I thought this game was hard if you were running out of time as I was -
I think the major rule from this game is that between F and G are exactly three positions on either side - Draw a circle putting F on one side and G on the opposite side - In between F and G on either side there are three slots - so the eight positions are set. O and I are a block coming in that order on either side. H cannot be next to F so if you are putting three slots on either side of F - H can never go in the first slot. (H is limited to two positions on either side between F and G.)IF H is paired with the OI block then it will be G H O I - thats the only way it can work.
I'm sure there's another deduction that I'm missing maybe someone else can add.