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Inspired by a riddle for 2015, I'm interested in the problem of representing the number 2017 using the numbers $$ 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7 \quad 8 \quad 9 $$ writtend down in this order, and the basic arithmetic operations $+, - \times, \div$, as well as parentheses.

It is fairly easy to find a such solution, such as: $$ - 1 + 2 + (3 × (4 + 5) − 6 + 7) × 8 × 9 = 2017 $$

How many such solutions exist? What is the simplest one (with reference to some reasonable notion of complexity)?

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    $\begingroup$ Would a brute force answer suffice? Or are you more interested in a general approach? $\endgroup$ – Dando18 Jul 1 '17 at 15:43
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    $\begingroup$ please check this question (puzzling.stackexchange.com/questions/47392/…) $\endgroup$ – W.R.P.S Jul 1 '17 at 15:44
  • $\begingroup$ @Dando18: I don't think there is a general solution to this kind of problem (but I'd be very happy to be proved wrong!) $\endgroup$ – Jakub Konieczny Jul 1 '17 at 15:59
  • $\begingroup$ @W.R.P.S Thanks! Related, but not the same. $\endgroup$ – Jakub Konieczny Jul 1 '17 at 15:59
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    $\begingroup$ 1+(2-3+4-5+6)×7×8×9=2017. $\endgroup$ – farruhota Jul 1 '17 at 16:00
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i found this: $$1+(-2+3+4+5-6)\cdot7\cdot8\cdot9=2017$$

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