Hi kells,
I think templating is a really fruitful strategy for this game, but I don't think P is the right variable to choose to organize templates around. There are two reasons for that: the uncertainty about how many times P goes, and the fact that P doesn't have a direct impact on other variables (looking at the rule list).
Choose L to build templates around. Why? We already know L goes twice, and one of those days is Saturday. So L can either go Thursday/Saturday, or L can go Friday/Saturday. That's only two, well-defined templates. Very doable! Plus, in the group where L
doesn't go, it has a direct impact on M (M can't go in that group either). So L (or, rather, the absence of L) also has a direct impact on another variable. That's a good variable to choose for templates.
Think about what happens when L is on Thursday/Saturday. That means L is NOT on Friday, which also means M is NOT on Friday, and now Friday is completed determined! It has to be the remaining three variables: N, P, Q. This template doesn't "fill out" any further, but it sure is helpful to me to have 5 out of 9 spaces determined! See below:
Thursday: L
Friday: N P Q
Saturday: L
Now, think about what happens when L is on Friday/Saturday. That means L is NOT on Thursday, which also means M is NOT on Thursday, and now Thursday is completely determined. It has to be the same remaining variables: N, P, Q. See below:
Thursday: N P Q
Friday: N L
Saturday: L
This template fills out even further! N has already been used twice, so you can't use it again. That means neither N nor P can go on Saturday, which means Saturday is completely determined: it's L, M, and Q. See below:
Thursday: N P Q
Friday: N L
Saturday: L M Q
Now we can see that Q has been used twice, and can't be used again, which means that the remaining variable on Friday must be one of M or P. That's a pretty powerful template!
Thursday: N P Q
Friday: N L M/P
Saturday: L M Q
So the best two templates I ended up with are the two depicted below (organized in accordance with our initial diagram on the previous page of posts):
June 2019 Game 4 Templates.png
I hope this helps!
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