Pentomino Puzzle

I came across this puzzle back in the 80s in a science fiction book, so this has a few extra pieces. I have seen store versions of this and they all use the same size box to fit them, but this is a math puzzle, so the box or shape to fit them in can change. This puzzle is 2 parts, first with 5 cubes, then with the pieces you can make with the cubes.

Think of the puzzle pieces made up of cubes, each piece is made with 5 cubes. So if you have 12 pieces, each made with 5 cubes, that is a total of 60 cubes.

Store bought box or frame to fit them is normally 6 cubes by 10 cubes (60 cubes). I am going to say there is more ways to do this.

This would be a great learning tool for children to teach math. Now when I made this, my mother had dementia, I gave her this, asked her to make the pieces from the 5 cubes, she completed that, then I gave her the pieces and the first template, after 2-3 tries, she said impossible. My Dad and I encouraged her to try, and she completed it in just a few more tries.

I used scrap 3/4 inch plywood, so this Instructable is based on that type of wood. 3/4 inch thick is ideal as you need to make some cubes first, and as you guessed it, we are going to make the cubes 3/4 inch wide as well.

Paint, I used 12 colors of acrylic paint that I bought at Walmart, you can also buy acrylic paints from craft stores. And you will need a artists paintbrush. Acrylic is great since it dries fast and clean up is with water.

For tools, only a scroll saw was used. Follow the safety precautions for your scroll saw, and use a push stick to prevent your fingers from getting too close to the blade.

Layout the plywood. You need 5 cubes, then layout the 12 pieces. Only 1 piece with 5 'cubes' in a unique shape, there is only 12 shapes possible. This is not a 3D version so no staking the cubes. The pieces you need are in the photo, not shown is the 5 cubes, but you can see my pencil lines on the pieces and see that each is 'made' with 5 cubes. There is only 12 pieces/shapes to make after you have the 5 cubes. Each piece is unique, do not make more than 1 piece shown.

Paint the pieces using acrylic paint, you only need to paint the top and bottom, not the sides. Paint each 5 cube piece 1 color and paint the individual cubes the same color.

From what I have seen, the store bought versions of this have a box or template to place the pieces to all fit within the box or template. Now the most common, and easiest is 6 cubes by 10 cubes, there is 1,000s of ways to place the pieces in that frame or template.

Get some cardboard. Measure out the first and most common one to 6 x 10 cubes (60 cubes total). I used 3/4 inch plywood so 3/4 inch 'cubes', this comes out to 4 1/2 inches x 7 1/2 inches. Easiest way.

Layout the next piece of cardboard to 5 x 12 cubes (60 cubes total), or 3.75 inches x 9 inches. Little harder.

Layout the next piece of cardboard to 4 x 15 cubes (60 cubes total), or 3 inches x 11 1/4 inches. A lot harder.

Layout the next piece of cardboard to 3 x 20 cubes (60 cubes total), or 2 1/4 inches x 15 inches. Hardest way, only 2 ways to solve this, and if you found 1 way, the other way is simple if you look at it.

Give a person the 5 cubes, ask them to arrange them in a pattern on a flat surface, no duplicating, no stacking the cubes, and no rotating a cube and saying that is different. Ask them make a shape using the 5 cubes, then give them the shape they made.

When they have completed all 12 patterns, there is no more, ask them how many cubes make up the total cubes of the pieces they have now? The person should have figured out there is 12 pieces and 5 cubes make up each piece, so 60 cubes.

Now ask the person, can all those pieces fit onto a shape that is 6 cubes x 10 cubes?

Now to the puzzle.

Pick a template, the 6 x 10 would be a good starting point if one has never done this before. Ask the person to arrange the pieces on the template, to fit on the template, nothing overhanging, nothing sticking upwards (not a 3D puzzle), until they get them all on the template.