A common element of scenario puzzle is checkers-like hopping on a limited play area. The triangle peg puzzle is probably the most popular of these games, frequently found on cafe tables in the U. S. A more difficult and more ancient variation “The Cross” has recently made a comeback in the form of a wooden playing board with marbles or gemstones instead of pegs as playing pieces.
Despite being a two player game, I believe the game Nim counts as a puzzle. The goal of Nim is to beat the seemingly unbeatable opponent at a deceptively simple game of picking up matchstick-sized tokens. The game is terribly unfair and devising the solution requires considerable effort, but once solved the player can win every time so long as they get to choose who goes first. Once the student becomes the master they can go on to torture others with the puzzle.
Many of the most popular puzzles today are scenario based. Games such as checkers and chess are not puzzles by themselves. But when such a game is arranged into a solvable scenario it becomes a puzzle. Solving chess puzzles in particular has become a sport, with regular competitions and national rankings.