Hoffman's Packing Box - Inequality of the Means Puzzle


Goal: Fit all 27 identical blocks within the boundary defined by the 3.6" cubic frame. 
This very challenging puzzle is a physical representation of the well know math principle “Inequality of the Means” and first proposed as a puzzle by Prof. Dean Hoffman of Auburn University in 1978.  Dr Hoffman was kind enough to allow to make this puzzle of his design.  We are pleased to offer it as something that may appeal to higher level puzzle enthusiasts as well as math scientists.

In mathematics, the Inequality of Arithmetic and Geometric Means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list. In practical terms with regards to this specific puzzle this means that 27 blocks of dimension .8" x 1.25" x 1.55" will fit within the confines of a 3.6" cube.  Note that 3.6 is the sum of the 3 dimensions of the puzzle (.8+1.25+1.55).
Further information on this concept is provided with the puzzle along with links to sites that will provide extensive analysis.
Wood used for the blocks is called Kauri or Agathis.  Such wood is often used to make guitars.  It has a nice look and feel.  The base sides we make from native cherry.  The floor of the base is made from floorboard to provide strength and rigidity.
You will likely be shocked at how difficult this puzzle is.  I suspect that a solution under 2 hours will be rare.
Made in our Spring Hill, FL shop.

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  • Model: hoffman
  • Shipping Weight: 1.1lbs
  • Manufactured by: Creative Crafthouse

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