I'm not sure if this falls under the solitaire category, but it is played with one player. Someone taught me this card game and was under the impression that it was called Kings, but apparently it's not, as upon looking it up, I didn't find this game.
The player deals the cards in 13 piles, 4 to each pile, face down. Jokers are not used. Each of the 13 piles represents a rank. The player starts by picking up a card from the top of the King rank pile, looks at the card, then places it underneath the corresponding rank pile, face up. Then the player picks up a card from the top of the previous rank pile and places it under the next corresponding rank pile. To win the game, the player must return each rank to its proper pile before all the Kings are returned to their pile.
For example, the player picks from the top of the King pile and receives a Four of Clubs. The player places the card underneath the Four pile face up, then draws a face-down card from the top of the Four pile. The player receives a Jack of Spades, which he/she places underneath the Jack pile face up, and so on.