Some challenging Mensa puzzles include detecting cloud patterns on a numbered diagram, rearranging dominoes with missing edges on a diagram, hex loops and tracing worm paths on triangular grids. Some puzzles have similar components to other well-known models such as the classic game Battleship.
A popular puzzle, fashioned after the Paterson's worm model created in the 1970s, involves a worm moving across an infinite triangular grid between one of the six grid lines available at each point. After each movement sequence the worm "decides" the next direction of travel based on the distribution of traversed and unexplored grid lines.
A point-of-view rule is implemented in this puzzle whereby the worm, encountering a distribution pattern for the first time, may leave along any unexplored grid line. In future encounters, it is required to repeat the exact movement.