Hi Vicki —
Nice to have you here and happy to try and help —
If I’m understanding you correctly, I think all of your concerns are related, in that they all stem from 3 and 9 having to be filled. Speaking of — here are the answers to your Q’s —
1) The reason why 3 and 9 must be filled is because it is stated, in the scenario, that the first friend visits in 3 and the last in 9.
2) For question #1, If P is in 7, per the fact that M must go before P and per the third rule, the only place for M to thus go is in 4, and 5 must be left open.
Now we have 3 elements left to place – N, O, and Q.
Per the scenario, 3 and 9 must be filled.
Per the first rule, because 5 can’t have an element 6 now must also be filled.
That means there is no other element to fill 8, and so 8 cannot have an element.
Since N must go in 8 or 9, and 8 cannot have an element, N must go in 9.
3. For #2, if O is right after Q but at some point before M, as you said, M must go in 6 and 7 must be blank.
And we know P must go after M so it will be in 8 or 9, and we know N must also be in 8 or 9.
And the reason the Q O pairing must be in 3 and 4, as opposed to 4 and 5, is because 3 must be filled, and otherwise there would be no other element remaining to fill it.
Hope that clears things up and let me know if you need anything else —