Could someone please give a general account of how to decide on (in assignment games) which one set of elements should serve as the 'base element-set' (i.e. the element set TO WHICH elements of the other set is assigned), when it is not explicitly stated in the relevant question.
An example from ch.8 of Logic Games Strategy Guide is this:
Exactly six performers---QRTVWX---will perform at the county fair. Each performer will perform one or more of the following three acts: juggling, sword swallowing, unicycle riding.
Take this as an example, do we have sufficient info for making a judgment about the 'base element-set'?
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Re: Determining the 'base element-set' in Assignment Games
Very good question!
This is such an important detail for assignment games. The example you speak of is on pg. 223 in chapter 8. We are not given any rules, which would help drive us to one setup over another most likely. However, with the limited amount of information in the prompt, we definitely have sufficient evidence that one setup can be more powerful than another.
The way this game prompt is listed is as follows (as you stated above):
Exactly six performers---QRTVWX---will perform at the county fair. Each performer will perform one or more of the following three acts: juggling, sword swallowing, unicycle riding.
So we do know for a fact that each performer will do at least one of those acts. We do not know for a fact that each act will have a performer. When doing setups for games, we want to go after the setups that we know have established fact.
JSU
Q __
R __
T __
V __
W __
X __
With no rules, this is a very simple diagram that shows a slot that must be filled with at least one of JSU. You will typically be given rules such as Q does more acts than T, and that R performs the most acts of all performers. This would mean that since each performer has to do at least one act, that Q must have at least 2 acts, but then when we read that R performs more acts than any other performer, this will "wall off" Q at 2, and will have R at 3. We would then "wall off" T at 1. We would then also know that the rest of the performers would have a maximum of two slots available to them.
You almost always want to line it up in this manner of what you know to be true of which group must have at least one of the other assigned to it. The only time this is not advocated would be when the rules go into such detail of telling you about fixed numbers of the "JSU" group, such as J will be performed by exactly 4 performers while S will be performed by exactly 2.
The most powerful thing to remember about these types of games is that you must know whether or not a variable set must have every member be used. That is typically the starting point of the base. The only time this concept is trumped is when you know a lot about the fixed numbers of variables.
This is such an important detail for assignment games. The example you speak of is on pg. 223 in chapter 8. We are not given any rules, which would help drive us to one setup over another most likely. However, with the limited amount of information in the prompt, we definitely have sufficient evidence that one setup can be more powerful than another.
The way this game prompt is listed is as follows (as you stated above):
Exactly six performers---QRTVWX---will perform at the county fair. Each performer will perform one or more of the following three acts: juggling, sword swallowing, unicycle riding.
So we do know for a fact that each performer will do at least one of those acts. We do not know for a fact that each act will have a performer. When doing setups for games, we want to go after the setups that we know have established fact.
JSU
Q __
R __
T __
V __
W __
X __
With no rules, this is a very simple diagram that shows a slot that must be filled with at least one of JSU. You will typically be given rules such as Q does more acts than T, and that R performs the most acts of all performers. This would mean that since each performer has to do at least one act, that Q must have at least 2 acts, but then when we read that R performs more acts than any other performer, this will "wall off" Q at 2, and will have R at 3. We would then "wall off" T at 1. We would then also know that the rest of the performers would have a maximum of two slots available to them.
You almost always want to line it up in this manner of what you know to be true of which group must have at least one of the other assigned to it. The only time this is not advocated would be when the rules go into such detail of telling you about fixed numbers of the "JSU" group, such as J will be performed by exactly 4 performers while S will be performed by exactly 2.
The most powerful thing to remember about these types of games is that you must know whether or not a variable set must have every member be used. That is typically the starting point of the base. The only time this concept is trumped is when you know a lot about the fixed numbers of variables.
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