Parallelogram 3 • Level 1 • 21 Sep 2023Use maths to tie your shoes fast

Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

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. Why waste time when you could use maths?

Watch this Numberphile video showing a super fast way to tie your shoes

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

2 marks

1.1 What was the name of Matt's "base knot", which had a minimum of three crossings?

The Trefoil Knot is the simplest non-trivial prime knot, it has been depicted in stone carvings and in art throughout human history.

2 marks

1.2 Before the loops are passed over to the other hand they must be going:

2 marks

1.3 This Trefoil Knot has three "crossings"

What is the combined total of the crossings of these knots?

Correct Solution: 18 crossings

From tying your shoelaces, to cutting a cake, to finding the quickest route on Google Maps, Maths can be used to make life easier and more efficient.

2 marks

2.1 You are organising a charity BBQ.

Veggie patties are sold in boxes of 9, but the buns are sold in packs of 12.

What is the smallest amount of assembled burgers you can make so that there will be no patties or buns left over?

Correct Solution: 36 veggie burgers

2 marks

2.2 Maths can even be used to make Maths easier!

One of these numbers can be divided by 4 to give a whole number. Without doing the division, can you tell which one?

(Hint: you only need to look at the last two digits)

If the last two digits of a number are in the 4 times table then the whole number is divisible by 4, no matter how big it is!

There are some big changes to the Parallel Universe, so here is a quick message from Simon.

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

2 marks

3.1 In the video, Simon talks about Parallel maths circles (you can find out more about maths circles here).

According to Simon, how many maths circles are available to join for free on the Parallel website every week?

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.