Being resourceful - algebra

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

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

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

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?

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?

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

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

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 develop a strategy to work out the rules controlling each light?