You could go in a little different direction that those listed above...
(1) Have a set size (like a wall hanging), then choose a "block" - like the Ohio Star or whatever - and everyone chooses their own fabrics.
or
(2) Again, have a set size, and a "focus fabric" (everybody buys FQ or 1/2 yard of the SAME FABRIC) then everyone do whatever.
My longarm group does a challenge every year. Of course, our focus is more on our stitching skills, but here's what we've done the past three years:
2014 - we all had the same pattern (about 40" square). We could use any colors we wanted, stitch it however we wanted and so on. It was amazing how different they all turned out.
2015 - 40" wholecloth. Any way we wanted. Just had to be cotton or dupioni silk, 40", one solid color, no piecing (duh, WHOLECLOTH!!) Again, the differences were amazing
2016 (we meet and share them in November) - 40" square, treat as a "round robin" except we do it all ourselves. Center must be 12", subsequent "rounds" no smaller than 3". Can be pieced, or wholecloth.
It will be interesting to see what comes up.