This question places O twice. I’ve put a box around the consequence: both Fall and Spring only have two open spaces:
That’s interesting. Because look at rules 1 and 2: rule 1 requires HM if H is in Fall. Rule 2 requires VT if V is in Spring.
Conclusion: to put H in Fall or to put V in Spring fills all the available space in the semester. So putting any other meeting in either semester will block either rule from happening.
We know each city has to go at least once. We can try building scenarios using one of the more restricted points to see what happens. I chose to use H: it’s restricted because it needs M if it goes in Spring. But you could also have made scenarios with VT.
So let’s make a scenario with H in Fall, and one with H in Spring. First we’ll place H in Fall. If H is in Fall, then M must be too:
V and T are left to place, and they have to go in Spring as those are the only open spots:
Now let’s see what happens if we put H in spring:
Notice that there is now no space to put VT in spring (rule 2): we’d need two spots but only have one. However, rule 3 says that we need either V or M in each season. So since V can’t go in Spring, M has to go there:
Next, V and T haven’t been placed. The only open space is Fall, so we need to put them both there:
So, comparing both scenarios, we see that HM and VT need to be together in either one. So look for answers that say either: “VT must be together” or “HM must be together”. E is CORRECT. It says that VT must be together.
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