Challenge #135: Locker Problem

[JoeM]

Thank you for participating in the Grand Prix challenges last week!

Next week's challenge will be posted during @NicoleJohnson's Inspire Europe Weekly Challenge (10:30AM on Wednesday 10/10)! Finally, those on GMT challengers will finally have first crack at the challenge. Unless @patrick_digan wakes up at 5:30AM Eastern. 

Onto this week's challenge!

There are 1000 lockers in a high school with 1000 students. The problem begins with the first student opening all 1000 lockers; the second student closes lockers 2,4,6,8,10 and so on to locker 1000; the third student changes the state (opens lockers closed, closes lockers open) on lockers 3,6,9,12,15 and so on; the fourth student changes the state of lockers 4,8,12,16 and so on. This goes on until
every student has had a turn.

When all 1,000 students have finished, which locker doors are open?

[NicoleJohnson]

Back to school! My solution :)

Spoiler

My favorite - iterative macros!! This was a fun one... and ended up with a pleasantly low number of tools!

Workflow - Fun using the Generate Rows tool without an input, rarely have had opportunities to do that.
Locker Macro, using a Floor formula to determine which lockers to open/close!

Cheers,

NJ

[bdaniels]

Spoiler

Kind of messy

[patrick_digan]

I've got my alarm set for 5:30 am next wednesday!

Spoiler

I went with the iterative macro approach


There are some really creative solutions when @Ned posted this problem a few years ago.

[ggruccio]

I'm imagining this is a very loud exercise!  

Spoiler

Helps to use the modulo (mod) function in the macro.

[danilang]

Fun challenge. 

Ok, all you Math gurus.  Can anyone explain why, iteratively applying the sieve of Eratosthenes, should generate that particular, very familiar, sequence of numbers?  Is all of math beautifully connected at a level just below what common folk like me can see? 

And what's up with Euler's Identity anyway

Spoiler

Dan

[GarthG]

Went macro-less this week!

[jasperlch]

Solution attached.

[KOBoyle]

Solution attached.

Spoiler

Used an iterative macro with an app to allow for user specified locker count.

[PhilipMannering]

Spoiler

I used the R tool to loop over all the lockers and change their state.


Workflow