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If you are making a picnic blanket I am wondering why you need the 8.5" block. It appears to me that you would be easier to alter the large block cut from the fat quarter rather than all those very odd size smaller squares for your 9 patch. For me it would be too much aggrivation to deal with an odd size smaller square and more precision to get it exact. More flexibility in the larger squares and considering all fat quarter are not the same size.
Bad Spellers of the World
U N T I E
I would cut a piece of paper to 8.5" square, and fold it into thirds. Then mark that fold, and put it under my ruler, to get an idea where it would fall . . ..
The math way is the way to go, for sure. but I would need a way to visualize that perfect cut.
Formula: finished block size divided by 3 and add 1/2" for seam allowances = 8 1/2" nine patch blocks