Parallelogram 28 • Level 2 • 14 Mar 2024Eleven eleven

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.
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.

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

2.

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.

3.

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.

4.

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.

5.

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.