Parallelogram 34 Level 1 25 Apr 2024Self-descriptive numbers

This is a preview of Parallel. You have to login or create an account, to be able to answer questions and submit answers.

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. What's your favourite Mega-Large Number?

Stand up mathematician, Matt Parker, put out a call for people’s favourite mega-large numbers.

Check out this response from Maths Teacher Chris Smith.

Can he convince you that this is one of the best large numbers out there?

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

1 mark

1.1 What number is missing from this seven digit self-descriptive number?


  • 1
  • 2
  • 3
  • 4
  • 5
  • (Not answered)

The missing number was in the "how many 3s column" and there is one 3 in the number.

So the full self-descriptive number is 3211000

  • 3 zeros
  • 2 ones
  • 1 two
  • 1 three
  • 0 fours
  • 0 fives
  • 0 sixes

So neat!

2 marks

1.2 Which of these numbers also has the self- descriptive property?

  • 1100
  • 21200
  • 2002
  • 123332
  • (Not answered)
3 marks

1.3 Can you find an eight digit self-descriptive number?

Some of the digits are given to help you get started.

Correct Solution: 42101000

Show Hint (–1 mark)
–1 mark

Since the number starts with a 4, we know there are four 0s to be placed.

The position of the one lets us know that there is a 2 which needs to be placed.

There is also at least one 4, so we can update the “how many 4s” column.

Now try to place the four 0s and the 2 in a way that keeps it self descriptive.

2. Some curiosities

2 marks

2.1 Maisie was telling me her mobile phone number but she sneezed in the middle.

She said it was divisible by 9.

I got her number as: 07922?03441.

Which of these numbers could replace the unknown number?

  • 1
  • 2
  • 3
  • 4
  • 0
  • (Not answered)
Show Hint (–1 mark)
–1 mark

If a number is divisible by 9 then the sum of it's digits is also divisible by 9.

Try adding up the digits and see how much more you would need to reach a multiple of 9.

2 marks

2.2 A number could be called self-descriptive for another reason, namely if the number has the same number of letters as the number itself.

Which is the only self-descriptive number according to this definition?

It is not ONE, because it has three letters, not one letter.

And it is not TWELVE, because it has six letters, not twelve letters.

  • 2
  • 3
  • 4
  • 7
  • (Not answered)

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.