Calibron 12 Puzzle of The Week Feature

This week's puzzle feature is on the Calibron 12. Out of all of our different brain teasers I rank the Calibron 12 in the top 5 in terms of difficulty. With that being said it is a wonderful puzzle because the concept is so simple. All you need to do is fit each of the 12 pieces in the available space. It is the type of brainteaser anyone can try, but very few will actually solve without assistance from the instructions.

The puzzle also has a pretty interesting:

Originally designed in 1933 by Theodore Edison, son of the famous inventor Thomas Edison, and made by his company Calibron Products of West Orange, N.J.   It was offered as just pieces and you were told they made a rectangle and there was only 1 solution.  

A friend of my Dad actually performed a computer analysis on the puzzle to verify this. It turns out the only possible solution is a square shape, as verified by Ken Irvine's computer analysis. Ken is working on a full analysis of the puzzle, with excerpts noted below.

From Ken Irvine:

After determining that there was only 1 solution to the square (using Burr Tools program), the second goal was to determine if there were any additional rectangles that could be made with the 12 pieces. The first step of this analysis was to determine how many possible rectangles needed to be checked. Since the total area of the pieces is 3136 units, the problem is to find the set of rectangles that have an area of 3136. This is done by factoring 3136 into its prime factors, which gives: 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7. Rectangles of area 3136 can then be found by finding all combinations of dividing the prime factors into 2 sets. This can be further constrained by the fact that both sides need to be at least 18 units to be able to fit the 21 x 18 piece. This results in the following 4 possible rectangles, including the original square:

(2 x 2 x 2 x 7) x (2 x 2 x 2 x 7) => 56 x 56 (Original Square)

(2 x 2 x 2 x 2 x 7) x (2 x 2 x 7) => 112 x 28

(2 x 2 x 2 x 2 x 2 x 2) x (7 x 7) => 64 x 49

(2 x 2 x 2 x 2 x 2) x (2 x 7 x 7) => 32 x 98  >>