to arrive at the 4-2/3 inch answer:
if one starts out with nine 4-1/2 inch blocks, and sews with a 1/4 inch seam - the size should be 12-1/2 inches
When the block is cut and re-sewn, one loses 1/2 inch both ways, so then the unfinished block size is 12 inches.
3 time 4-1/2 is 13-1/2 inches. We need to add 1/2 inch to that to make up for that seam - so that would be 14 inches
now we need to divide 14 inches by 3
= 4-2/3 inch squares
(if you cut 4-3/4 squares and sew and resew them together - it will be only a tiny bit overly big - you can always trim the block down to size - it would probably only be a sliver from each side)