Parallelogram 19 Level 1 11 Jan 2024Lucky numbers

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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. How lucky is your lucky number?

Different countries and cultures have different lucky numbers, you might even have your own!

Watch this video as Dr Ria Symonds shows us a particularly lucky set of numbers which dodge her number seive.

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

1 mark

1.1 Are all lucky numbers prime?

  • Yes
  • No
  • (Not answered)
2 marks

1.2 31 is a lucky number, and it is also prime.

On top of that it is an emirp (prime backwards) because the number when the digits are reversed, 13, is also prime.

Which of these numbers is NOT also an emirp?

  • 17
  • 37
  • 71
  • 53
  • (Not answered)
2 marks

1.3 The number 4 is considered lucky in many places (other than Dr Symond’s list).

The number of letters in the word FOUR is equal to its numerical value.

For how many other single-digit numbers is this true?

  • 0
  • 1
  • 2
  • 3
  • 4
  • (Not answered)
2 marks

1.4 What is the difference between the largest single-digit prime number and the smallest three-digit prime number?

  • 94
  • 95
  • 96
  • 97
  • 98
  • 99
  • (Not answered)

2. On a roll

2 marks

2.1 You would have to be lucky to win a coin toss, and roll a 6 on a standard dice at the same time.

What is the probability of this happening?

  • 1 in 100
  • 1 in 36
  • 1 in 12
  • 1 in 3
  • (Not answered)

The probability of wining a coin toss is 12.

The probability of rolling a 6 on a standard dice is 16.

So the combined probability of both of these independet events happening is 12×16=112.

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.