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The equation below is not true. The only allowable way to change the equation is to insert plus signs between some of the digits. Find an example of using as few plus signs as possible to make the expression on the left equal to the expression on the right.

$123456789 = 987654321$

This puzzle was inspired by this one: How to solve 1 2 3 4 5 = 5 4 3 2 1 (insert five pluses to make it equal)? A thorough solution needed

  • 10
    $\begingroup$ I have a solution with 16 plus signs. The clock is ticking! $\endgroup$ Dec 11, 2023 at 6:08
  • 4
    $\begingroup$ Truly the best mathematician of all time @DanielMathias $\endgroup$
    – Stevo
    Dec 11, 2023 at 6:12
  • $\begingroup$ I have a solution with zero, but you’re not gonna like what I’ve done with bases. $\endgroup$
    – Sneftel
    Dec 11, 2023 at 8:20
  • $\begingroup$ @Sneftel I am curious about your solution; please post it. $\endgroup$ Dec 13, 2023 at 5:42

1 Answer 1


Here is a solution using 5 plus signs, which I believe is the minimum based on an exhaustive* search:
123 + 456 + 789 = 987 + 6 + 54 + 321


By "exhaustive search" I mean I tried to find solutions with four or fewer plus signs by hand (and with quick mental math) but couldn't find any (I suppose I did not thoroughly check all combinations, as I skipped over areas which seemingly would not lead to a solution). It's quite possible that I missed a solution with fewer than 5 plus signs.

The first solution I found with 5 plus signs was this, and I assume it is the minimum solution. Unfortunately I didn't have much of a method; I tried the even spacing of the plus signs on the left since it looked nice, and it happened to lead to a solution.


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