Get Rich or Buy Trying - Part 2
Puzzle for the week of 10/13/24
Inspired by the Fiddler on the Proof (formerly The Riddler), X’s Puzzle Corner aims to produce a weekly puzzle for readers that enjoy math, probability, and algorithms. Please submit your solution! Solutions will be accepted until 11 pm the following Sunday after the puzzle is posted (in this case 10/20/24). While it isn’t required, I encourage you to opt to have your solution shared so that we all get the chance to see how others thought about and attempted the problem!
The answers of all those that volunteered their solutions will be posted around Wednesday at 10 am.
In many cases, I expect the readers will be better puzzlers than me so I make no guarantees the solutions are correct. I also make no promises about having worked out the solutions to the puzzles ahead of time so it may be the case that they’re very challenging. Part of the fun is finding out!
Last week we were presented with the opportunity to be gifted two stock market oracles by some guy named Warren—if we can answer his question! To prepare ourselves for Warrens question, we had two warm-up questions. This week, we will add another warm-up question:
Consider the following stock behavior:
The stock’s value will change by a factor of (1+δ) from it’s pervious value each minute where δ is uniformly distributed from [-1/1000, 1/1000]. For example after two minutes, the value would be p_0 * δ_1 * δ_2.
Your job is to determine the distribution of the value of the stock after 1 day. Assume the stock is traded for 7 hours a day (a bit off, I know).
Good luck solving!
Please submit your answers here.