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One can obtain a total of $16$ using each of the numbers $10, 12, 14$, and $17$ exactly once, combining them using any of the four common operations $+$, $-$, $*$, and $/$ along with parentheses, by writing $10/(17-12)+14$. Demonstrate how to obtain $2$.

I know how to do this, but is there any way to do it without bashing?

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    17*10-12*14. No, there is no 'smart' way, just the brute force search. Well, you may slightly shorten the search by noticing that just + and - are not enough, as the result would always be odd... – 2017-01-20
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    Read the tag descriptions and only add the ones that are relevant! – 2017-01-20

2 Answers 2

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These type of questions do not have any particular method to solve them. You have to derive answers from options if options are given. And in case no options use brute force to solve them like in this case.

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Sadly, there is no general way to do this, other than intuitively guess. If you haven't seen it already, I would suggest watching: 'The 10,958 problem' by Numberphile.

It is a great video about obtaining values of 1 to 11,111 using the numbers 1,2,3,4,5,6,7,8,9, once, and the operations $\frown$, *, ^, +, /, -, and (). The problem was that 10,958 was unsolved, however, the solution is provided in the video, Matt Parker who is the one seen on camera finds the solution and submits it.

It is a great video, and it could possibly spark some ideas that you could use when doing problems like this.

By the way, here's how to do your problem: $$17*10-12*14$$