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The TetractysTM System

Learn about...
  • The unique referencing system of the puzzle
  • How solutions are embedded in each puzzle
  • How digits can be both numbers and names
Benefits to the student:
  • Learning how the system works develops pattern-recognition
  • The system makes finding puzzles and solutions easy
  • A rational and consistent system encourages rational and consistent thinking

Finding the Right Solution

The beauty of a system is that in it everything has its place. And once you know how the system works, you know where everything is.

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.

Pairing Puzzles


    The Tetractys™ Number Puzzle uses pairs of puzzles in order to embed each puzzle's solution in a different puzzle grid. In fact, when puzzles are paired, only one puzzle of each pair is shown on the same page; the other puzzle is always shown on the opposite side of the page.

  • Pairing puzzles makes efficient use of space
  • Solutions are built into each puzzle grid
  • Puzzles can now be solved bi-directionally
  • Pairing puzzles is systematic and predictable

Numbering Puzzles


    Since the number of puzzles in the Tetractys™ Number Puzzle is finite, each puzzle can be numbered uniquely so that it can be referenced easily and quickly found. Numbering puzzles in this way can also be another way to reference solutions, ensuring the right solution has been found.

  • Numbering puzzles makes referencing easy and quick
  • Numbering puzzles shows which puzzles are paired
  • Numbering is unique and follows a system
  • Systematic referencing aids rational thinking

Naming Puzzles


    In addition to assigning each puzzle a unique reference number, each puzzle can also be named by simply using the four digits of each puzzle. Having an easy and unique reference name can make referencing even more effective, since it provides an alternative to the unique reference number.

  • Naming puzzles makes referencing more efficient
  • One can reference by either the puzzle's unique number or unique name
  • Puzzle names identify puzzles transparently, that is, they are the puzzles four digits

A Built-in, Unique Reference System

It is sometimes said that the journey is just as important as the destination. If we think of this in terms of a reference system, then we might say equivalently that knowing how to find the right solution is just as important as getting 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.

Tetractys Number Puzzle: A Mathematical Learning System for Students

ONLY$9.95
Product Details

  • Publisher: POIS Research; First edition
  • Language: English
  • ISBN-13: 978-0-9959504-0-5
  • Product Dimensions: 8.5" x 5.5" x 0.2"
  • Paperback: 64 pages in full color (Saddle Stitch)

  • Note: Dry Erase Marker and Dry Eraser not included.
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