Pentominoes

thingiverse

The pentominoes created in these files represent various geometric figures that fit together like a puzzle to create thousands of different rectangular solutions. The challenge is presented as follows: Given 18 pentominoes, the task is to find a rectangular arrangement using every piece - this puzzle is very reminiscent of tetris. Print Settings Printer Brand: SeeMeCNC Printer: Rostock MAX Notes: There are 18 pieces to this pentomino set. Six unique geometric shapes are found in the “single print” file and six shapes are found in the “double print” file. You will need to do three prints to get your 18 pentominoes: one of the single print and two of the double print. The six duplicates then need to be flipped so you have no two pieces that are exactly the same formation. If we were to work further with the pentominoes, we would want to make it more clear which side of the pentominoe needs to be face up. One solution that we had for this problem was to pause the print and switch colors about halfway through each print. This allows you to easily see if your pieces are oriented correctly - the puzzle solution should be only one color, if you see both colors you know that those pieces are not correctly oriented. How I Designed This We got our original inspiration from John Rausch’s puzzles (http://www.johnrausch.com/PuzzlingWorld/figures.htm). We came across our biggest challenge with figuring out the sizing and spacing of the pentominoes to make sure they fit together like a puzzle. Drawing them out on paper first, we started with each unit being 10mm, illustrated in the attached picture. We then 'shaved off' .25 mm on each side of every pentominoe. This creates a snug fit that still allows the user to move the pentominoes around with no problems. It was then a fairly simple process to create the files using Rhino. Overview and Background JC, ML, CO 12/2016 Lesson Plan and Activity We designed the pentominoes with the intent that they could be used in math classrooms. Students can explore the concept of different shapes having the same area by finding different solutions for the pentominoes. Students can also use the puzzle to practice their problem-solving techniques or to create a little friendly competition in the class. If many people are finding solutions, you can keep track of which solutions are unique and which are duplicates. Despite the huge number of possible solutions, the puzzle is incredibly difficult. Whatever your pentominoes are for, they are a great piece to show anyone how fun it is to bring math to life with a 3D printer.