Parallelogram 24 Level 1 15 Feb 2024Why 7 is weird

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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. Seven and its mysterious multiples

Its easy to tell if a number is divisible by two, the knowledge appears in your brain as if by magic by just looking at the number.

With a little more work you can check if a number is divisible by 3 and so on … apart from seven!

Not to worry, Dr. James Grime has not one, but two weird tricks to help you tell if a number is divisible by seven.

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

1 mark

1.1 How can you tell if a large number is divisible by 7?

  • Multiply the last digit by 5, add it to the rest of the number and see if it is divisible by 7
  • Add the digits, see if it is divisible by 7
  • If the number ends in a 7
  • If the last two digits of the number are in the 7 times table
  • (Not answered)
1 mark

1.2 Which of these sums shows the alternate way to check if 315 is divisible by 7:

  • 3 × 1 × 5
  • 3 + 2 × 15
  • 31 - 2 × 5
  • 31 - 5 × 5
  • (Not answered)
1 mark

1.3 Is 315 divisible by 7?

  • Yes
  • No
  • (Not answered)
3 marks

1.4 If the digits 4, 8 and 7 are randomly placed in the spaces 1_6_2_8 to form a seven digit number - what is the probability that number will be divisible by 18?

  • 16
  • 13
  • 23
  • 1
  • (Not answered)
Show Hint (–1 mark)
–1 mark

To be divisible by 18 a number must be divisible by both 2, and 9.

Use divisibility checks to see if this is the case for the different options.

2. Divide and conquer

3 marks

2.1 Arrange the digits 0 to 9 to create a ten digit number where: the first digit is divisible by 1, the first two digits are divisible by 2, the first three digits are divisible by three, and so on until the ten digit number is divisible by 10.

I’ll start:

  • 3 is divisible by 1
  • 38 is divisible by 2
  • 381 is divisible by 3
  • 3816 is divisible by 4

Continue on to find the ten digit number. Remember you can only use each digit once.

Correct Solution: 3816547290

Show Hint (–1 mark)
–1 mark

To find the 5 digit number divisible by 5, it must end in a 0 or 5.

But since you only get to use each digit 0-9 once, you might want to save the 0 for making a number divisible by 10 later.

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.