Parallelogram 45 • Level 3 • 10 Jul 2025Bluberry planet
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.
1.1 Which of these diagrams could be drawn without taking the pen off the page and without drawing along a line already drawn?
- A
- B
- C
- D
- E
- (Not answered)
For it to be possible to draw a figure without taking the pen off the paper and without drawing along an existing line, there must be at most two points in the figure at which an odd number of lines meet.
Only E satisfies this condition.
2.
2.1. The diagram shows a single floor tile in which the outer square has side 8cm and the inner square has side 6cm.
If Adam Ant walks once around the perimeter of the inner square and Annabel Ant walks once around the perimeter of the outer square, how much further does Annabel walk than Adam?
- 2 cm
- 4 cm
- 6 cm
- 8 cm
- 16 cm
- (Not answered)
Adam Ant walks 24 cm, while Annabel Ant walks 32 cm, so Annabel walks 8 cm further.
3.
3.1. Sir Lance has a lot of tables and chairs in his house. Each rectangular table seats eight people and each round table seats five people.
What is the smallest number of tables he will need to use to seat 35 guests and himself, without any of the seating around these tables remaining unoccupied?
- 4
- 5
- 6
- 7
- 8
- (Not answered)
There are 36 people to be seated so at least five tables will be required. The number of circular tables must be even.
However, five rectangular tables will seat 40 people and three rectangular and two circular will seat 34. So at least six tables are needed.
Two rectangular and four circular tables do seat 36 people: so six is the minimum number of tables.
4. What if the Earth was made of Blueberries?
Liv Boeree is a physics graduate who has an insatiable curiosity, which includes asking questions about what would happen if the Earth was made of blueberries?
(If you have problems watching the video, right click to open it in a new window)4.1 After a while, what would the atmosphere consist of?
- Oxygen
- Nitrogen
- Carbon dioxide
- Helium
- Steam
- (Not answered)
5.
5.1 Nicky has to choose 7 different positive whole numbers whose mean is 7.
What is the largest possible such number she could choose?
- 7
- 28
- 34
- 43
- 49
- (Not answered)
Since the mean is 7, the total must be
The seven numbers must total 49 if their mean is to be 7. The largest possible number will occur when the other six numbers are as small as possible, that is 1, 2, 3, 4, 5, 6.
So the required number is 49 - 21 = 28.
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.