After playing around on the first level for a bit it feels like on the big enough empty field it's always possible to get 4 into any position you want, but I can't quite understand how to do it. The problem is certanly intriguing, I feel like we will learn a lot about dice cube and it's mathematical properties as a sideeffect of this jam :)
As for the levels I am not sure, how many I have completed like that.