Sounds like an incredibly complicated system. I can't imagine being the parent having to keep track of what days your child goes, especially if a school closure means the weeks can completely swap.
We get a school day calendar so we just keep track of what school day it is and what school day we follow for our child - 1, 3 & 5 or 2, 4, & 6. I prefer it better then all mornings all week or all afternoons. Not everyone can arrange pickup/drop off at lunchtime.
I know of school boards that do Tues/Thurs for JK and Mon/Wed/Fri for SK. This makes sense to me as they only ever go on their set days every week and if there happens to be a holiday they just miss that day. This at least allows for easy daycare planning as the daycares offer a Jk spot and an SK spot to make up a full spot.
That said, I suppose like anything you just adapt to what you know so it may very well not be as complicated as it seems!