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- Wed Aug 17, 2011 12:00 am
#80599
Setup and Rule Diagram Explanation
This is a Mapping—Supplied Diagram game.
The game provides a diagram that should be used for your main setup. In examining the diagram, note that the small squares in the middle of cities 1-2-3-4 and cities 3-4-5-6 are there so that cities that are diagonal from each other, such as 1 and 4 or 4 and 5, do not share a common border. This fact plays an important role when considering the fifth rule.
The first rule is a cleanup rule, one that limits the number of solutions in the game.
The second rule establishes that the maximum number of jails in a city is one, and the maximum number of hospitals in a city is also one.
The third rule is a negative grouping rule, and it establishes that jails and universities do not appear in the same city:
The fourth rule indicates that if a jail is in a city, then a hospital must also be in that city:
As a complete aside, these two rules are kind of funny if you think about them literally: prisoners and college kids can’t be in the same city, but if you have a jail, you need a hospital (are they expecting a prison riot to break out?).
The fifth rule indicates that the universities are located in two cities that do not share a common border. More on this rule in a moment.
The sixth and final rule places two of the institutions: a university in city 3 and a jail in city 6. This can be diagrammed as:
With these two institutions placed, a number of inferences can be made. With a jail in city 6, from the fourth rule there must be a hospital in city 6, and from the third rule there cannot be a university in city 6. There can also not be another jail in city 6 according to the second rule:
With a university in city 3, from the fifth rule we can infer that there are no universities in cities 1, 4, and 5 (nor can there be another university in city 3 according to the second rule). Combining these inferences with the information above, we have one more university to place, but that university cannot be in cities 1, 3, 4, 5, or 6. Thus, the second university must be in city 2:
Finally, from the third rule, we can eliminate jails from cities 2 and 3, both of which contain universities:
The above diagram contains all of the institutions that can be placed, and all of the Not Laws that follow from the rules. At this point, there are only three hospitals and one jail that remain to be placed. Of course, the jail must be placed in a city with a hospital, and because the jail cannot be placed in cities 2, 3, and 6, we can infer that a jail and a hospital will be placed in city 1, 4, or 5:
The remaining two hospitals have no restrictions, and they can be located within any city.
Thus, the final diagram for the game is:
This is a Mapping—Supplied Diagram game.
The game provides a diagram that should be used for your main setup. In examining the diagram, note that the small squares in the middle of cities 1-2-3-4 and cities 3-4-5-6 are there so that cities that are diagonal from each other, such as 1 and 4 or 4 and 5, do not share a common border. This fact plays an important role when considering the fifth rule.
The first rule is a cleanup rule, one that limits the number of solutions in the game.
The second rule establishes that the maximum number of jails in a city is one, and the maximum number of hospitals in a city is also one.
The third rule is a negative grouping rule, and it establishes that jails and universities do not appear in the same city:
The fourth rule indicates that if a jail is in a city, then a hospital must also be in that city:
As a complete aside, these two rules are kind of funny if you think about them literally: prisoners and college kids can’t be in the same city, but if you have a jail, you need a hospital (are they expecting a prison riot to break out?).
The fifth rule indicates that the universities are located in two cities that do not share a common border. More on this rule in a moment.
The sixth and final rule places two of the institutions: a university in city 3 and a jail in city 6. This can be diagrammed as:
With these two institutions placed, a number of inferences can be made. With a jail in city 6, from the fourth rule there must be a hospital in city 6, and from the third rule there cannot be a university in city 6. There can also not be another jail in city 6 according to the second rule:
With a university in city 3, from the fifth rule we can infer that there are no universities in cities 1, 4, and 5 (nor can there be another university in city 3 according to the second rule). Combining these inferences with the information above, we have one more university to place, but that university cannot be in cities 1, 3, 4, 5, or 6. Thus, the second university must be in city 2:
Finally, from the third rule, we can eliminate jails from cities 2 and 3, both of which contain universities:
The above diagram contains all of the institutions that can be placed, and all of the Not Laws that follow from the rules. At this point, there are only three hospitals and one jail that remain to be placed. Of course, the jail must be placed in a city with a hospital, and because the jail cannot be placed in cities 2, 3, and 6, we can infer that a jail and a hospital will be placed in city 1, 4, or 5:
The remaining two hospitals have no restrictions, and they can be located within any city.
Thus, the final diagram for the game is:
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Dave Killoran
PowerScore Test Preparation
Follow me on X/Twitter at http://twitter.com/DaveKilloran
My LSAT Articles: http://blog.powerscore.com/lsat/author/dave-killoran
PowerScore Podcast: http://www.powerscore.com/lsat/podcast/
PowerScore Test Preparation
Follow me on X/Twitter at http://twitter.com/DaveKilloran
My LSAT Articles: http://blog.powerscore.com/lsat/author/dave-killoran
PowerScore Podcast: http://www.powerscore.com/lsat/podcast/
