I don't know whether it's trial and error or just a lot of work, but it definitely involves quite a bit of writing.
If we know M = 2, then we know where our 8 things are coming from
M = 2
Q = 2
O = 2
L = 1
P = 1
So we have a few limitations to reconcile ..
- M is in spot 5
- we can’t have consecutive M’s, Q’s, or O’s
- both of our non-consecutive Q's come before the 2 O's
- we have an LP chunk
When I'm in doubt in an Ordering game, I lean on the chunk.
I would consider its possibilities and see if I can fill in the blanks.
L P _ _ M _ _ _
_ L P _ M _ _ _
_ _ L P M _ _ _
_ _ _ _ M L P _
_ _ _ _ M _ L P
For the first three, where the LP is before the M, we know that the two O's must come AFTER spot 5, and since they have to be split up, it's 6 and 8.
L P _ _ M O _ O
_ L P _ M O _ O
_ _ L P M O _ O
_ _ _ _ M L P _
_ _ _ _ M _ L P
Still focusing on the first three, we have to squeeze in two non-consecutive Q's before the M in spot 5. That kills off the first line and the third line. In both of those, we'd have to put the two Q's consecutively (3/4 on the first line and 1/2 on the third line).
I would cross them out on my page, but here I'll just delete them.
_ L P _ M O _ O
_ _ _ _ M L P _
_ _ _ _ M _ L P
So we know how the first line would look.
Q L P Q M O M O
_ _ _ _ M L P _
_ _ _ _ M _ L P
For the 2nd and 3rd lines, we know that the last available spot in both cases will be O, because there's no way to get both O's and both Q's (non-consecutively) BEFORE spot 5.
So we have
Q L P Q M O M O
_ _ _ _ M L P O
_ _ _ _ M O L P
So what's left?
Q, Q, O, M
The Q's have to come before the O, and the M can't be in spot 4 (no consecutive repeats).
So we get
Q L P Q M O M O
Q M Q O M L P O
Q M Q O M O L P
There are a lot of scenarios to consider (5), but remember to use whatever chunk you have as the backbone of possible scenarios.
Hope this helps.