@kuma this is actually a game I would NOT setup a diagram for. I would spend some time thinking about what we know must be true for each person / office.
We know that the EARLIEST round each person would pick a given office is described by their preference order.
Now let's compare that to the LATEST round a given office will be available. For example, for office Y, we know the latest it will be available is round 3. Listing out all the offices latest rounds:
W: 4 X: 2 Y: 3 Z: 3
Comparing the preference orders to the latest round a given office will be available gives us the list of offices that each person will never choose (i.e. earliest round chosen > latest round available):
J: None L: Y (4 > 3) P: X (3 > 2) T: None
We can then use this to answer Must be True questions - for example this answer is (E). If the question gave us more information with an "If.." statement, we would want to update our earliest chosen / latest available #'s accordingly to accommodate the new information.
