Parallelogram 47 • Level 1 • 24 Jul 2025Monkey Multiplication
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.
Chris Smith is a maths teacher with a very interesting toy.
It is a monkey that does your times tables for you! Clever monkey, eh?
Watch the video for a demonstration of how the toy works, and see if you notice any interesting patterns in the grid of numbers:
(If you have problems watching the video, right click to open it in a new window)1.1 How does the monkey carry out the multiplication?
- It uses Artificial Intelligence
- It is just a monkey-shaped electronic calculator
- You drag its two feet to the numbers you wish to multiply and the answer shows in its hands
- You simply ask the monkey to do a multiplication and the correct answer lights up
- (Not answered)
1.2 What is true of the series of rightmost numbers in each row?
- They are the counting numbers, starting at 2
- They are random numbers
- They are prime numbers
- They are square numbers
- (Not answered)
1.3 How many numbers are there in the grid?
- 72
- 78
- 100
- 144
- (Not answered)
There are 12 numbers in the top row, then 11 in the next row, then 10 in the next row, and so on.
There are 12 numbers in the top row, then 11 in the next row, then 10 in the next row, and so on.
The total amount of numbers is therefore 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 78.
This corresponds to how many different products you can find in the times tables up to 12 (where
1.4 Which of the following describes the monkey’s process for working out the product 5 × 7?
- Find the row containing the 5 and count along the row until you get to the 7th space
- Find the row containing the 7 and count along the row until you get to the 5th space
- Find the 5 and go along its diagonal until you get to the 7th space
- Find the 7 and go along its diagonal until you get to the 5th space
- (Not answered)
For each diagonal starting with a number
For each diagonal starting with a number
Therefore, to compute 5 × 7 we need to find the larger number, 7, and then go up its diagonal until we get to the fifth space, which gives the answer to 5 × 7.
2. Odd numbers and uneven tables
2.1 Astrod adds up all the positive odd numbers under 100 and gets a total of 2,500.
Steven then adds up all the positive even numbers up to and including 100.
What total should he get?
- 2,500
- 2,502
- 2,540
- 2,550
- 2,600
- (Not answered)
They both add up 50 numbers, but for each of Astrod’s numbers, Steven has a number that is larger by 1
They both add up 50 numbers, but for each of Astrod’s numbers, Steven has a number that is larger by 1.
Therefore Steven’s total is 50 more than Astrod’s total.
2.2 In the left-hand diagram below, a table stands on piles of three bricks. The height of the top of the table is 150 cm above the ground.
In the right-hand diagram, the same table stands on the floor, but with one brick on top of it.
The distance from the top of the brick to the floor is 140 cm.
What is the actual height of the table?
- 120 cm
- 125 cm
- 128 cm
- 130 cm
- 135 cm
- (Not answered)
In terms of the height, adding an extra 2 bricks on the left contributes a total of 10 cm.
In terms of the height, adding an extra 2 bricks on the left contributes a total of 10 cm.
Therefore each brick has a height of 5 cm.
Since the table and a single brick have a height of 140 cm (from the diagram on the right), the table must contribute a height of 135 cm.
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...
- 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.
- 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.
- This was our last Parallelogram of the year, but be sure to come back in September for more puzzles and problems.
Cheerio, Simon.