Parallelogram 5 • Level 1 • 5 Oct 202310!

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. 10!

We’re not shouting 10 at you! Although we are always excited about numbers, that’s not quite what we mean when using that exclamation mark.

Watch this video to find out the Mathematical meaning behind 10!

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

Now you might be able to get this joke:

2 marks

1.1. How could you calculate 5!

2 marks

1.2. How many seconds are there in 12 weeks?

2 marks

1.3. Three pieces of fruit are sitting on a shelf: an apple, a banana, and a coconut.

How many different ways are there to arrange them on the shelf?

There are 6 different ways to arrange 3 objects. You might notice that 3×2×1=6.

So to arrange 4 objects, you could do 4!=4×3×2×1=24.

There are 24 different ways to arrange 4 objects.

2 marks

2.1. If the numbers 5, 10, 15 and 20 are all multiplied together, how many zeros are at the end of the answer?

Correct Solution: 3 zeros

You can think about splitting the 15 and 20 up into factors, 5×10×3×5×2×10, then grouping the 5×2 to give another 10.

Multiplying by three tens will give us three zeros at the end of the answer.

2 marks

2.2. Four different whole numbers multiply to give 100 (which means that A×B×C×D=100). What is their sum?

Correct Solution: 18

Show Hint (–1 mark)

–1 mark

All the numbers are positive, whole numbers.

You might want to think about the factors of 100.

The four different whole numbers which multiply to give 100 are 10×5×2×1=100, but the question asks for the sum of those numbers, so 10+5+2+1=18.

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.