There are a number of difficult solitaire games that require you to plan ahead, sometimes way ahead. Here’s a game of this type that uses a tiny card deck:
Chainn is a challenging game played with 16 cards: take the four aces, four kings, four twos and four threes from any bridge deck. There are two ways to score this game; decide which way you're scoring (see below) before you deal.
Shuffle and deal the sixteen cards in a 4x4 layout. You win the game when you move the cards so that the four cards of each suit are "contiguous". By contiguous I mean that you can step from any club to any other club by stepping orthogonally or diagonally from club to club without stepping on cards of another suit; and the same for the other three suits.
Here's how you move the cards. Pick up any card but a king and place it under another card. Now pick up the upper card and move it, in a straight line (orthogonally or diagonally), the number of spaces as the card you just put underneath it. In other words, if you put a two under an ace, you now have to move the ace two steps. If you put an ace under a three, you have to move the three one step.
If that card winds up in an occupied space, place it under the occupying card. Now you must move the occupying card as many spaces as the card underneath it. For example, you place an ace under a two and move the two sideways one space, where it lands under a three that you must now move two spaces.
You keep making a series of moves like this until you place a card in the empty space from which you started the sequence. If you have to move a card out of the layout, you lose. (So NEVER put a three under any of the four middle cards.) If you put a card under a king, you can ONLY move it to the empty space; a king is never allowed to be placed under another card. If you cannot move a king legally, you lose.
Now pick up any ace, two or three and start another sequence. Keep moving until you make a winning layout. You can either count sequences, or moves. Either way, try to keep your score very low; winning with a single sequence, or just a few moves, is elegant.
(This item was posted partly in response to some of Wiggin's free Advice.)