Parallelogram 44 • Level 3 • 3 Jul 2025Spuds Sums

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.
Finish by midnight on Sunday if your whole class is doing parallelograms.
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 mark

1.1 Which of these calculations produces a multiple of 5?

1×2+3+4
1+2×3+4
1×2+3×4
1+2×3×4
1×2×3×4
(Not answered)

The results of the five calculations are 9, 11, 14, 25, 24 respectively.

2.

2 marks

2.1. At Spuds-R-Us, a 2.5kg bag of potatoes costs £1.25. How much would one tonne of potatoes cost?

£5
£20
£50
£200
£500
(Not answered)

The cost of 1 kg of potatoes is £1.25 ÷ 2.5 = 50p. So the cost of 1 tonne, that is 1000 kg, is 1000 × 50p = £500.

3. Is it Better to Walk or Run in the Rain?

MinutePhysics is a great YoutTube channel, so dive in and watch loads of them. But, for now, take a look at this video about running in the rain.

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

2 marks

3.1 If you are outside in the rain and you want to minimise how wet you get, you should…

Stand still
Walk slowly
Run fast
Use an umbrella
(Not answered)

2 marks

3.2 If you are outside in the rain and don’t have an umbrella and you want to minimise how wet you get, you should…

Stand still
Walk slowly
Run fast
Borrow an umbrella
(Not answered)

2 marks

3.3 If you are outside in the rain and don’t have an umbrella and can’t borrow an umbrella and you want to minimise how wet you get, you should…

Stand still
Walk slowly
Run fast
(Not answered)

4.

4 marks

4.1 Sam's 101st birthday is tomorrow. So Sam's age in years changes from a square number (100) to a prime number (101).

How many times has this happened before in Sam's lifetime?

1
2
3
4
5
(Not answered)

The other times that this has happened previously are when Sam's age in years went from 1 to 2; from 4 to 5; from 16 to 17 and from 36 to 37.

Note that since primes other than 2 are odd, the only squares which need to be checked, other than 1, are of even numbers.

5.

5 marks

5.1. In the diagram on the right, the number in each box is obtained by adding the numbers in the two boxes immediately underneath.

What is the value of x?

300
320
340
360
More information needed
(Not answered)

Show Hint (–2 mark)

–2 mark

You do not have any two entries given which lie in the same three-box stack, so instead of working out a particular value, label the box next to 12 as a. Now label the box next to 78 with an expression, using the fact that this box plus a=90.

Let the numbers in the boxes be as shown in the diagram.

Then b=90−a; c=12+a; d=b+78=168−a.

Also, e=90+c=102+a; f=90+d=258−a.

So x=e+f=102+a+258−a=360.

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.