Please take part in our weekly maths challenge, with problems and puzzles posed by Gordon Burgin, Andrew Holt and the U3A Maths and Stats Subject Adviser - David Martin.

If you would like to share your ideas on how to solve these puzzles please join our learning forum or discuss within your U3A and interest group. **Check back this time next week for the solutions** and let us know how you get on by contacting National Office. New maths puzzles will go up onto the website every Thursday for the next six weeks.

Week One

#### Question 1

My family travelled to Scotland from our home in Nottingham in two cars. I am a slower driver at an average speed of 40 m.p.h. while my wife set off on the same route an hour later at an average speed of 50 m.p.h. How far had we travelled before my wife overtook me?

#### Question 2

How many squares are there in this diagram?

#### Question 3

Visiting a U3A friend, Ina, the other day I’d forgotten the number of her house.

Quite unfortunate as the street she lives in has about 300 houses. At least I

could eliminate the first dozen as they are all shops. I feared I would have to

visit each house in turn, but then I remembered that at a previous ‘Maths for

Fun’ meeting Ina had said that her house number left remainders of 1 when

divided by each of the first four primes (2, 3, 5 and 7). I never thought that this fact would come in handy then. What is the house number I am looking for?

#### Question 4

I have 10 sq. cm. of metal and need to construct a box with a square base (including both its top and bottom). What is the maximum volume of box I can construct?