There are $20$ cards facing down. We call a move turning a face down card up and the turning the card to its immediate right. Prove that this sequence of moves must terminate.
My approach:
Treating face down cards as 1. We will soon reach a stage where cards will be like $00101101.....1$
If we shuffle $11$ we get $00$
If we shuffle $10$ we get $01$
i.e. a decreasing binary number.