Challenge: 5th grade math

[Ned]

This is a problem our 5th grader came home with today: tag @Nathalie

There are 1000 lockers in a high school with 1000 students. The
problem begins with the first student opening all 1000 lockers; next
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?

Can you solve it in Alteryx?  I solved it in 4 tools - so don't overthink it.  The answer has a cool surpise twist.  Post your solution - I'll post mine in a few days if no one else does the identical solution.

[cbridges]

Oh dear...do you mean that when I learned square root in 5th grade I should have been paying attention? LOL!

[chris_love]

So I'll come clean, I didn't spend all day Friday adding 1001 tools to the canvas to solve this, I used Alteryx to generate the module. After all it's just XML. This technique can be quite useful if you have lots of the same tools to add, here's how I did it:

[SteveA · Accepted solution]

Alright, I'll play along.  I shall flog myself appropriately for using six tools instead of one...