A 25-dimensional ball (a 25-ball) with radius 3 and a 25-dimensional hypercube with edge length 2 are concentric. What is the 25-dimensional volume of their intersection? Estimate with high confidence of at least three correct leading digits.
Know the answer? Send your solution to ar@casact.org.
Turning into Traffic
To recap the puzzle: You are at a stop sign on a two-lane road that intersects a four-lane (two lanes going each way) road without a stop sign. In each individual lane of the four-lane road, on average, a car passes by the stop sign every four seconds. Given your car’s performance, cars on the intersecting road need to be at least four seconds away for you to safely make the turn. If you are in a right-hand traffic country, like the U.S, how long do you expect to wait to make a right-hand turn? How long is it for a left-hand turn? What if you are unlucky and have to wait a long time (worst 10%,
worst 1%, …)?
Independent estimates from Bob Conger and John Berglund are very close. So, there is a very good chance they are right! Answers are in the table below, and details of their solutions are posted below in PDF.
Bob Conger’s rounded estimates
| Right Turn | Left Turn | |
| Mean waiting time | 2.9 seconds | 21.4 seconds |
| 90th %ile waiting time | 7.9 seconds | 50.7 seconds |
| 99th %ile waiting time | 17.3 seconds | 101.4 seconds |
See Bob Conger’s full solution.
John Berglund’s rounded estimates
| Right Turn | Left Turn | |
| Mean waiting time | 2.873 seconds | 21.447 seconds |
| 90th %ile waiting time | 8 seconds | 51 seconds |
| 99th %ile waiting time | 17 seconds | 102 seconds |
