Parallelogram 35 • Level 5 • 2 May 2024Pi

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.
When you finish, remember to hit the SUBMIT button.
Finish by Sunday night 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 examine the solution sheet to learn from your mistakes.

1. Dihydrogen Monoxide

Here is an important video about the chemical dihydrogen monoxide.

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

2 marks

1.1 Should you sign a petition to ban dihydrogen monoxide?

Yes, ban it.
No, don’t ban it.
Not sure – I need more information.
(Not answered)

You might need more information, but you really should know that dihydrogen monoxide is simply water, H₂0. If you’re confused, then just rewatch the video above (everything is true) or this other video.

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

2. Intermediate Maths Challenge Problem (UKMT)

3 marks

2.1. Which of these numbers is biggest?

19×99
199×99
1999
19×99
1999
(Not answered)

19×99 and 199×99 are both less than 1992 and hence less than 1999; 99<1999; 1999=19=1.

3. Intermediate Maths Challenge Problem (UKMT)

4 marks

11.1 "20% off everything", screamed the sale poster. I paid £60. What would I have paid before the sale?

£60
£66
£72
£75
£80
(Not answered)

Let the original price be £x. Then 0.8x = 60, therefore x = 60 ÷ 0.8 = 75.

4. Staggering Pi Phenomenon

This is one of the most shocking videos I have ever seen. Watch in awe.

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

4 marks

4.1 If the small block is 1 Kg, and you want to calculate 3 digits of π, then what mass would the large block have to be?

1 Kg
10 Kg
100 Kg
1 tonne
10 tonnes
(Not answered)

4 marks

4.2 If the small block is 1 Kg, and you want to calculate 20 digits of π, then what mass would the large block have to be?

Same as the Moon
Same as the Earth
Five times the mass of the Sun
Ten times the mass of a supermassive black hole
Twice the mass of the universe
(Not answered)

All the answers are in the video, but if you want to know more, if you want to know why, then watch this follow-up video... it is hard, but worth a look if you are curious.

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

5. Intermediate Maths Challenge Problem (UKMT)

5 marks

5.1 When exactly is the value of the product 1+121+131+14 ... 1+1n equal to an integer?

when n is odd
when n is even
when n is a multiple of 3
always
never
(Not answered)

Show Hint (–1 mark)

–1 mark

The product = 32×43×54×65× ... ×n+1n.

The product = 32×43×54×65× ... ×n+1n. The numerator of each fraction except the last cancels with the denominator of the next fraction, leaving n+12. This is equal to an integer only when n is odd.

6. Riddle

3 marks

6.1 Two mothers and their two daughters go out for lunch. They order 6 slices of pizza and can share the slices equally between them. How?

There is only one mother.
There is only one daughter.
There is a grandmother in the group
There are six people altogether
They are one person
(Not answered)

If we have a grandmother and a daughter and a grand-daughter, then we have two mothers and two daughters, but only three people.

7. Parallel emails

If you use Parallel on an email address from your school, some school IT systems prevent you from receiving the emails we send out to remind you when a new Parallelogram is released, or when we have another exciting and nerdy maths thing to tell you about. To avoid this, you could give us a different email address we can contact you on - either a personal email address, or one for you parents or guardian. If you'd like to do that, you can put it in this form, but please ask a parent first if you are not yet 13 years old.

1 mark

7.1 If you do want to give us an alternate email address, be sure to click the link above (if you haven’t already). Either way, here's a free mark, just for being a fan of Parallel.

Thank you!
(Not answered)

There will be more next week, 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.

When you see your % score, this will also be your reward score. As you collect more and more points, you will collect more and more badges. Find out more by visiting the Rewards Page after you hit the SUBMIT button.

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.