*by Jake Jacobs*

29 June 2018

Jake Jacobs

Last month I administered Paul Magriel's Genius Quiz. While your brains are still reeling, I'll revisit it.

But first, to keep you sharp, here is a bonus quiz!**1)** Imagine that you have built a railroad line, or at least a section of track. It is precisely 100 km long, and for purposes of this quiz, we shall assume that the stretch of ground on which it sits is perfectly flat; those tracks are as straight as straight can be. Being a punctilious sort, someone who simply hates wobbling, you have braced each end so that the tips of the rails are snugly fitted, with not a micrometer of give to them. What you've overlooked is the heat of the sun. The metal expands and each rail in the pair is now precisely 1 mm longer. (If you are American, and don't do metric, borrow a scientist to translate.) Because your braces won't give - Sproing! – the rails bend and rise up in an inverted V. At the center, how high are they off the ground: a) .01 micrometers; b) 10 micrometers; c) 3 centimeters; d) 0.4 meters; e) Higher than your garage; f) higher than the Burj Khalifa?**2)** Someone hands you a straight stick. You happen to have a very sharp axe which can make infinitesimally thin cuts. You make two random cuts in the stick. What is the probability that you will have a piece of stick after cutting that is 50% or more as long as the original: A) 5%; b) 20%; c) 33%; d) 50%; e) 67%; f) 75%; g) 90%?**3)** Let's play dice! Or rather, let's play with a die. Roll the die over and over recording the results until either a 1 is followed immediately by a 2, or a 6 is followed immediately by another 6. In other words, 6-3-6 is not a winner, nor is 1-4-2, but 3-6-6 or 4-1-2 would be. Once a winner occurs, you may start over if you are having fun. If you do play the game would you prefer: a) 12 over 66; b) 66 over 12; c) It makes no difference?

While you are working on those, let me discuss one of the questions from last month. Like the three above, seven of the eight questions can be solved in your head. The eighth cannot. The question in question is #3, which asks your strategy for playing, or not playing, single-zero roulette, while flat betting on either red or black, knowing that any net loss will be reimbursed with 50% of the loss. My answer claimed that you should risk only one unit, but keep playing as long as you were winning. I said in part: "The further you go, the uglier and more tedious the math, so take my word for it: keep going." It turns out that the first part is an understatement, and the second part is probably wrong.

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