Parallelogram 4 • Level 1 • 28 Sep 2023Polyominoes
Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/
- a portmanteau word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.
- Tackle each Parallelogram in one go. Don’t get distracted.
- Finish by midnight on Sunday if your whole class is doing parallelograms.
- Your score & answer sheet will appear immediately after you hit SUBMIT.
- Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.
1. Polyominoes
Yes, Polyominoes are just like Dominoes, but better!
Watch this Numberphile video about Pentominoes and answer a few questions.
(If you have problems watching the video, right click to open it in a new window)1.1 What type of Polyominoes are used in the retro game Tetris?
- Pentominoes
- Triominoes
- Tetrominoes
- Flamingoes
- (Not answered)
1.2 How many different Pentominoes are there?
Correct Solution: 12
Investigate the perimeter of the Pentominoes.
1.3 How many Pentominoes have a perimeter of 10?
Correct Solution: 1
1.4 How many Pentominoes have a perimeter of 11?
Correct Solution: 0
1.5 How many Pentominoes have a perimeter of 12?
Correct Solution: 11
1.6 What is the total perimeter of all the Pentominoes?
Correct Solution: 142
All but one of the Pentominoes have a perimeter of 12.
The odd pentomino out has a perimeter of 10.
(12 × 11) + (10 × 1) gives us a total combined perimeter of 142.
2 Hexominoes and nets of cubes
2.1 All nets of cubes are hexominoes, but not all hexominoes are nets of cubes.
Which of the following polyominoes will NOT fold up to make a cube?
- A
- B
- C
- D
- (Not answered)
2.2 Which of the following cubes can NOT be made from the net shown?
- A
- B
- C
- D
- (Not answered)
Before you hit the SUBMIT button, here are some quick reminders:
- You will receive your score immediately, and collect your reward points.
- You might earn a new badge... if not, then maybe next week.
- Make sure you go through the solution sheet – it is massively important.
- A score of less than 50% is ok – it means you can learn lots from your mistakes.
- The next Parallelogram is next week, at 3pm on Thursday.
- Finally, if you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.
Cheerio, Simon and Ayliean.