Parallelogram 2 • Level 3 • 14 Sep 2023Jurassic Park mathematics

Welcome to the second of our Parallelograms, 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. More on the number 6,174

Last week we looked at 6,174, the Kaprekar constant. 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.

As well as being the Kaprekar constant for 4-digit numbers, the number 6,174 has a few interesting qualities. For example, it equals (18¹ + 18² + 18³), which is (18 + 324 + 5,832).

6,174 is also known as a harshad number, because it is divisible by the sum of its digits:

6,174 = (6 + 1 + 7 + 4) x 343.

The number 18 is another harshad number, because it is also divisible by the sum of its digits:

18 = (1 + 8) x 2.

By the way the word "harshad" comes from the ancient Indian Sanskrit language and it means joy-giver. So, I hope they are giving you at least a tiny bit of joy.

2. Jurassic Park mathematics

Jurassic Park is one of Steven Spielberg’s most famous films, and it is based on the idea that biotechnology could use preserved DNA to bring dinosaurs back to life. However, one of its main characters is a mathematician, Dr Ian Malcolm (played by Jeff Goldblum), who specializes in a branch of mathematics known as "Chaos Theory". He tries to explain chaos theory in this clip (but he does not bother discussing the mathematical equations behind chaos theory).

3. Junior Maths Challenge Problem (UKMT)

If you are a Year 8 student, then it 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 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.

4. Parallel Circles

Parallel Circles, our weekly online maths sessions with bestselling science author Simon Singh, Countdown champion Junaid Mubeen and a range of guest speakers, start next week.

We have Circles designed for each Level of Parallel, and the best session for you to join is our Level 3 Parallel Circle.

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.