Publications by Jason Shaw
Average Steps to Favorite Song
How Fast Can You Skip To Your Favorite Song? There are 100 songs on your smart song device. You begin at a random song. You are allowed to push the random button or the next button. The random button will take you to a random song in the 100 song playlist, with a 1% chance that you get the same song that you are on. The next button takes you to t...
2608 sym R (1769 sym/19 pcs) 5 img
Matching Pair of Socks
Riddler Classic From The Riddler at FiveThirtyEight: "From Kathy Bischoping comes a question we’ve all asked ourselves at one time or another: I have 10 pairs of socks in a drawer. Each pair is distinct from another and consists of two matching socks. Alas, I’m negligent when it comes to folding my laundry, and so the socks are not folded int...
7793 sym R (4580 sym/47 pcs) 1 img
Tiffany's Barbershop Part 2
Rational Convergence to Log2(10) The Riddler Express for 03/13/2020 described how \(2^{10} = 1024\) is only 2.4% different than \(10^3 = 1000\). The Express question asked for the next power of 2 that was closer (in terms of percentage) to a power of 10. Using a quick program, finding the next three was easy enough. x <- 10 y <- 3 for(i in 1:3)...
2574 sym R (3196 sym/26 pcs)
Golden Spheres
Golden Spheres This Riddler Classic on 06/19/2020 was submitted by Dean Ballard. King Auric adored his most prized possession: a set of perfect spheres of solid gold. There was one of each size, with diameters of 1 centimeter, 2 centimeters, 3 centimeters, and so on. Their brilliant beauty brought joy to his heart. After many years, he felt the t...
3062 sym R (4312 sym/23 pcs)
Deep Space and Hampster Corrals
Problem Statement These riddles were posted on August 21, 2020 under the Riddler on FiveThirtyEight. Riddle Express When you started your doctorate several years ago, your astrophysics lab noticed some unusual signals coming in from deep space on a particular frequency - hydrogen times tau. After analyzing a trove of data measured at many regula...
4427 sym R (1329 sym/17 pcs)
Ring Stacks for Riddle 230
Introduction and Problem Statement Riddle 230 from Five Thirty Eight’s column “The Riddler” was suggested by Austin Shapiro. It is as follows: Mira has a toy with five rings of different diameters and a tapered column. Each ring has a “correct” position on the column, from the largest ring that fits snugly at the bottom to the smallest ...
5821 sym R (2193 sym/7 pcs) 1 img
The Tortoise and the Hare
The Problem The tortoise and the hare are about to begin a 10-mile race along a “stretch” of road. The tortoise is driving a car that travels 60 miles per hour, while the hare is driving a car that travels 75 miles per hour. (For the purposes of this problem, assume that both cars accelerate from 0 miles per hour to their cruising speed insta...
5100 sym R (1712 sym/36 pcs)
Summing Nematodes
Introduction and Problem Statement Riddle 234 from Five Thirty Eight’s column “The Riddler” was suggested by Kareem Carr. It is as follows: We usually think of addition as an operation applied to a field like the rational numbers or the real numbers. And there is good reason for that - as Kareem says, “Mathematicians have done all the har...
5949 sym R (1371 sym/43 pcs)
One Way Streets - Riddle 266
One Way Streets Let me model a specific assignment of streets with a 12-tuple logical string. Going left to right, top to bottom, (R,R,D,D,D,R,R,D,D,D,R,R) will model the directions. FALSE in the first spot would mean the direction between the top left and top middle vertex is NOT Right (rather Left). A TRUE in the fourth spot means the direction...
890 sym R (1821 sym/5 pcs)
Eating Cake in 4th Grade
Eating Cake The 271st Riddler presents us with a fun problem about your infinite number of friends trying to share some cake. In the first question, friend 1 eats 1/2 of the cake, friend 2 eats 1/3 of what remains of the cake, friend 3 eats 1/4 of what remains of the cake and so on. If we let \(R_0 = 1\) represent the whole cake at step 0, and \(...
4376 sym R (173 sym/6 pcs)