Parallelogram 28 • Level 1 • 14 Mar 2024Number knights
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. A puzzle you can use your calculator for!
Watch this video of where maths teacher and author, Chris Smith, takes chess knights out of their normal realm and into the world of numbers.
Pause the video when prompted and give yourself three minutes to think about the puzzle before watching the answer!
(If you have problems watching the video, right click to open it in a new window)1.1 Starting from the 6, where can the knight move to?
- 8 and 2
- 7 and 1
- 3 and 9
- 0 and 7
- (Not answered)
1.2 Which button only has one available move when the knight is placed on it?
- 5
- 0
- 3
- 7
- (Not answered)
1.3 Using the digits 1, 2, 3 and 4 exactly once, along with the four operations add, subtract, multiply and divide - and () if you need them - what is the largest number you can make?
For example, (1 + 2 + 3) × 4 = 24, but I am sure you can do better than that!
- 25
- 30
- 36
- 42
- (Not answered)
At first you may think of multiplying them all together 1 × 2 × 3 × 4 = 24, but then notice that the 1 is not adding value to this sum.
We could then multiply all of the numbers and then add the 1: 2 × 3 × 4 + 1 = 25
But we can do even better!
It is possible to make 36 by adding the 1 to the 2 first, and then multiplying: (1 + 2) × 3 × 4 = 36
2. Cube Loop
Chris Smith, Scotland’s nerd in shining armor, also noticed a peculiar property of the number 136.
If you cube the digits then add them, you get 244:
1 3 + 3 3 + 6 3 = 244
And then if you follow the same process with 244, you get back to 136!
2 3 + 4 3 + 4 3 = 136
2.1 Which of the following numbers have the same property?
- 616
- 666
- 919
- 999
- (Not answered)
2.2 This same process can even form a loop of 3.
1 3 + 6 3 + 0 3 = 352 3 3 + 5 3 + 2 3 = 217 2 3 + 1 3 + 7 3 = 160
Which of the following numbers also creates a loop of 3 when the digits are cubed and added?
- 55
- 66
- 77
- 88
- (Not answered)
-
5 3 + 5 3 = 250 -
2 3 + 5 3 + 0 3 = 133 -
1 3 + 3 3 + 3 3 = 55
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.