Parallelogram 28 Level 2 14 Mar 2024Eleven eleven

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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.


5 marks

1.1 What is half of 1.01?

  • 5.5
  • 0.55
  • 0.505
  • 0.5005
  • 0.055
  • (Not answered)

We obtain half of 1.01 by dividing 1.01 by 2. We can do this as a long division sum, or alternatively, we can use fractions:

1.01=1+1100. So half of 1.01 is 12+1200=0.5+0.005=0.505


5 marks

2.1 Laura wishes to cut this shape, which is made up of nine small squares, into pieces that she can then rearrange to make a 3×3 square.

What is the smallest number of pieces that she needs to cut the shape into so that she can do this?

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

In a 3×3 square each row and column contains just 3 squares. So none of the pieces that Laura uses to make the square can be more than 3 squares long. It follows that the squares labelled a and b must be in different pieces, as must be the squares labelled b and c. So there must be at least three pieces. The diagrams below show how Laura can fulfill her task using 3 pieces.


5 marks

3.1 How many minutes are there from 11:11 until 23:23 on the same day?

  • 12
  • 720
  • 732
  • 1212
  • 7212
  • (Not answered)

The time difference is 12 hours and 12 minutes, that is 732 minutes.


6 marks

4.1 Only one of the following statements is true. Which one?

  • A ‘B is true’
  • B ‘E is false’
  • C ‘Statements A to E are true’
  • D ‘Statements A to E are false’
  • E ‘A is false’
  • (Not answered)

For statement A to be true, B would also have to be true. But we are told that only one statement is true, so this is not possible. We deduce that statement A is false. Therefore statement E is true.

In the context of the JMC you could stop here, because we have found one statement that must be true. However, we really ought to satisfy ourselves that statement E is the only one that is true.

As statement E is true, statement B is false. Statement D can never be true, because if statement D were true, all the statements, including D, would be false, and we would have a contradiction. Because statement D must be false, statement C cannot be true.

So statement E is true and all the other statements are false.


6 marks

5.1 Aaron says his age is 50 years, 50 months, 50 weeks and 50 days old. What age will he be on his next birthday?

  • 56
  • 55
  • 54
  • 53
  • 51
  • (Not answered)

50 months is 4 years and 2 months. 50 weeks is around 11 12 months and 50 days is about 1 23 months.

So Aaron's age is approximately (50 + 4) years + (2 + 11 12 + 1 23) months = 54 years + 15 16 months = 55 years and 3 16 months. So he will be 56 on his next birthday.

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.