Parallelogram 11 Level 1 16 Nov 2023Year of the mathematician

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. 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. Why 1980 was a great year to be born but 2184 will be better

Any year is a good year to be alive, but some are more mathematically interesting than others.

Watch this video where mathematician Matt Parker explains why 1980 was the second best year to be born (although he is biased).

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

1 mark

1.1 What is the best thing about the year 2025?

  • It's a leap year
  • It's 452 and people born in 1980 will turn 45
  • Microsoft will retire the use of Windows 10
  • The World Men’s Handball Championship will be held in Croatia
  • (Not answered)

The year 2025 is a square number, it is in fact 452 so anyone who was born in the year 1980 will celebrate their 45th birthday in the year 452.

2 marks

1.2 When is the next power of 2 year?

  • 2048
  • 2222
  • 2040
  • 2024
  • (Not answered)
2 marks

1.3 At what ages will people born in 2184 be a root of their current year?

  • age 1, age 2, and age 4
  • age 3, and age 9
  • age 3, and age 13
  • age 4, and age 16
  • (Not answered)

For people born in 2184, they will turn 3 in 2187 and 2187 = 37.

But that's not all! When these mathematically lucky babies turn 13 the year will be 2197 and 2197 = 133.


2 marks

1.4 What is the only non-zero number with the property that its square root is equal to its half?

  • 2
  • 4
  • -4
  • 81
  • (Not answered)
Show Hint (–1 mark)
–1 mark

Think about which of these numbers have an integer square root.

Is the root the same as halving the original number?

2. Time for a past UKMT challenge question!

3 marks

2.1 Abi, Brenda, Clair, Denise and Erin are friends who always eat school dinners together.

They decide that each school day they will line up in a different order.

There are 5 days in every school week.

How long can they do this before they have to repeat an order they have used before?

  • 1 week
  • 5 weeks
  • just over 11 weeks
  • 24 weeks
  • over 100 weeks
  • (Not answered)
Show Hint (–1 mark)
–1 mark

To find the number of ways to order a group of items, consider putting 3 books on a shelf: A, B and C.

There are three options for the first book.

Once that has been picked, there are only two options for the second book.

Then after the first two books are picked there is only one choice left for the final book being placed on the shelf.

This gives us 3×2×1=6 different options.

Try thinking about using this method for 5 things being ordered.

To put the 5 friends in order, there are 5 options for who will stand at the front of the queue. Once they are in place there are 4 options for who will stand behind them, then 3 options after that and so on.

So there are 5×4×3×2×1=120 different orders for the friends to stand in.

Since there are 5 days in the school week 120÷5=24weeks

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 and Ayliean.