Day 93 - 100 Doors
Another little puzzle. You have 100 doors that are initially closed. First, you go through each door and toggle it (if it’s closed, open it; if it’s open, close it). On the first pass, we just open each door. On the second pass, don’t visit every door, but visit every second door, and toggle it. On the third pass, visit every third door and toggle it. Continue this pattern (i.e on the 47th pass, you visit every 47th door - which is just the 47th door and the 94th door) until you’ve performed 100 passes through the doors. What’s fascinating about this puzzle is that the open doors will always be the perfect squares; that is, the 1st door, the 4th, the 9th, the 16th, 25th, 36th, and so on.