Rings Puzzle app for iPhone and iPad

Chinese rings puzzle
The object is to remove all of the rings from the horizontal loop of stiff wire, and/or put them back on. As it is shown in game, the first two rings can be moved off the left end of the stiff wire. One or both of those can then be slipped through the stiff wire loop (from top to bottom). Then the fourth ring can be slipped over the end. If just one of the first two was removed, then the third ring could have been slipped over the end. Anyway, over and over again, rings must be put back onto the stiff wire loop, in order to remove other rings. The solution takes many moves. The seven rings here take 85 moves, although this can be shortened by making more than one move simultaneously (removing 2 rings from the end, simultaneously). In general, the number of moves is (2^(n+1) -2)/3 if n (the number of rings) is even, and (2^(n+1) -1)/3 if n is odd (2^x means 2 to the x power, by the way).
There are three parts in our game.
The first, there seven rings above, someone said that it takes 64 moves (not 85) to remove the rings in the above 7-ring puzzle, not counting multiple moves. Several sources say 85. Whos right? You can try.
The second, only one ring above, if you remove it, you win.
The third, all nine rings above, when you remove all, you win.