There are few good puzzle games. Puzzles rarely make good games, and good games rarely contain puzzles.
The first classical exception is mastermind. In recent years, Escape room shave become popular. A game which I learned as a student is Eleusis. This post concentrates on Eleusis. I wrote about Eleusis before in December 2013, you can find that post here.
The game of Eleusis was invented by Robert Abbott in 1956, and is totally different from such games as bridge or poker. Eleusis is played with a standard card deck of 52 cards. One player thinks of a secret rule and preferably writes this down. He plays two cards which obey the secret rule. All other players receive a number of cards, for example each player receives 5 cards.
The two cards are the beginning of a line of cards. The other players now take turns in playing a card to the end of the line. When a player plays a card, the Rule Inventor indicates whether the card obeys the rule. If it does, it is added to the end of the line. If it does not, the card is placed below the line and the player draws two extra cards from the deck. In both cases, the turn passes to the next player. The player who first gets rid of all his cards wins.
In the image above, the Rule Inventor started the row with 10 of clubs and jack of spades. The first player played 3 of spades, which was wrong. The next two cards, 3 of diamonds and 6 of spades, were also wrong. The fourth player tried 9 of hearts, which was correct.
The question is of course: With your hand depicted at the bottom, which of the 5 cards labeled A-E do you play?
You can check your solution here