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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:
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:
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:
The last three rules are conditional, and each addresses player sport assignments and rankings:
Applying the two-value system to the contrapositive of each of these rules leads to several interesting statements:
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:
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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