Parallelogram 48 • Level 2 • 31 Jul 2025Sporting Loopholes
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.
It’s summer and the school year is over (or maybe it’s nearly over), but that doesn’t mean that it’s the end of mathematics. If you are taking mathematics seriously and if you are having fun with it (being serious and having fun can go together), then it is important that you keep the numbers and geometry parts of your brain at least a little bit busy over the summer. I am hoping that your teacher will have set you some holiday work, but if you have missed any earlier Parallelograms then the summer is a great time to do some catching up.
1. QI : Curious Sporting Loopholes
Mathematics is about rules (e.g., odd plus odd equals even), but it is also about understanding the rules in such detail that you know how to gain an advantage in solving problems. In that spirit, here is a clip from the BBC show “QI” about taking advantage of loopholes in sporting rules.
(If you have problems watching the video, right click to open it in a new window)1.1 Because of cricketer Thomas White, cricket bats can no longer be infinitely wide. Today, what is the maximum permitted width of a cricket bat in first class cricket? (You might have to googly this.)
- 4.25 mm
- 38 mm
- 108 mm
- 965 mm
- (Not answered)
1.2 In the previous question, why did I write that you might have to “googly” the answer, rather than writing “google” the answer?
- Googly was a typo
- Googly is a way of bowling a cricket ball
- Thomas Googly invented cricket
- Googly is the Indian word for Google
- (Not answered)
2.
2.1 Which of the following has the largest value?
6 ÷ 1 2 5 ÷ 1 3 4 ÷ 1 4 3 ÷ 1 5 2 ÷ 1 6 - (Not answered)
The values of the expressions are as follows:
6 ÷ 1 2 = 12 5 ÷ 1 3 = 15 4 ÷ 1 4 = 16 3 ÷ 1 5 = 15 2 ÷ 1 6 = 12
3.
3.1. Which of the following has the largest value?
1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 4 1 2 - (Not answered)
The values of the five expressions are:
1 2 1 4 3 4 1 2 1 4 1 4 1 2 1 4 1 8 1 2 1 4 2 1 4 1 2 1 2
So
4. Remainder riddle
4.1 What is the remainder when you divide
Correct Solution: 6
The pattern for the last digit (which is also the remainder when dividing by 10) is 2, 4, 8, 6, ... repeated.
Every 4th remainder is 6.
As 100 is a multiple of 4, then the remainder for
5. How to See Without Glasses
The video channel “minutephysics” has some great short explanations of scientific mysteries. Take a look at this one about a simple way to fix your eyesight without glasses.
(If you have problems watching the video, right click to open it in a new window)5.1 What is the disadvantage of a pinhole when trying to see clearly?
- You need to have a pin
- You need to have a hole
- The image is relatively dark
- The image is stripy
- The image seems further away
- (Not answered)
5.2 What is another word for a hole?
- Aperture
- Apparition
- Apartment
- Aperitif
- Appendicitis
- (Not answered)
6.
6.1 Each letter in the abbreviation UKMT is rotated through 90° clockwise.
Which of the following could be the result?
- A
- B
- C
- D
- E
- (Not answered)
In A, the letter T is incorrect; in B it is U which is incorrect; in C and D the incorrect letters are M and K respectively.
And that’s it for this academic year. I hope you’ve enjoyed doing Parallel this year and make sure you come back in September, when we will have another year of Parallelograms.
But, before that, a few important points.
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...
- 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.
- This was our last Parallelogram of the year, but be sure to come back in September for more puzzles and problems.
Cheerio, Simon.