Parallelogram 46 • Level 5 • 17 Jul 2025Bananas!
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.
- 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 In Britain in 1996 we consumed on average 9.6kg of bananas per person per year (that is, around 60 bananas each). In some parts of Africa, the consumption of bananas is as high as 250kg of bananas per person per year. Roughly how many bananas is that?
- 4 or 5 a day
- 1 or 2 a day
- 4 or 5 a week
- 1 or 2 a week
- 4 or 5 a month
- (Not answered)
250 kg is approximately 25 times 9.6 kg. The consumption in some parts of Africa is therefore approximately 25 × 60, ie 1500, per person per year. 4 bananas per day are equivalent to 4 × 365, ie 1460, per year and the best answer is therefore 4 or 5 a day.
2.
2.1 A pencil AB lying on a table is given a half-turn about the end B (so that A moves to A') and then a half-turn about A' (so that B moves to B').
The point C on the pencil is one third of the way from A to B.
What is the ratio of the total distances moved by A and by C?
- 3:1
- 3:2
- 1:1
- 2:3
- 1:3
- (Not answered)
Let AB be of length 3r. The distance moved by A is then the circumference of a semicircle of radius 3r, ie 3πr. C moves along the circumference of a semicircle of radius 2r, ie 2πr, followed by the circumference of a semicircle of radius r, ie πr. The total distance moved by C is therefore also 3πr.
3. Ice ages
(If you have problems watching the video, right click to open it in a new window)3.1 What is the current tilt of the Earth?
- 0°
- 7.2°
- 23.5°
- 45°
- 90°
- (Not answered)
3.2 What helps to stabilise the tilt of the Earth?
- The moon
- The Earth’s spin
- The Earth’s mass
- The Earth’s flatness
- The Earth’s ice
- (Not answered)
4.
4.1 In Worcestershire, Wyre Piddle is 12km south of the village of North Piddle, and Abbotts Morton is 12km east of North Piddle. What is the direction of Abbotts Morton from Wyre Piddle?
- South East
- South West
- North East
- North West
- West
- (Not answered)
5.
5.1 The diagram shows two rectangles which enclose five regions. What is the largest number of regions which can be enclosed by any two rectangles drawn on a sheet of paper?
- 10
- 9
- 8
- 7
- 6
- (Not answered)
A rectangle could be a square.
Imagine 2 squares on top each other and rotate one of them slightly.
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...
- 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.
- 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.