Parallelogram 14 • Level 1 • 7 Dec 2023Googolplexed
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. With great power comes great responsibility
A number so large the mind boggles, its impossible to write it all down, and if you tried you would become googley eyed - yes, its the googolplex!
Watch this video where Tony Padilla and Ria Symonds try to explain just how ginormous this number is.
(If you have problems watching the video, right click to open it in a new window)1.1 How many zeros does a googol have?
- ten
- one hundred
- one thousand
- one million
- (Not answered)
A googol is 10100 so it has 100 zeros
1.2 How many zeros does a googolplex have?
- one hundred
- ten hundred
- a googol
- one hundred million
- (Not answered)
A googolplex is 10a googol, so it has a googol zeros.
1.3 Which of these represents a million?
10 3 10 4 10 5 10 6 - (Not answered)
A million has six zeros, so 1,000,000 can be written as
1.4 How many zeros are left after you divide a Googolplex by a Googol?
- none
- a Googol
- a Googol - 100
- one
- (Not answered)
To divide numbers with indices we can subtract the index.
Think about
Now consider what it would look like in index form,
it is as if we have subtracted the indices.
Now apply this to a googolplex divided by a googol:
10a googol / 10100 = 10a googol - 100.
2. I've Got The Power!
Try these past UKMT Primary Maths Challenge puzzle questions:
2.1 You are given that
What is the value of
- 2
- 3
- 4
- 6
- 8
- (Not answered)
After doing the substitution we have the equation:
so
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.