Week 2The Melancoil

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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.

Welcome to the second of our Parallelograms designed for Year 7 students, a collection of mathematical challenges designed to stretch your brain and make your neurons more squiggly.

These challenges are a random walk through the mysteries of mathematics. Be prepared to encounter all sorts of weird ideas, including some questions that have nothing to do with mathematics.

  • 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.

IMPORTANT – it does not really matter what score you get, because the main thing is that you think hard about the problems... and then look at the solution sheet to see where you went wrong, and then next time you’ll know what to do.

1. Melancoil Numbers

Last week we looked at happy numbers. If you have not completed last week’s Parallelogram, then take a look at it after you complete this week’s list of questions. Remember, you can still earn reward points on a past Parallelogram.

This week, Matt Parker takes a look at melancoil numbers, the opposite of happy numbers. Watch carefully and answer the questions below. By the way, melancoil is partly derived from the word “melancholy”, which means a sense of sadness.

1 mark

1.1. 13 is a happy number. Which of the following is very obviously also a happy number?

  • 12
  • 14
  • 26
  • 31

Of course 31 is happy, because it has the same digits as 13, but reversed. Happiness is about the digits, not the order they appear in. 32 + 12 = 10. And 12 + 02 = 1.

2 marks

1.2. How many numbers are in the melancoil?

  • 7
  • 8
  • 9
  • 10

Just take a look at Matt’s video. The melancoil is described from 3 minutes 30 seconds onwards.

2 marks

1.3. Which statement seems to be true from Matt’s diagram?

  • Most 2-digit numbers are linked to the happification tree.
  • Most 2-digit numbers are linked to the melancoil.
  • 2-digit numbers are equally likely to be linked to the happification tree or the melancoil.

A quick look at Matt’s diagram shows that most 2-digit numbers (roughly 80%) link to the melancoil.

2. A very silly song with a very silly maths joke

One of my favourite bands is Barenaked Ladies. Now that some of the band members have become parents, they have written some songs for children, including this song aimed at 5-year-olds and silly mathematicians like me. Have a listen and answer the question below.

2 marks

2.1 The song has the lines:

“Once upon a time in our solar system,
We couldn't make do without 9,
But Pluto's not a planet now,
So 8 will do fine.”

Why is Pluto no longer classified as a planet? You will probably have to Google this.

  • Pluto is made of gas, not rock.
  • Pluto does not have any moons.
  • Pluto is too far from the Sun.
  • Pluto is a comet.
  • Pluto has a messy neighbourhood.

A planet must be round and orbit the Sun, two conditions satisfied by Pluto. However, there is a third condition, that Pluto fails to meet: a planet should have cleared its orbit of any junk, because its gravity should be big enough to sweep up any nearby space rocks.

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 What is the value of ((1−1) −1) − (1− (1−1))?

  • -2
  • -1
  • 0
  • 1
  • 2

We have ((1−1) −1) − ((1− (1−1)) = (0 −1) − (1− 0) = (−1) − (1) = −2 .

If you missed the first Parallelogram, then try to go back and complete it. 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.