Question

In a magic trick 4 playing cards are stacked together, 3 face up and 1 face down with a heart at the bottom, then a club then a diamond then a spade (facing down). There are 3 ways in which packet of cards are allowed to mix: the packet can be cut, the top 2 cards can be turned over as one, or the entire packet can be turned over together. Prove that for any n>=0 after n allowed shuffles there will be exactly 1 card facing the wrong way that is different from the other 3. In a magic trick 4 playing cards are stacked together, 3 face up and 1 face down with a heart at the bottom, then a club then a diamond then a spade (facing down). There are 3 ways in which packet of cards are allowed to mix: the packet can be cut, the top 2 cards can be turned over as one, or the entire packet can be turned over together. Prove that for any n>=0 after n allowed shuffles there will be exactly 1 card facing the wrong way that is different from the other 3. @Mathematics