I haven’t explored all the submissions for this challenge, but I’ll assume that others have had the same thoughts. A student only changes a locker door if their student number is a factor of the locker number, i.e. IF MOD([LockerNum], [Iteration])=0. That means that a locker door is changed based on the number of factors it has. Factors come in pairs, so a quick (erroneous) conclusion would be that the door’s status is changed an even number of times, leaving them all closed. However, even the very first locker, whose pair of factors is 1x1, only gets switched once since student #1 only gets one turn. Similarly, locker 4 (1x4, 2x2) gets switched 3 times (1,2,4). Inductively, only those lockers whose numbers are perfect squares are left open since these are the only lockers with an odd number of distinct factors. Using this principle allows for a more scalable solution in case you would like to play this game at a major university or set up lockers for everyone in the country. I set the limit on the Numeric input at 500M but modify all you want. Have fun.
