} I believe there are no solutions with three or fewer operators (confirmed by exhaustive search).

That's interpreting the question as "inserting only the operators $-, +, \times, \div$, only inserting them between digits, and evaluating the resulting expressions as arithmetical expressions using infix notation with the usual order of precedence". There might be more/shorter solutions if you think outside the box more!

I hope I've followed all the right rules! Please do let me know if I haven't. I made an extremely quick-and-dirty (and very inoptimal) little script that I used to confirm, in case that's of any interest!

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    $\begingroup$ Izaak: Welcome to PSE (Puzzling Stack Exchange)! $\endgroup$ Commented Jun 7 at 19:01
  • $\begingroup$ @IzaakVanDongen Use this powerful program instead of wasting time: perchance.org/brute-forcer $\endgroup$ Commented Jun 7 at 19:06
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@bobble's link to a previous question (which only allowed + signs) shows this can be done with 5 + signs.

To start this off, here a couple of simple solutions that beat that by using different operators as allowed by this question.

9876-5432+1 = 1-2345+6789 (4 operators, both sides evaluate to 4444+1=4445)

9-8765+4321 = 1234-5678+9 (4 operators, both sides evaluate to 9-4444=-4435)

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  • $\begingroup$ Good answer, but not the best. $\endgroup$ Commented Jun 7 at 16:03