The Broom Riddle (Solution) ft. Kurt Hugo Schneider part 3/3

Regarding the mass distribution broom: just attach a long, skinny segment of some essentially-weightless material to the broom head end, and you've increased the length without at all changing the mass distribution. So the masses and CoG are the same, but now the broom head end is much longer.

With the two 2's problem, the best I can come up with is "sqrt(sqrt(sqrt(sqrt(sqrt(...(2)...))))) / .2" with an infinite number of square roots. The idea is to get 5 from doing "1 / 0.2" but we have to make a 1 from a single 2. If we take an infinite number of square roots, we approach 1, and I'm not sure how else to do it. (...) Huh, Kurt came up with the same thing. Also, the proper solution actually does follow from "1/0.2" - we just get rid of the "1 /" part in a very different way.

As for the final riddle, I think I've seen this before, but I don't remember at all the solution. My instinct says equal, but let's see if I can work it out (...) Oh actually it's not too bad if you draw it on a good grid. Draw the leftward-leaning diagonal of a vertical 9 x 3 rectangle (which has angle a). This line passes both (1,6) and (2,3), which are equidistant from each other, so we can use this diagonal as the side of a 2:1 rectangle (one with a diagonal at angle b): the corners are (3,0), (1,6), (-2, 5), and (0,-1). If you draw the diagonal of this rectangle (from (3,0) to (-2,5)), you clearly see that it passes straight through (0,3). This means that a + b gives the same as the diagonal as just the diagonal of a 1:1 square, which is the same as c.