Parallelogram 44 • Level 5 • 3 Jul 2025Ice cream pie charts
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. QI mathematics
Here is a neat video from the BBC show “QI”, which demonstrates a lovely maths trick.
(This trick was mentioned in a Parallelogram last year, but the video clip is a lovely and funny demonstration of the trick, so it is worth watching and following the explanation again.)
(If you have problems watching the video, right click to open it in a new window)To summarise...
- write down a three-digit number whose digits are decreasing and different.
- reverse the digits to create a new number.
- subtract this new number from the original number to get a SUB-RESULT.
- Add the SUB-RESULT to the reverse of itself.
- The final RESULT will always be 1089.
I like how QI turned it into a magic trick, predicting the 10th word on page 89 of a book. You might like to try this trick.
The big mystery is this – why does it work?
If the person picks the number ABC, then the reverse would be CBA, and result of the subtraction would be (100A + 10B + C) - (100C + 10B + A) to get 99(A - C).
Because the digits were decreasing, (A - C) is between 2 and 9, so the result must be 198, 297, 396, 495, 594, 693, 792, or 891.
When you add any one of these numbers to the reverse of itself, the result is always 1089.
2.
2.1 In March 1998, a book called "The Shadow of the East" was returned to a library in Sussex. It had been borrowed on January 3rd 1924! The library charges a fine of 60p per week for overdue books. Approximately how big a fine should the person who returned the book have paid?
- £45
- £180
- £230
- £2200
- £16000
- (Not answered)
The fine should be approximately 74 × 52 × 60p ≈ 75 × £30 = £2250. Although in reality, the person who returned the book disappeared without paying a fine at all!
3.
3.1 Four wiggles are the same as three woggles; two woggles are the same as five waggles, and six waggles are the same as one wuggle. Which is smallest?
- 1 wuggle
- 2 woggles
- 3 waggles
- 4 wiggles
- two have the same value
- (Not answered)
Try converting everything to waggles.
1 wuggle = 6 waggles;
2 woggles = 5 waggles;
4 wiggles = 3 woggles = 7.5 waggles.
All are therefore greater than 3 waggles.
4.
4. An ice cream stall sells vanilla, strawberry and chocolate ice creams.
The pie chart illustrates the sales of ice cream for last Saturday.
The number of vanilla and the number of chocolate ice creams sold were the same.
The stall sold 60 strawberry ice creams.
How many chocolate ice creams were sold?
- 90
- 99
- 100
- 120
- 135
- (Not answered)
The angle occupied by the 'chocolate' sector is
5.
5.1 My bargain settee cost me £240 in a sale offering 25% reductions on all items. How much did I save?
- £25
- £40
- £60
- £80
- £100
- (Not answered)
The sale price is 75% of the original price. Therefore the amount I saved, 25% of the original price, is one third of £240, ie £80.
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.
Cheerio, Simon.