Okay, I really hate to give out solutions. I'm going to give you one more chance to reconsider. Both variations of puzzle really can be solved. In the meantime I'll give you a hint (at least for the original version).
Tricky Dick Hint: This puzzle is much easier to solve in reverse, so think through the problem backwards; i.e., imagine the ring is off and you want to put in back on. If you can do this by visualizing it in your head, then great. Otherwise, (on my version of the puzzle at least) you can untie the large ring, remove the small ring, then retie the large ring. Work the puzzle in reverse several times to get the idea of the solution. If the small ring doesn't come off by cheating (untying the large ring), then you might find another small ring of the same size and try putting it on. Warning! A ring has to be of pretty much the same size for this to work.
Please try again to solve it on your own. Then, if you still want the solution to the original Tricky Dick click here, or if you want the solution to the "Return of Tricky Dick" click here.