Being resourceful

Charlie has moved between countries and the average income of both has increased. How can this be so?

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

Can you match up these equivalent algebraic expressions?

Can you work out the probability of winning the Mathsland National Lottery?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

Which numbers can we write as a sum of square numbers?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

What is special about the difference between squares of numbers adjacent to multiples of three?