If you’re looking for a great maths puzzle to keep the kids entertained for hours, then pentominoes might be just the thing! A pentomino puzzle is a tiling puzzle with lots of different solutions, that helps build problem solving skills and strategic thinking.
Pentominoes are geometric blocks or tiles made of five equal-sized squares connected edge-to-edge. It’s a bit like ‘Tetris’, but with each piece made of five blocks instead of four.
Although they first appeared in puzzle books as far back as the early 1900s, it was American professor Solomon W. Golomb who coined the term ‘pentomino’, after the Greek word for the number five (pente) and the -omino of domino.
The five equal-sized squares can be combined in twelve different ways. Six of the resulting shapes can be mirrored, which would give you a total of eighteen different shapes, but for the standard pentomino puzzles below the mirrored shapes are considered to be one and the same. Solomon W. Golomb named the twelve pentominoes after the letters of the Latin alphabet that they resembled the most:
While there are ready-made pentomino puzzles available to buy, it’s easy to make your own, for example using Lego like we've done here. We used 2x2 Lego 'dots' to represent each square, and held each pentomino shape together with a second layer of Lego.
In a standard pentomino puzzle, the challenge is to arrange all twelve shapes in to a rectangle, without any gaps or overlaps. Since each of the twelve pentominoes is made up of five square units, the rectangles must be made up of sixty units (5 x 12 = 60). Possible rectangle sizes are 3 x 20, 4 x 15, 5 x 12, and 6 x 10 units.
Each rectangle has multiple solutions. Here are some examples for each of the different sizes.
3 x 20 rectangle (2 possible solutions)
4 x 15 rectangle (368 possible solutions)
5 x 12 rectangle (1,010 possible solutions)
6 x 10 rectangle (2,339 solutions)
Remember that six of the pentomino pieces can be mirrored, so you may need to flip them over to solve the puzzle!
Another fun pentomino puzzle is an 8 x 8 square with a 2 x 2 hole in the centre. This puzzle has 65 possible solutions.
So what are you waiting for? Dig out some Lego, and get puzzling! Which pentomino puzzle will you try to solve first?
Maths skills involved: geometry, spatial reasoning, logical deduction, problem solving
If you create your own pentomino from Lego, we'd love to see it! Please feel free to tag us on Twitter or Facebook, and use the hashtag #MathsWeekScot.
