Take your link to the design, for example:
www.fantasticcontraption.com/?designId=11301336Change it to this by adding "design" in :
www.fantasticcontraption.com/design?designId=11301336Go to that page, and it will have all the info on the design, including the level it solves, which is on the right. For example, you can see that mine is a solve for the level "Down and Up" Hope that helps