The Tetractys™ Number Puzzle is not just a random collection of individual, isolated puzzles but a system of puzzles. In fact, the number of puzzles that are possible under the rule of the puzzle is finite: there are only 737 puzzles that meet the requirements of the rule out of 10,000 possible combinations of four digits. In the Tetractys Number Puzzle these puzzles are organized and referenced in a systematic way, taking advantage of the fact that there is a small, finite number of them. What's more is that the puzzles are paired in such a way that the puzzles and their solutions are never shown together but are 'shared' between the puzzles in each pairing. This way of organizing the puzzles makes finding puzzles and their solutions easy, fast, and always consistent. Once you learn the system, you can always find the right solution.
The unique referencing system of the Tetractys Number Puzzle exploits the fact that there are only a small, finite number of puzzles that follow the puzzle's rule. Within that small, finite number there are many different number patterns that can be found, and hence puzzles can be grouped in order to highlight or teach these patterns. This, of course, is where the benefits of an efficient reference system come into play, since it is as simple as referencing a number or name when grouping puzzles for study. For example, there is a Tetractys puzzle 164 (or simply Tetractys 164), just as there is another puzzle called Tetractys 372. Each puzzle grid is numbered this way, along with a reference name, so that it can be easily referenced and its solution easily found. The naming and numbering is systematic, and it can be easily learned by parent, teacher, or student, and employed when needed.
The pairing of puzzles belongs to the reference system, too. The benefits to this are numerous. Each puzzle grid displays not only its own puzzle digits but also its own paired puzzle's solution, and each pair shows one puzzle per page side, so that puzzles are always on opposite side of a page. This format allows for efficient use of space, makes finding solutions easier and faster, and even makes puzzles "bi-directional", that is, it is often possible to start with the solution and work one's way back to the original puzzle itself.