Take the 2-minute tour ×  I was tooling around over on
stackoverflow and happened upon this question. To summarise,
given the set of digits $\{1,2,3,4,5,6,7,8,9\}$ and a set of
basic arithmetic (binary) operators $\{+,-,\times,/\}$, what is
the least number of operations you need to construct a given
integer? For example $239 = 8\times6\times5-1$, requires 3
operations.  My conjecture is that division doesn't help you.
There is no number that can be constructed using division, that
can't be constructed without division using the same number
operations (or fewer). Can anyone prove or disprove this?
share|improve this question I have a feeling that you do need
division sometimes. For instance, take numbers like
1+9+81+729+...+9^k. These are easy to make with division:
(9*9*9*...*9-1)/8. But I'm not sure how to prove this works;
that is, that at least some of these numbers are "rough" enough
that there's no more efficient way to make them. –  Lopsy Feb 10
'12 at 2:48 Lopsy: You can calculate with a computer the