Pentomino Puzzles

As a parent, I’m always on the lookout for challenging brain-boosting games or puzzles for kids that provide different levels of skill. The Pentomino puzzle is one such puzzle that I recently found out. It’s a fantastic mathematical puzzle with tons of solutions that helps build problem solving skills and strategic thinking.

Instead of buying a pentomino puzzle kit, I decided to make use of my kids legos. After all, there are numerous ways of using legos to teach math, ranging from basic counting to difficult math concepts like probabilities. To begin, I asked my kids to gather 2×2 legos bricks in as many different colors as possible. Then I gave them a little more information about the puzzle before they started building the puzzle pieces.

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WHAT IS A Pentomino PUZZLE

Pentomino puzzle is a tiling puzzle, just like how the game of Tetris is. Pentominoes are shapes made of five equal-sized square pieces that are joined together from edge to edge. In a typical pentomino puzzle, we have to tile a rectangular box with the pentominoes, ie , cover it without overlaps and without gaps.

To arrange these five squares, there are only twelve different ways. Any shape that can be rotated or flipped to look like another shape, is considered the same. These twelve different shapes are named T,U,V,W,X,Y,Z,F,I,L,P and N. It is based on the letter of the alphabet that most closely resembles it. You might notice that 6 out of the 12 shapes F, L, P, N, Y and Z can be mirrored ( rotated or flipped ).

Each of the 12 pentominoes has an area of 5 unit squares, so the area of the rectangular box has to be 60 units. There are 3 x 20, 4 x 15, 5 x 12 and 6 x 10 possible sizes.

• 3 x 20 rectangle has only 2 solutions.
• 4 x 15 rectangle has 368 solutions.
• 5 x 12 rectangle has 1,010 solutions.
• 6 x 10 rectangle has 2,339 solutions.

How to Solve the Pentomino TILING Puzzle

I began by asking my kids to draw all the different possible shapes on a graph paper that they can create using 5 unit squares.

They then used it as a guide to build the shapes of the pentominoes out of lego pieces. They created each of these shape using 5 pieces of 2 x 2 lego bricks. To keep the five 2 x 2 lego units together, each piece is constructed over a base layer of legos.

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The pentominoes puzzle was ready to be assembled. But, I wanted my kids to get acquainted with the Pentominoes pieces before jumping into solving a Pentomino puzzle.

I asked them to use 3 pentominoes to create a rectangle of 15 square unit.

Afterwards, they put together 4 pentominoes to fill a rectangle which covers an area of 20 units.

Similary, 5 pentominoes to create a rectangle of 25 units. This gave them a better understanding of how each piece fit together.

Lastly, I asked them to use 6 pentominoes to put together to make a 5 by 6 rectangle of 30 units. Later, they had to use the other 6 pentominoes from the complete set of 12, to make another 5 by 6 rectangle.

Once the kids felt comfortable working with the pentominoes pieces, I asked them to create a rectangle of different sizes : 3 x 20 , 4 x 15, 5 x 12 and 6 x 10. No doubt, it was tough for them and I did advice them couple of times. We realized that since we used Lego pieces, it made more sense to make the 6 pentominoes ( F, L, P, N, Y and Z ) mirrored shapes also. It helped visualize the pieces better while solving the puzzle.

Further Extension

Ask your kids to create any figure they like : figures of animals, houses, vehicles etc. This will help them to think methodically and learn spatial skills. It will be a good brain boosting activity for them and they will definitely enjoy doing it.

Also, for a math enthusiast kid, take a look at this example of how critical thinking skills can be used to solve difficult math problems.

I will recommend these books if you will like to learn more about Pentomino puzzles.

This book introduces important mathematical concepts of measurement ( unit, area, perimeter), triangular numbers and geometry to kids in a playful way.

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