Parallelogram 44 • Level 2 • 3 Jul 2025Bananas and monkeys

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.
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.

1 mark

1.1. What is the value of 0.1+0.2+0.3×0.4?

0.24
0.312
0.42
1.0
1.5
(Not answered)

0.1+0.2+0.3×0.4=0.3+0.12=0.42.

2.

2 marks

2.1 What is the remainder when 354972 is divided by 7?

1
2
3
4
5
(Not answered)

Note that 7 divides 35, 49 and 7, so it divides 354970. So the remainder is 2.

3. Bananas

Here is a tweet that caught my eye:

It turns out a major new study recently found that humans eat more bananas than monkeys.

I can't remember the last time I ate a monkey.

(from Charina91)

3 marks

3.1 How many bananas do humans eat each year?

100 thousand
100 million
100 billion
100 trillion
(Not answered)

4.

4 marks

4.1. Which of the following has the largest value?

12 + 14
12 - 14
12 × 14
12 ÷ 14
14 ÷ 12
(Not answered)

The values of the five expressions are:

12 + 14 = 34
12 - 14 = 14
12 × 14 = 18
12 ÷ 14 = 2
14 ÷ 12 = 12

So 12 ÷ 14 has the largest value.

5.

5 marks

5.1. The sculpture ‘Cubo Vazado’ [Emptied Cube] by the Brazilian artist Franz Weissmann is formed by removing cubical blocks from a solid cube to leave the symmetrical shape shown.

If all the edges have length 1, 2 or 3, what is the volume of the sculpture?

9
11
12
14
18
(Not answered)

Consider the sculpture to consist of three layers, each of height 1. Then the volumes of the bottom, middle and top layers are 5, 2, 5 respectively. So the volume of the sculpture is 12.

Alternatively: the sculpture consists of a 3×3×3 cube from which two 2×2×2 cubes have been removed. The 2×2×2 cubes have exactly one 1×1×1 cube (the cube at the centre of the 3×3×3 cube) in common. So the volume of the sculpture =27−2×8−1=12.

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.