This is one of the more infamous rooms from the original game, since it pretty much required taking out a pencil and paper to plot out some paths.
Some tips to make the process go faster: You can actually reason backwards, which is sometimes more useful than reasoning forwards. Since orb 7 has to be hit last, you need a direct path from orb 7 to the end gate 8, and since orb 6 needs to be hit before orb 7, you need a direct path from orb 6 to orb 7. Orb 5 is in the same column as orb 6, so you may as well just reserve the eastmost column and go directly from orb 5 to orb 6.
If you reserve those tiles, stick to the middle when trying to get orbs 1 and 2, and avoid dropping tiles too close to other orbs before it's time to go hit them, you should be able to solve the room.
Let us know if you want a spoiler as to the path to take.
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[Last edited by Chaco at 03-19-2014 10:23 PM]