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Exploring Polyominoes: A Fun Puzzle Adventure

Dive into the world of polyominoes - from monominoes to octominoes, explore the rules, properties, and symmetries in this engaging puzzle journey. Challenge yourself with systematic thinking to find and draw various polyomino shapes while avoiding duplicates. Discover interesting properties like line and rotational symmetries among pentominoes and hexominoes, and even fold open-top boxes from specific shapes. Can you construct different size rectangles and explore the vast combinations of polyomino solutions available? Test yourself with worksheets and puzzles for an interactive learning experience!

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Exploring Polyominoes: A Fun Puzzle Adventure

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  1. P T O E N I S E N M O 6 x 10

  2. More of that later! Poly-ominoes Many-squares Rules  Full edge to edge contact only.

  3. P Y O E L I S O N M O ? ? Mon-omino Domino Triominoes 1 2 1 Find all of the? Tetrominoes Think systematically! Don’t forget to avoid duplicates. Remember, rotations and reflections are not allowed! 5

  4. P T O E N I S E N M O The pentominoes have lots of interesting properties. Find and draw all of the pentominoes.? Don’t forget to think systematically! 12

  5. P T O E N I S E N M O Alphabet Pentominoes!

  6. P T O E N I S E N M O Some of the pentominoes (like the one shown)can be folded to make open-top boxes. Can you find them all and shade their bases?

  7. P T O E N I S E N M O Find the pentominoes with line/mirror symmetries

  8. P T O E N I S E N M O Find the pentominoes with turn/rotational symmetry.

  9. P T O E N I S E N M O Find the pentominoes with turn/rotational symmetry. ¾ turn ¼ turn Full turn ½ turn Order 2

  10. P T O E N I S E N M O Find the pentominoes with turn/rotational symmetry. Order 2 Full turn ¾ turn ½ turn ¼ turn Order 2

  11. P T O E N I S E N M O Find the pentominoes with turn/rotational symmetry. Order 2 Order 2 Full turn ¾ turn ½ turn ¼ turn Order 4

  12. Do they all have the same perimeter? 12 12 12 10 12 12 12 12 12 12 12 12

  13. 3 6 20 10 5 12 4 2 15 30 1 60 How many different size rectangles can be made using 60 squares?

  14. P T O E N I S E N M O 6 x 10 1 of 2339!

  15. P T O E N I S E N M O 1 of 2339 2 of 2339 3 of 2339 1 of 1010 2 of 1010 2 of 368 1 of 368

  16. Build the 12 pentominoes using the 2 cm cubes provided. Use you’re A3 worksheet to try and find a solution of your own!

  17. P T O E N I S E N M O 1 of 2339 2 of 2339 3 of 2339 1 of 1010 2 of 1010 2 of 368 1 of 368

  18. X O E E I S H N M O There are 35 distinct hexominoes. You will need patience and systematic thinking to find all of them.

  19. X O E E I S H N M O Some of the hexominoes can be folded to make closed boxes. They are nets of cubes. Can you find them?

  20. X O E E I S H N M O Hexominoes with line symmetry?

  21. X O E E I S H N M O Hexominoes with rotational symmetry?

  22. X O E E I S H N M O 14 12 14 14 12 14 14 14 14 14 14 14 14 12 14 14 14 14 14 14 14 14 14 14 10 14 12 12 14 12 12 They all have the same area but do they all have the same perimeter? 14 14 14 14

  23. X O E E I S H N M O Possible rectangles with an area of: 15 14 210 units2 1 x 210 2 x 105 3 x 70 5 x 42 It is not possible to cover any of these rectangles with the 35 hexominoes. 6 x 35 7 x 30 10 x 21 14 x 15

  24. P Y O E L I S O N M O Monominoes 1 Dominoes 2 Triominoes 2 Tetrominoes 5 Pentominoes 12 Hexominoes 35 Heptominoes 108 Octominoes 369 A formula for calculating the number of n-ominoes has not been found.

  25. Pentominoes Hexominoes Worksheet 1

  26. Worksheet 2

  27. P T O E N I S E N M O 6 x 10 2339 solutions 3 x 20 2 solutions Worksheet 3: A3 front(enlarge)

  28. P T O E N I S E N M O 5 x 12 1010 solutions 4 x 15 368 solutions Worksheet 3: A3 reverse(enlarge)

  29. Worksheet 4

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