Parallelogram 47 • Level 5 • 24 Jul 2025The Oxford Bell

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.

3 marks

1.1 Which is smallest?

2+34+6
2÷34÷6
2346
2−34−6
2×34×6
(Not answered)

The values are respectively 12, 1, 12, 12, 14.

2.

4 marks

2.1 Here are three statements:

(i) 310 is even
(ii) 310 is odd
(iii) 310 is square

Exactly which ones are true?

(i) only
(ii) only
(iii) only
(i) and (iii)
(ii) and (iii)
(Not answered)

All powers of 3 are odd and 310=35×35 which means that 310 is also square.

3.

5 marks

3.1 A rectangular sheet of paper with sides 1 and 2 has been folded once as shown, so that one corner just meets the opposite long edge.

What is the value of the length d?

12
2−1
716
3−2
23
(Not answered)

Show Hint (–2 mark)

–2 mark

The fold is made along BE. A folds onto A’.

A’B=AB=2, therefore A’C=1 (by Pythagoras).

The fold is made along BE. A folds onto A’.

A’B=AB=2, therefore A’C=1 (by Pythagoras).

Triangle A’BC is therefore a right-angled isosceles triangle, therefore BA’C=45°, therefore EA’D=45°.

Thus ED=A’D=2−1.

4.

3 marks

4.1 In a magic square, each row, each column and both main diagonals have the same total.

In the partially completed magic square shown, what number should replace x?

15
18
21
24
27
(Not answered)

Show Hint (–1 mark)

–1 mark

The leading diagonal sums to 58. So every row and column should add to 58.

The numbers along the leading diagonal total 58 and this is therefore the sum of each row and column. We can now calculate that the number to the left of the 10 must be 20, and the number below that is 7. Hence x=58−16+14+7=21.

5. The Battery That's Lasted 176 Years

Sally Le Page tells the story behind the world’s longest running battery!

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

2 marks

5.1 Sally explains that the bell requires 1 nanoamp (nA) of current. How much is a nanoamp?

A trillionth of an amp.
A billionth of an amp.
A millionth of an amp.
A thousandth of an amp.
A hundredth of an amp.
(Not answered)

Before you hit the SUBMIT button, here are some quick reminders:

You will receive your score immediately, and collect your reward points.
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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.