Being curious

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

There are nasty versions of this dice game but we'll start with the nice ones...