Rolling Papers - Part 3

Puzzle for the week of 11/17/24

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 exploring the number of different ways we can cut a paper so that we could fold it and adhere the necessary edges to create a cube (i.e. the nets of a cube). This week will take some inspiration from The Fiddler (like I don’t already take enough inspiration from there lol)!

Imagine you have 6 square Magna tiles. These tiles have magnets on the side so that edges of shapes will stick together. Let’s assume for a moment that toss these six square tiles onto the ground and they will land in a random configuration such that they all six are connected edge-to-edge in one large piece. What’s the probability that this configuration will be foldable into a cube without rearranging the squares?

Good luck!

Please submit your thoughts, progress, or answers here.