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 Dave Killoran
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Setup and Rule Diagram Explanation

This is a Grouping: Defined-Moving, Balanced, Identify the Templates Game.

This is a challenging game because it combines so many different elements: grouping, sequencing, and a two-value system. The initial scenario appears as follows:
pt25_j98_g3_1.PNG (5.74 KiB) Viewed 242 times
This is a two-value system, and all players must play one of two alternate sports (or values): golf or tennis. Thus, if a player is not playing golf, he or she must play tennis, and if a player is not playing tennis, he or she must play golf. When we examine the final three rules, the presence of this system will have significant effects.

The first two rules helpfully assign two of the people to specific sports:
pt25_j98_g3_2.PNG (6.28 KiB) Viewed 242 times
The third rule establishes that L is the highest ranked golf player, which will be designated with a subscript “1.” O’s tennis ranking is not established:
pt25_j98_g3_3.PNG (6.38 KiB) Viewed 242 times
The last three rules are conditional, and each addresses player sport assignments and rankings:
pt25_j98_g3_4.PNG (16.64 KiB) Viewed 242 times
Applying the two-value system to the contrapositive of each of these rules leads to several interesting statements:
pt25_j98_g3_5.PNG (20.96 KiB) Viewed 242 times
Since when M plays golf then S must also play golf (rule #4), and when S plays golf then M must also play golf (contrapositive of rule #5), we can infer that S and M always play the same sport. Thus, S and M form a block within the game, and this is one of the critical inferences of the game.

Because this block must be placed into either the golf group or the tennis group, two basic templates apply in the game:
pt25_j98_g3_6.PNG (24.5 KiB) Viewed 242 times
In template #1, K is the only variable yet to be placed and there are no restrictions on its placement.

In template #2, K and P are the only variables yet to be placed. According to the rules, if K plays golf, then P plays golf, and if P plays tennis then K plays tennis.

These two basic templates provide a solid base with which to attack the questions. The biggest issue then becomes the ordering of the players within each sport.
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I did not understand the wording of the conditional rules on this game. How do you know that M triggers all the other variables to go into either category? I interpreted the sequencing rules as additional to the conditional rules. If M and these other variables are in the same category then here is the sequence for them. I don't see how the M rules force all the sequencing rules to occur.
 Emily Haney-Caron
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Hi amagari,

This is a tricky one, especially figuring out how the rules work together. Each conditional rule is saying IF a certain variable is in a certain sport, THEN these other variables are also in that sport, AND they have to be in this certain order. You can see this if you look at the placement of the if and then in those statements.

After that, I think what you need to do here is make sure you've taken the contrapositive of each rule.

So, for Rule 4, we have MG :arrow: MG > PG > SG
The contrapositive is, SG OR PG :arrow: MG

For Rule 5, we have MT :arrow: OT > ST > MT
The contrapositive is, ST OR OT (which I know is not possible in this game, since O has to do tennis, but this would be part of the contrapositive) :arrow: MT

For Rule 6, we have PT :arrow: KT > OT > PT
The contrapositive is, KT OR OT (which I know is not possible in this game, since O has to do tennis, but this would be part of the contrapositive) :arrow: PT

If you look at how those rules work together, you'll see that, if S played golf, S could not play tennis; based on the contrapositive for Rule 4, that would also mean M couldn't play tennis. So, if S plays golf, M has to play golf, which means rule 4 is in effect and P also plays golf. If S plays tennis, S could not play golf, which means M could not play golf. Therefore, if S plays tennis, M also plays tennis.
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Is there a set up of this game available somewhere?

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