A puzzle cache is a mystery cache that requires you to solve one or more puzzles.
The mystery (unknown) cache type is a "catch-all" types for listings that don't meet the guidelines for other types. Therefore, many mystery caches have no real puzzle to solve.
Some puzzle caches are hidden at the posted coordinates, but cannot be retrieved/opened without solving a puzzle. An example would be a locked container, where the puzzle solution is the lock combination.
Some puzzle caches post the coordinates of a physical puzzle. Solving this puzzle gives you the location of the cache. Unlike offset caches (which provide clear instructions), these puzzle caches do not tell you exactly where/how to obtain the final location.
Many (if not most) puzzle caches present a puzzle in the cache description. Solving this puzzle gives you the location of the cache. The posted coordinates are often completely bogus, although they may provide the location of convenient parking, the location of a landmark related to the puzzle theme, etc.
Some puzzle multi-caches combine these approaches. For example, a puzzle in the cache description might provide the location of a physical puzzle, which would provide the location of the cache (or perhaps the location in the next of a series of physical puzzles).
Here are some common types of puzzles used in puzzle caches.
These puzzles require you to research something related to the theme of the puzzle, usually to determine the numbers associated with information provided in the puzzle. These numbers provide the coordinates for the cache. For example, a puzzle themed after a popular TV show might list episode titles from the 4th season, the 7th season, etc., yielding coordinates that start with N 47°.
These puzzles require you to follow the provided instructions. They often present a logic, word, or similar puzzle, and tell you how to derive coordinates from the solution. The puzzle itself might be a well-known type (e.g., a Sudoku puzzle) or it might be something unique.
These puzzles require you to solve a math problem. There are often multiple ways to solve the problem, some of which will be easier than others.
These puzzles require you to figure out how the coordinates are hidden before you can determine what they are. Sometimes the puzzle information is clearly identified, and you must figure out how to extract coordinates from it. Unlike research puzzles, these puzzles require you to figure out the theme of the cache, and how the provided information can be converted to coordinates. Other times, the puzzle itself may not be obvious. In a sense, before you can solve these puzzles, you must first find them.
These puzzles require you to decrypt encrypted information. Some will clearly identify the encryption algorithm and key, leaving you to decrypt the information as instructed. Others will leave it to you to determine the encryption algorithm, the key, or both, thus resembling hidden coordinates puzzles.