Game Setup
This is a grouping game. There are three films and seven film buffs. We have to see which film buffs go to see the films.
The game involves numbers. The first rule splits the game into two scenarios. Twice as many people see the Hitchcock film as the Fellini film.
We could put four with Hitchcock and with two Fellini. One will see Kurosawa:
Or we could put two with Hitchcock and one with Fellini. Four will see Kurosawa:
G can never see Hitchcock. I drew that directly on the diagram.
Different things are going to be true in each scenario. From our rules, we can’t put G with R, we can’t put I with M and we have to put V with Y. L goes in the Hitchcock film.
This is unusual. There’s no random variable: every variable has a rule. Our main restriction will be keeping G, R, I and M apart. We should see how this works in each scenario.
We’ll start with the scenario where two see Hitchcock.
We should see where we can put V and Y. Only Kurosawa has space.
There are four variables left. G and R, and I and M. We have to keep those pairs apart.
We will have to put one from each pair in Kurosawa. One from each pair will fill the two empty spots left: one in Fellini, and one in Hitchcock.
The other scenario is where there are four at Hitchcock. We must put V and Y in Hitchcock along with L.
We’re left with the two pairs that must be kept apart. One from each pair goes to see Fellini.
The other person from each pair goes into the empty spots in Hitchcock and Kurosawa.
It looks like there is a third scenario. Couldn’t we put V and Y in Fellini? There are two spaces there. But it doesn’t work. Here’s why:
We need to put G, R, I and M in separate groups. We’ve got three spaces in Hitchcock and one in Kurosawa. There is no way we can keep them all apart.
We’re going to have to put at least one pair of them together in Hitchcock. So V and Y can’t go see Fellini.
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