This is an oldie - from the 1930s - but is a neat quilt. First...here's a link to a picture...
http://quiltcontemplation.blogspot.c...ye-blocks.html
And here are instructions:
http://www.geocities.ws/qtracy23/Bullseye_Quilt.html
You wouldn't have to cut the blocks into quarters & resew the 4 in blocks. Leave them as 10" blocks mixed with solids like in the picture. Brights & kids prints would make a great quilt!