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This is a Pure Sequencing game.
The game scenario establishes that seven librarians are scheduled for desk duty for one week—Monday through Saturday. Except for Saturday when two librarians must be on duty, there are no ties. The following linear scenario underpins the sequence:
Although Pure Sequencing games involve relationships that are relative and not precisely fixed, a linear diagram can help us represent inferences that could result from the application of the rules.
The first rule establishes the following sequence:
- H L
The third rule establishes the following sequence:
The fourth rule establishes the following sequence:
- K Z
Since only F and H could be scheduled for duty on Monday, we can represent this as a Dual Option on our Linear setup. Also, since two librarians must be scheduled for duty on Saturday, it follows that two of G, L, and Z must be scheduled on Saturday:
The fifth rule establishes the following conditional sequence between F and L:
The implications of the contrapositive deserve a closer look. If L is not on duty on Saturday, then the two librarians on Saturday must be G and Z:
Since L must be scheduled earlier than F, and H must be earlier than L (first rule), the placement of H, L and F is now completely determined:
Thus, our final diagram looks like this: