# Stretch your students this easter... Maths questions

10 March 2014
Hello mathematicians!

Here are some amazing questions to really stretch your students;

1. If you write the numbers one to one million out, how many digits have you written in total?

2. If you drive away from your house at 8mph to an unspecified point, then turn round and immediately drive home again at 10mph, what is you average speed for the journey as a whole?

3. How many different subway sandwiches is it possible to buy? Could you have a different subway every day for the rest of your life?

4. Can you raise an irrational to the power of an irrational and get a rational answer?

5. What is i to the power i?

6. What is the angle between the hands of a clock at 3.15?

7. I run a rope around the equator of the Earth. If I then want to pull it out so that it's one metre from the surface at all points, how much extra rope do I need?

8. I have 12 marbles. One has a different mass to the others, but I don't know whether it's heavier or lighter. I am allowed to use a standard set of weighing scales three times. How do I work out which marble is the one odd out and whether it's heavier or lighter?

9. Prove that the bonding angle in methane is 109.5 degrees (very cross curricular!)

10. If an HIV test is 99% accurate and one in every 10000 people has HIV, what is the probability of you actually having the disease if you test positive?

11. How many people need to be in a room for it to be likely that there is at least one shared birthday amongst those in there?

12. If the probability of winning a single point in tennis is p, what is probability of winning a game?

13. What do you think the world record is for throwing a cricket ball as far as you can and still being able to run after it and catch it?

14. How many zeroes are there at the end of 50!

15. If it takes Bob an hour to mow a lawn and Andy 30 minutes, how long does it take them if they mow it together?

16. In the song 'The twelve days of Christmas' how many presents are given in total? What about if it was 'The n days of Christmas'?

Enjoy!