Reverse the order of the numbers to make the subtraction normal.
There are 10! possible order of erasures correspond to various ways of inserting 9 sets of parentheses. But many of these are repeats.
Once simplified to remove the parentheses some of the subtractions become additions, except for the very first: 3^9 will always be subtracted (and 3^10 will always be positive.)
It turns out that for the other 9 that every possible combination is possible in at least one way.
The powers of 3 are far enough apart that no two combinations will give the same value.
So there are 2^9=512 possible values for this number ranging from a low of
to a high of
Posted by Jer
on 2015-09-16 09:34:03