Week 4Matt’s Favourite Number

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. a portmanteaux 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.
  • When you finish, remember to hit the SUBMIT button.
  • Finish by midnight on Sunday if your whole class is doing parallelograms.
  • Make sure you check the solution sheet, celebrate your successes and (most important of all) learn from your mistakes.

1. Matt’s favourite number

Maths Inspirations offers lectures each morning and afternoon, aimed at schools across England and sometimes beyond. Here is a clip from one of their lectures, featuring Matt Parker talking about his favourite number… or at least his favourite number that week.

1 mark

1.1. It is possible to regenerate 3,435 by raising each digit to its own power. What percentage of 3,435 is given by raising 4 to its own power?

  • 0.075%
  • 2.6%
  • 7.5%
  • 25.6%
  • 256%
2 marks

1.2. What percentage of 3,435 is given by raising 5 to its own power? Give your answer to 1 decimal place, but do not enter the % sign. So, if you think the answer is 1.1234%, enter 1.1.

Correct Solution: 91.0

2 marks

1.3. Matt talked about some numbers, such as 48,625, whereby the digits are written in order and then each digit is raised to the reverse ordered digit power in order to generate the number:

45 + 82 + 66 + 28 + 54 = 48,625.

What difference does reversing the order of the powers make? Does it make the sum bigger or smaller? Consider a 2-digit number XY, where X and Y are different. Which statement is true?

  • XX + YY is always smaller than XY + YX
  • XX + YY is always the same as XY + YX
  • XX + YY is always bigger than XY + YX

This is not a proof, but if you experiment with a few numbers, then you will see that this is the case. For example, 11 + 99 > 19 + 91.

2. The Big Bang explained

Last week’s Parallelogram included the theme tune to The Big Bang Theory, written and performed by the band Barenaked Ladies. Here is a short explanation of the big bang theory for you to watch, and after just a couple of minutes you will have some understanding of where the universe came from, and how we know that the big bang actually happened.

2 marks

2.1 Who invented the name Big Bang?

  • Fred Boyle
  • Fred Doyle
  • Fred Hoyle
  • Fred Foyle
  • Philippe Floppe

3. Junior Maths Challenge Problem

If you are a Year 7 student, then it is likely that you will be taking part in the United Kingdom Maths Trust (UKMT) competition known as the Junior Maths Challenge (JMC). If you do particularly well, you might earn yourself a gold, silver or bronze certificate, but you will have to work hard as you will be competing against Year 7 and Year 8 (!) students from across the country.

Your teachers will help you prepare for this national maths competition, but in each week's Parallelogram we will always include one UKMT Junior Maths Challenge question.

3 marks

3.1 The Grand Old Duke of York had 10 000 men. He lost 10% of them on the way to the top of the hill, and he lost 15% of the rest as he marched them back down the hill.

What percentage of the 10 000 men were still there when they reached the bottom of the hill?

  • 7612%
  • 75%
  • 7312%
  • 6623%
  • 25%

After losing 10% of the men, the Grand Old Duke of York was left with 90% of them. After losing 15% of these, he was left with 85% of the remaining 90% men. So he is left with 85100 × 90100 = 765010000 = 76.5100 of the men he started, that is, 7612% of the original number of men.

If you missed any previous Parallelograms, then try to go back and complete them. After all, you can earn reward points and badges by completing each Parallelogram. Find out more by visiting the Rewards Page after you hit the SUBMIT button.

There will be another Parallelogram next week, and the week after, and the week after that. So check your email or return to the website on Thursday at 3pm.

In the meantime, you can find out your score, the answers and go through the answer sheet as soon as you hit the SUBMIT button below.

It is really important that you go through the solution sheet. Seriously important. What you got right is much less important than what you got wrong, because where you went wrong provides you with an opportunity to learn something new.

Cheerio, Simon.