by cyruswhittaker Tue Sep 14, 2010 6:20 pm
This was game was really tough when I studied it a few weeks ago, and even after doing a lot of games, it's still tough.
But for me the difficulty lies in keeping track of the setup and more crucially, the impact and restrictions formed by the rules.
So for the setup, I put the factories vertically and the years horizontally. I realize that this is contrary to the solution given in the book, but I found this easier to conceptualize because I normally diagram progression in time from left to right. But I also played around with the horizontal setup, and it didn't make too big of a difference. Five models are being made each year by five factories, but we only have 4 models to choose from. Since each model must be represented each year at least once, it means that ONE model will appear twice. From this, it would make sense to see the rules revolve around restrictions on which models can repeat.
For rule two, in any particular factory, X cannot be followed in the next year by V or W. This is the same way as saying that V or W can't be assembled in any factory in which X was assembled the previous year.
At this point it helps to conceptualize what we're doing: we are looking at restriction within a factory and in regards to consectuive years.
Combined with rule 1, we know that X can also not another X in the same factory in consecutive years. But that means that ONLY Z can follow X, in the same factory, in consecutive years.
But then rule 4 tells us that Z can only occur once in a year. Remember, X MUST occur during a year, and it MUST be followed by Z only, so that means that for years 1 and 2, XZ form a block, and there can only be one X in years 1 and 2. The reason we can't say this about year 3 is because nothing follows year 3 (it's the end of our time period).
Rule 3 is slightly different in that it says that neither V nor X can follow Z in any factory for consecutive years. And of course, due to rule 1, Z can't follow Z. So, what this says is that any model that follows Z MUST be W. But W COULD follow a variable besides Z if it occurs more than once in a year.
This game is a good example of when implications of the rules become very important. These implications weren't clear to me when I first did the game, and it was extremely brutal and time-consuming.
By getting these rules down, you can annihilate the questions:
20: Apply the rules and eliminate the choices that don't conform.
21: Rules 1 and 4 eliminate A, D, and E. Our discussion of rule 3 eliminates C (remember, Z can only occur once and it must be preceded by X). So B remains.
22: B is quickly evident from discussion of rule 3. If X was assembled more than once, then since Z follows X, it would create more than one Z in year 3, which violates rule 4.
23: Again, the discussion of rule 3 makes E quickly evident.
24: Use the rules and quickly eliminate B-E.