000000

The second student closed each other locker starting from locker 2, all the odd ones are currently open.

010101

Next, the 3rd student changes the state of each 3rd one, so now it’s like this

011100

See the shift? yet the number of open lockers is constant. Now the fourth one changes the state of the fourth locker…so now just expand the previous diagram to a multiple of four to better illustrate what it looks like. (6 block diag to 12 now)

011100011100 turns into

011000001101 (7 open, 5 closed)

Yet 12 does not go into 1000 perfectly, theres four left over…so, just take the beginning four and add that to the total.

In all, there are 583 open and 417 closed.

just write it all out.

you’ll get the answer in about an hour

jk

but good luck. just wanted to give ya some support even tho i’m horrible at word problems.

<3