# A riddle for 2017

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)?

• Would a brute force answer suffice? Or are you more interested in a general approach? – Dando18 Jul 1 '17 at 15:43
• please check this question (puzzling.stackexchange.com/questions/47392/…) – W.R.P.S Jul 1 '17 at 15:44
• @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!) – Jakub Konieczny Jul 1 '17 at 15:59
• @W.R.P.S Thanks! Related, but not the same. – Jakub Konieczny Jul 1 '17 at 15:59
• 1+(2-3+4-5+6)×7×8×9=2017. – farruhota Jul 1 '17 at 16:00

i found this: $$1+(-2+3+4+5-6)\cdot7\cdot8\cdot9=2017$$