Setup and Rule Diagrams

[Adam Tyson]

This game reminds me a bit of the last game on PT77, Tami, which is the December 2015 test. That game involves 3 groups of 3, just like this one, with 5 variables to fill them, also just like this one. Not exactly the same, but it would be a good one to try to see some of the same ideas in action.

[Tami Taylor]

Hey Adam! Awesome -- I'll take a look. Thank you!!!

[kells__w]

Hi
would you recommend doing templates for this game? I did mine based on P being in once or twice (1 in Thursday, 1 in Friday, and lastly on both Thursday and Friday) I did several templates for the last one where P is in twice to figure out which variables could be in only once. I'm not sure if this approach is too time costly.
Thanks in advance!

[Jeremy Press]

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):

I hope this helps!

[ashpine17]

How do you know to consider the distribution? And how do you know it is (2-2-2-2-1)

[nyc431]

Is there any similar grouping game -- similar in terms of difficulty and inferences -- that you'd recommend for practice?

[Adam Tyson]

Ashpine, the thing that should get you thinking about the numeric distribution is that there are only 5 variables but 9 spaces that need to be filled. An imbalance in the numbers like that should just shout out the importance of something numeric that requires your consideration! When you couple that with the rule that none of the variables can be in all three groups, the only distribution that's possible is 2-2-2-2-1. Anything else would require someone going 3 times or else not all 9 spaces being filled!

And nyc431, as I suggested earlier in this thread, try Game 4 from PT 77, the December 2015 test, to see something similar.