Can you survive The Great Bar Crawl? - Part 2

Puzzle for the week of 3/16

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 3/23/25). 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 solution and submitted responses will be posted around Wednesday at 10 am.

I make no guarantees my solutions are correct! You are all smart people so please comment if you think I made a mistake!

In last week’s puzzle, we attempted to do a little bit of planning for a Mardi Gras bar crawl. As it turns out, the bar crawl was such a success that it continues to this day. Incredible!

In fact, it looks like it’s going to last all the way until St. Patrick’s Day. However, as it happens with any great bar crawl, the group has begun to splinter. Your group of N people has rather miraculously separated such that each person is at a different one of the N bars in the neighborhood. You want to reassemble so that you can properly toast for St. Patrick’s Day, but in your stubborn drunken state, none of you could agree on a bar to meet up at. Instead, you all decide to proceed as you were—going to a different bar each hour—but if you end up at a bar with one of the N people in the group, you stick together and travel as a group. The question this week is how long will it take for your whole group to reassemble?

Again, we may assume that in your drunken state, you can’t remember the previous bars you’ve been to so you go to a random bar each hour.

Please submit your answers here. Please ask any questions in the comments.