Turtle Teasers Pentominoes Puzzles 


I have been fascinated by the mathematical concept of Pentominoes for a long time now. Briefly, a Pentomino is made from 5 connected squares (compare to a domino which is made from two connected squares or a Tetris piece which consists of 4 connected squares). If you ignore rotations and reflections, there are 12 distinct Pentominoes. These pieces can be incorporated into a puzzle, similar to a jigsaw puzzle, but with the big difference that there can be more than one correct solution. There is a lot of Internet literature on the concept of Pentominoes, and perhaps the best starting point is Wikipedia (http://en.wikipedia.org/wiki/Pentomino). I have made two types of Pentominoes puzzle. The first is the classic Pentominoes puzzle (A), consisting of the 12 Pentominoes to be placed in a 6 x 10 rectangle. Amazingly, this puzzle has exactly 2339 solutions, yet it can take an hour or so to find even one! The second puzzle (B) adds a 2 x 2 square to the 12 Pentominoes, and the problem is to cover an 8 x 8 square with the 13 pieces. This puzzle has 16146 solutions, and again it can be a challenge to find even one of them. The photos below show the two types of puzzle. I have made stock of each type, so if you buy one it may not be identical to the photo, but it will be very similar. Click on either of these photos to see larger and more varied photos. Each piece of a puzzle is cut from a different species of hardwood. The wood is left in its natural state  it is not stained, just wiped with tung oil to bring out its natural color and grain. The Pentomino pieces are based on unit squares measuring 3/8” on a side, so that the dimensions of the solution tray for puzzle A is 21/4” x 33/4” and its box measures 3” x 41/2”. For puzzle B, the solution tray measures 3” x 3” and the box measures 33/4” x 33/4”. Each box consists of a tray and a lid, which fit together snugly and hold with a compression fit. Both tray and lid are surfaced with hardwood veneer, and the lid has a turtle inlay in contrasting hardwood, identifying it as a Turtleteasers puzzle. This also helps to avoid the box being opened upside down, spilling the pieces! One solution is printed out and placed inside the box to serve as a guide to replacing the pieces inside the box. You can download a compact list of all the solutions to either puzzle by clicking one of the photos at the bottom of this page, I am often asked “Which is the more difficult puzzle?” and have always felt that Puzzle B (the 8 x 8 version) is more difficult even though it has nearly 8 times as many solutions, but I couldn’t be sure of that. Now I have some insight into this. Before I constructed my first Pentominoes puzzle, I had written a computer program to perform an exhaustive check of every possible placing of every piece to determine exactly how many correct solutions there were to each version of the puzzle. Recently I updated this program to count how many times it reached a deadend in its attempts and had to backtrack  that is, it found an “incorrect” solution. Puzzle A encountered 1000 deadends for every correct solution, but Puzzle B had about 6000 deadends for every correct solution found. So I think this reinforces my feeling that Puzzle B is the more difficult. US domestic shipping for these Pentomino puzzles is included in the price. To order one of these puzzles, send an email to sales@turtleteasers.com. 



To download the complete PDF file of 2339 solutions to the 6 x 10 puzzle or 16146 solutions to the 8 x 8 puzzle, click anywhere on the appropriate report image below. You will need to have a copy of the free Adobe Acrobat Reader installed on your computer to be able to see the solutions. 