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The Art of Packing Math Puzzles by Timothy Sharkey RSS Feed AddThis Social Bookmark Button

Packing puzzles go back centuries like many math based puzzles seem to. These type of puzzles can be two or three dimensional. The three dimensional variety are far more common and popular today. The two dimensional packing puzzles are used mostly for educational math problems as opposed to a fun pastime solving puzzles. Packing puzzles are made mostly of wood or plastic, but glass, metal and even stone puzzles exist. The varieties seem endless but each type falls into a specific category.

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The first packing puzzles appeared in Greece around 300 BC. The puzzle was two dimensional and involved a square with 14 parts. In the 1600s small complex packing puzzles were used as locks and the solution was given to the owner of the home or chest that had the lock. Tangrams showed up a century later even though Tangrams are not true packing puzzles, but more of a building type puzzle that allows pictures and shapes to be created using seven pieces. The first book on packing puzzles was written around 1900 and had diagrams of over three dozen puzzles. Patents appeared around this time as well. Early puzzles were made of wood, but plastic puzzles appeared later and allowed for more intricate parts.


Wooden puzzles are still very popular as they make great collectables, feel better in the hands and have a more attractive appearance. If different colored woods are used, the final completed puzzles can look very beautiful. Wood is more costly as there is more machine and hand work involved and the raw materials cost more. Plastic will lost longer, but wood can last very long too if well cared for. Wood is still more commonly used today. For the more die hard collector with more money to spare, there are metal, stone and glass packing puzzles, that can still be solved, but are mainly used for display. The cost for one puzzle can run into hundreds of dollars.

Solving packing puzzles involves geometry which is a branch of mathematics. For instance, trying to pack different shapes will most inevitably lead to problems. The different shapes are not geometrically similar to each other and use different mathematical properties for obtaining their volume or area which is vital for packing objects together in these puzzles. Puzzles involving cubes are the simplest to figure out geometrically since the volume formula for a cube is simply the length of the side cubed. Simply packing cubes would be no challenge, so these types of packing puzzles, which are the most common, involve several cubes stuck together to form different shapes. Now, the puzzle is considerably more challenging and enjoyable to solve. Due to the mathematical properties of the volume of a sphere, there is no way to pack spheres without leaving spaces, but puzzles do exist involving spheres that allow gaps.

Packing puzzles fall under the category of put-together puzzles, which in turn fall under the category of three dimensional puzzles. Some packing puzzles are categorized as two dimensional, so you might be wondering how they can be categorized as three dimensional. In reality, the 'two dimensional' packing puzzle is actually three dimensional, but since they only consist of one layer of packing they are often referred as a 'two dimensional' packing puzzles.

One of the earliest put-together packing puzzles was Hoffman's packing puzzle. This puzzle had 27 different blocks with each block having slightly different length sides. These had to be placed in a box just barely large enough to fit them all. Gaps were allowed in this puzzle, but it only had one solution. The larger completed block did have even sides however. Each block was also made of a different type of hardwood, with each piece numbered to identify each type of wood. Needless to say this puzzle probably carried a high price tag and would be worth quite a but today.

Another fine packing puzzle is the triangle based Bermuda Hexagon. This award winning challenging puzzle had three layers and one solution. The pieces were made of two different sizes of triangles, with the smaller size being exactly one quarter the size for the larger to allow easy fitting of the pieces. This puzzle was also made of wood.

There are countless variations of packing puzzles. They can be found both online and in specialty stores. Stores that sell games and puzzles will offer a wide variety of packing puzzles, but the best finds can be found in specialty stores in bigger cities or classy tourist destinations.

About the Author

Timothy Sharkey works for Softgame Company, maker of card games, video poker and puzzles.

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