In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

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?

How many moves does it take to swap over some red and blue frogs? Do you have a method?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Can you find the values at the vertices when you know the values on the edges?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Can you find a way to identify times tables after they have been shifted up or down?

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Can you find the hidden factors which multiply together to produce each quadratic expression?

Where should you start, if you want to finish back where you started?