Can you solve it? Are you smarter than a Singaporean 10-year-old?

It’s raining mental arithmetic Photograph: Alamy

Hi guzzlers,

On Tuesday we will again learn how much better Asian children are at maths, science and reading than we are with announcement of the OECD’s Pisa rankings, which compare the abilities of 15-year-olds from around the world.

In the last two Pisa tables, in 2009 and 2012, the top three countries for maths were Shanghai*, Singapore and Hong Kong*, and this year’s results are expected to be the same or similar.

(*Yes, OK, not countries, but I didn’t make the rules.)

Even though many educationalists are cautious about what we can infer from international comparisons, they are a major reason why the UK government recently announced £41m funding for primary schools to copy the east Asian approach to maths teaching.

But just how good are these Asian kids? Today I am setting you ten questions from this year’s International Singapore Maths Competition, aimed at primary Years 5 and 6. (That’s kids aged 10-11 and 11-12). The questions are all based on Singapore’s much lauded maths syllabus, which aims to teach fewer topics in greater depth. I think you will be impressed at the level of these problems, and many adults may find them quite challenging!

The children taking these tests had a total of 25 questions to answer in 90 minutes. They did not have the multiple choice responses, but had to work everything out by themselves. They were, however, allowed to use calculators.

Make a note of your answers since the form will not give you a score but instead give you the answers. I will collate your submissions so when I post full explanations of the answers at 5pm GMT you can see how well you did compared to everyone else. [The percentage in square brackets is the percentage of Singaporean schoolchildren expected to get the right answer.]

UPDATE: The interactive element has ended but you can still answer the questions below.

For Year 5 pupils:

1. Mary cut off 2/5 of a piece of string. Later, she cut off another 14 m. The ratio of the length of string remaining to the total length cut off is 1 : 3. What is the length of the remaining string?

• A. 5 m
  
• B. 7 m
  
• C. 10 m
  
• D. 14 m

2. The areas of the faces of a rectangular box are 84 cm², 70 cm² and 30 cm². What is the volume of the box?

• A. 300 cm³
  
• B. 420 cm³
  
• C. 490 cm³
  
• D. 504 cm³

3. There are four numbers. If we leave out any one number, the average of the remaining three numbers will be 45, 60, 65 or 70. What is the average of all four numbers?

• A. 50
  
• B. 55
  
• C. 60
  
• D. 65
  

4. A march goes through the streets from the School (S) to the Community Centre (CC). One of the streets is closed. If the march can only travel East or South, what is the number of different possible ways to get to the Community Centre? [10 per cent]

• A. 16
  
• B. 19
  
• C. 20
  
• D. 22
  

5. Sally was given a set of 5 cards numbered 1 to 5 and Peter was also given a set of 5 cards numbered 1 to 5. They were then blindfolded and told to pick a card from their respective sets. The sum of the numbers from the two cards was told only to Sally and the product of the numbers was told only to Peter. They were then told to guess the two numbers. Below is what each of them said:

Peter: I do not know the two numbers.

Sally: Now I know the two numbers.

Peter: I still don’t know the two numbers.

Sally: Let me help you. The number I was told is larger than the number you were told.

Peter: Now I know the two numbers.

What are the two numbers?

• A. 1 and 4
  
• B. 1 and 5
  
• C. 2 and 4
  
• D. 2 and 5

For Year 6 pupils:

6. There are 4 keys and 4 locks. What is the maximum number of times you need to try the locks so as to match all 4 keys to their locks?

• A. 4
  
• B. 6
  
• C. 10
  
• D. 16

7. In the diagram (not drawn to scale), the sloping line divides the area of the rectangle in the ratio 1 : 6. What is the ratio a : b?

• A. 2 : 3
  
• B. 1 : 2
  
• C. 2 : 5
  
• D. 1 : 3
  

8. What is the number of times the hour hand and the minute hand of a clock form a right angle with each other between 0600 and 1200 on the same day?

• A. 11
  
• B. 12
  
• B. 12
• D. 24
  

9. There are 240 Primary 6 students. The ratio of the number of students who like Science to the number who do not is 5 : 3. The ratio of the number of students who like Mathematics to the number who do not is 7 : 5. The number of students who like both Science and Mathematics is 86. How many students dislike both Science and Mathematics?

• A. 32
  
• B. 36
  
• C. 40
  
• D. 48

10. My teacher had 3 big boxes of sweets. Each box contained sweets of a different colour. Each pupil was given 5 sweets of two different colours. If each pupil in the class received a different combination of colours. What was the largest possible number of pupils in the class?

• A. 8
  
• B. 12
  
• C. 16
  
• D. 64

UPDATE: If you want to find the answers, they are now available here.

If you like puzzles - or are facing the eternal conundrum about what to get a puzzle-lover for Christmas - you may enjoy my latest book, Can You Solve My Problems? A Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles. Available from the Guardian Bookshop and other retailers.