Parallelogram 40 Level 5 6 Jun 2024Classic Countdown

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. 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.
  • When you finish, remember to hit the SUBMIT button.
  • Finish by Sunday night if your whole class is doing parallelograms.
  • Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.

1. Classic Countdown

Take a look at this classic number game from Countdown.

(If you have problems watching the video, right click to open it in a new window)

Here is an explanation of what happened by Junaid Mubeen, Director of Education, at Whizz Education, who was also a Countdown octochamp.

(If you have problems watching the video, right click to open it in a new window)

If you want to practice some Countdown problems, then you can visit this interactive website.


3 marks

2.1 Think of a number, double it, then add 3. Multiply your answer by 4 and from this take away 5. Now also take away the number you first thought of. No matter what your first number was, your answer will always be a multiple of:

  • 2
  • 3
  • 5
  • 7
  • 11
  • (Not answered)

Let the number thought of be x. Then the final number is 42x+35x=7x+7=7x+1.


4 marks

3.1 It has been estimated that the mass of insects caught by spiders in a year in the UK is equal to the mass of the human population of the UK. Assuming this population is 60 million and the average mass of a human is 70kg, what is the mass, in tonnes, of insects caught by spiders per year in the UK?

  • 4.2
  • 42
  • 4200
  • 420000
  • 4200000
  • (Not answered)

60 million × 70 kg = 4200 million kg = 4.2 million tonnes, since 1 tonne = 1000 kg.


4 marks

4.1 The diagram shows three semicircles, each of radius one.

What is the size of the total shaded area?

  • π+2
  • 3
  • 32π+1
  • 4
  • 2π1
  • (Not answered)
Show Hint (–2 mark)
–2 mark

Redraw the diagram as shown below and the problem becomes much easier.

The shaded area may be divided into a 2 × 1 rectangle plus a semicircle and two quarter circles, all of radius 1.

Hence the total area is that of the rectangle plus that of a circle of radius 1, ie 2 + π.


5 marks

5.1 Suppose that e, i, n and t represent different positive whole numbers, n+i+n+e=9, t+e+n=10 and i=1.

What is t?

  • 2
  • 3
  • 4
  • 5
  • 6
  • (Not answered)

We are given that 2n+e=8 and t+e+n=10. Subtracting the first equation from the second gives tn=2.

As n cannot equal 1, the minimum value of t is 4 but this gives n=2, e=4 which is impossible.

If t=5 then n=3 and e=2, which is allowed. If t>5 then n>3 and e is not a positive whole number, so 5 is the only possible value of t.

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.