How a Nerd Walks Up the Stairs

Your steps should be in a cycle: short, long, long. Long in this case means a double step. Thus, you will cover five stairs in one short-long-long cycle. In addition, you should always start the first cycle on the same foot. Suppose you start on the left foot, then after two cycles you are back on the left foot, having covered ten stairs. While you are walking the stairs in this way, it is clear where you are in the cycle. By the end of the staircase, you will know the number of stairs modulo...

 1/9998 Produces Binary Output

The pattern will break down once you get past 8192, which is 2^13. That means that the pattern continues for an impressive 52 significant figures (well, it actually breaks down on the 52nd digit, which will be a 3 instead of a 2). The reason it works is that 9998 = 10^4 - 2. You can expand as   1 / (10^n - 2) = 1/10^n * 1/(1 - 2/10^n) = 1/10^n * (1 2/10^n 2^2 /10^2n 2^3 /10^3n ...) which gives the observed pattern. It breaks down when 2^k has more than n digi...

 Torture Methods Used on Those Accused of Witchcraft

One might glance at some of the special tortures at Bamberg, for example, such as the forcible feeding of the accused on herrings cooked in salt, followed by denial of water - a sophisticated method which went side by side with immersion of the accused in baths of scalding water to which lime had been added. Other ways with witches included the wooden horse, various kinds of racks, the heated iron chair, leg vises [Spanish boots], and large boots of leather or metal into which (with the feet ...