Setup and Rule Diagrams

[Adam Tyson]

It's possible for I to serve all three buildings, nzLSAT, in which case S would not be able to serve Y but could still serve X or Z or both. Or, S could serve Y only, and then I would have to serve X and Z and not Y. There's a lot of flexibility there! Here's one possible solution to the game:

F: XY
H: XYZ
I: XYZ
P: Z
S: XZ
T: XZ

Note that this solution does comply with all the rules, including the last rule: T is serving two buildings that I also serves. It just so happens that I ALSO serves the third building, which is Y!

Here's another solution that would work:

F: YZ
H: XYZ
I: XZ
P: X
S: Y
T: XZ

In this case, we can have S serving Y, but then I cannot also serve Y, so I has to do X and Z and nothing else, and S is limited to just Y. Again, this complies with all the rules!

You may have made an incorrect inference that I can only serve two buildings, perhaps based on a misunderstanding of that last rule. I and T must have two in common, and those two must be X and Z since T cannot serve Y, but it's still possible that I serves more than that. I hope that clears things up for you!