Parallelogram 46 • Level 3 • 17 Jul 2025Chess conundrum
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.
1.1 All of the Forty Thieves were light-fingered, but only two of them were caught red-handed.
What percentage is that?
- 2
- 5
- 10
- 20
- 50
- (Not answered)
2.
2.1. Mr Owens wants to keep the students quiet during a Mathematics lesson. He asks them to multiply all the numbers from 1 to 99 together and then tell him the last-but-one digit of the result.
What is the correct answer?
- 0
- 1
- 2
- 8
- 9
- (Not answered)
As 2, 5 and 10 are all factors of the correct product, this product is a multiple of 100. So the last digit and the last-but-one digit are both zero.
3.
3.1 One of the examination papers for Amy’s Advanced Arithmetic Award was worth 18% of the final total. The maximum possible mark on this paper was 108 marks.
How many marks were available overall?
- 420
- 480
- 540
- 560
- 600
- (Not answered)
As 108 marks represented 18% of the final total, 6 marks represented 1% of the final total. So this total was 600.
4.
4.1. In the diagram on the right,
What is the value of
- 20
- 25
- 30
- 35
- 40
- (Not answered)
Since
Since
As
So
As
Consider the interior angles of triangle
So
5. Can You Solve This Chess Conundrum?
This puzzle was featured on the BBC TV show “QI”. First, you need to know that the knight in chess moves in an L-shape, as shown in the image below. “L” means 2 squares left/right and 1 up/down, or 2 up/down and 1 left/right. The below diagram shows all of the spaces the knight could move to next.
5.1 What is the maximum number of knights that you can place on a chess board (8 x 8 squares), so that none of the knights can take any other knight?
Correct Solution: 32
When a knight starts on a black square, what colour squares can it attack? Only black? Only white? Black and white?
This QI clip explains why the answer is 32 knights.
(If you have problems watching the video, right click to open it in a new window)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.