In this case, I couldn’t possibly have passed anyone. Now suppose I had been the first person in the queue at the starting line. And so, on average, I was faster than half of the runners and slower than the other half. Since I didn’t know how my pace compared to that of the other runners, you could assume (for the purposes of this puzzle) that I was equally likely to be anywhere in that ordering. Suppose you ordered all the runners from fastest to slowest. While the puzzle gave you no information about the distribution of paces among the different runners, the shape of this distribution didn’t matter. On average, what fraction of the other runners could I have expected to pass during the race?įirst off, this was equivalent to asking what fraction of the runners in front of me were also slower than I was. What is the farthest the ball can travel before hitting a wall for the third time?Įxtra credit: What is the farthest the ball can travel before hitting a wall for the N th time? Instead, it will hit both sides that are adjacent to the corner. 2 Also assume that it’s impossible for Maryam to hit the ball precisely in one of the corners of the table. Note that the ball doesn’t necessarily have to hit three different walls of the table.Īssume the ball travels in a straight path and that it bounces off a wall as you’d expect. She places the ball in one of the corners, aiming to strike the ball so that it travels as far as possible before hitting a wall for the third time. Maryam is playing billiards on a 1 meter by 1 meter square table. Please wait until Monday to publicly share your answers! If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter or send me an email. Submit a correct answer for either, 1 and you may get a shoutout in the next column. Two puzzles are presented each week: the Riddler Express for those of you who want something bite-size and the Riddler Classic for those of you in the slow-puzzle movement. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability.
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