Challenge #135: Locker Problem

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?

challenge_135_start_file.yxmd

Macros

Preparation

Advanced

Intermediate

Data Preparation

Interface

Accepted answers

clant

I couldnt work out what i was doing wrong until i actually read the instructions properly. I originally worked it so every person would change the status of every locker higher than them not just multiples.

Spoiler

Locker Completed.yxzp

All comments

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,

challenge_135_NicoleJohnson.yxmd

bdaniels

Spoiler

Screen Shot 2018-10-01 at 11.31.31 AM.png

Kind of messy

challenge_135_start_file.yxmd

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.

challenge_135_start_file.yxmd

Challenge135.yxmc

ggruccio

I'm imagining this is a very loud exercise!

Spoiler

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

challenge_135_gg_finish.yxzp

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 $e^{i\pi }+1=0$

Spoiler

Dan

challenge_135_solution_dl.yxzp

GarthG

Went macro-less this week!

challenge_135_GG.yxmd

jasperlch

Solution attached.

challenge_135_JL.yxzp

KOBoyle

Solution attached.

Spoiler

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

challenge_135_solution_KO App.yxzp

philipmannering

Spoiler

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

Workflow

Challenge 135 - Locker Problem.yxmd

Alt_JP

Spoiler

Found a solution without using input files or macros. Takes 0.8 sec to run on my machine.

challenge_135_jp.yxmd

DavidP

I discovered the Modulo function and what it does!!! And iterative macros are now a little less scary... My solution attached.

However, that was my 2nd attempt. With my 1st attempt I tried to update a sample tool with the IterationNumber as shown below, but for some reason it wouldn't work - it doesn't seem to update the value of N in the sample tool. Does anyone know what I'm doing wrong?