Puzzles are a staple of RPGs; they are a way to challenge players that isn't simply about rolling dice.
Sometimes, though, you're running a table and the puzzles are slowing down the pace of the game. Maybe your players aren't into solving puzzles at all, or they don't have the knowledge necessary to solve it. (I've seen an RPG puzzle that asked players to identify the formula for the Theory of Relativity!)
The easiest way to solve it is to just handwave it away; have someone make an ability check to "solve" the puzzle. But I feel that solution teaches players that they can just skip a challenge they don't like.
Here's a quick-and-easy formula you can use to help players engage with a puzzle. The details are specific to 5th Edition, but the concept can be used in any RPG system.
Ask the players what they are doing to solve the puzzle
Ask each player how they want to approach solving the puzzle and pick an appropriate ability check.
- Do they want to examine the pieces? Wisdom (Perception)
- Do they want to discuss what the available clues might mean? Intelligence (Investigation)
- Do they want to manipulate any physical components of the puzzle? Dexterity or Strength
If they are stuck for ideas, figure out which element of the puzzle that players are hung up on and pick an appropriate ability check:
- Are they overlooking an important clue? Wisdom (Perception)
- Do they not recognize the significance of a clue? Intelligence (Investigation); Arcana, History, Nature, or Religion can be used as appropriate
Have the party make a group ability check
Have the party make a DC 15 group ability check. Each party member can use the ability you decided on; particularly creative or insightful approaches could merit giving them advantage on the check. If the group check succeeds (half or more of the players make their ability check) then they gain the information necessary to solve the puzzle.
Alternately, you could lower the DC to 10 and success means they gain an additional clue: they recognize that the names of the forgotten kings aren't in alphabetical order, or someone moving pieces on a dragonchess board learns that some pieces glow when placed on specific squares.
But the goal is to allow the players to engage with puzzles in a way that's immersive and interesting, without making them feel foolish or stupid because they can't figure it out.