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?