Arithmetic sequences

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

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

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.