> For mental math, it often helps to change the
>problem to a bunch of easy steps. To do 18x31,
>which is ugly if not hard, the first step would
>be 20x31=620, then 2x31=62, then 620-62=600-
>42=560-2=558. Lots of steps to it, but all easy
>ones, so it ends up taking very little time.

None of these are easy steps to me. In fact, the very fact that I have to hold so many *more* numbers in my head before getting to the number I want probably makes this method *more* difficult for me.

Also, I seem to have no faith in my understanding of basic arithmetic rules. For instance, several people have said they would accomplish my sample problem, 24x7, by doing the problem (20x7)+(4x7) instead. I wouldn't be able to do this, because I wouldn't *believe* that it would work. To me, those are completely separate problems that coincidentally have the same answer.

I wish I could think of a good example of what I'm really talking about. Basically, when confronted with a problem and a "short-cut" method I think will work but don't really understand *why* it might work, I usually have to convince myself it'll work by working out a much simpler, more basic problem in this method to see if it works for that. Then I usually try it again with another simple problem before I'm convinced it's not just a fluke and will work for all sets of numbers. But the real kicker is the next time I got to use this trick, if it's been sufficiently long since the last time I used it, I have to convince myself all over again that it really works before I use it again.

As an aside, does anyone else visualize numbers the way I do? Anytime I see numbers in my head, unless I'm arranging them to do a problem, I see them on a clock face. So the numbers 1-12 are arranged in order like they are on a clock, and starting with thirteen, they snake up into oblivion in my mind's eye. So 13 is above and to the right of 12, 14 is above and to the right of 13, but they sort of start going up more straight after 15, until they kind of hit a peak at 20 and flatten out again. Then they slope up much more slowly until 35 or 40 or so, then shoot up again. Somewhere around 70 or so they start bending back towards the left, because I get the distinct impression of 90-100 ascending right-to-left instead of left-to-right.

Ok, I guess I'm just crazy. :-(