Adam Tyson wrote: ↑Tue Nov 02, 2021 2:12 pm
You could, but instead try setting up the two schools as the groups, and then play around with the possible numeric distributions to see how many teachers can be at each school. The first rule will really restrict how that can play out, and you may get some additional inferences from there! All this will be made clear when we get our official explanation posted, but work with that for now and see how it goes.
The key, in my opinion, is about the numbers. Each teacher goes exactly once, but the schools will each need multiple teachers. Generally a numeric relationship like that indicates that the set with the flexible numbers is the better base, while the set that goes exactly once is the best choice for the "moving" variable set, the ones that we are trying to assign to the different groups. It also makes what I think of as "holistic" sense: the schools are fixed in place (I literally picture two school buildings in different parts of town, and of course those buildings don't move) while the teachers literally move around (any one of them can go to either school, and in my mind's eye I see them commuting to work).
This was very helpful! But, I am still a bit confused by the number aspect
Since the first rules states that "Any two of the teachers who teach at the same school do not teach the same language as each other." (and there are only 3 languages) I assumed that the junior and senior highschool both had 3 teachers (one for each language). So I just set up my diagram to look like this (but I am definitely still missing a key aspect of this game):
Junior | Senior
M/L | M/L
____ | _____
____ | ______
N = R
O = F
P *** (free agent)
KL block (same school, so different language)
ML NOT block (same language, so different school)
Inference: KL are at a different school than M
Inference: KM teach different languages