So in being reunited with my Bulgarian math coach and working on a problem, I have discovered this tidbit--currently Pepsi offers a contest where 1 in 3 bottles win--now one might naively expect that this would only require you to buy 3 bottles to win, but of course if you buy 3 bottles your probability of winning is only 1-(2/3)^3, or 21/27, roughly about 70%. What happens if this continues? When will buying n bottles not be enough? The answer, naturally, is the limit of 1-[(n-1)/n)]^n, which is of course 1-1/e, which may or may not have something to do with our derangements. So I guess you could say in this case your naivest intuition is still about 60% correct.

More disturbingly, one of my contacts did rip, apparently in my eye, today, so that was a little painful and hopefully none too scratchy, but I'm committed to them, even if it means an inconvenient detour tomorrow between school and kendo.