Being resilient

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 out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Can you match these calculations in Standard Index Form with their answers?

Is it possible to find the angles in this rather special isosceles triangle?

Two ladders are propped up against facing walls. At what height do the ladders cross?

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?