Being resourceful

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

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?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Like a bit of help getting into the game? Then have a look at this.

If you'd like to explore the game freely, without any nudges from us, choose this version.

Want some suggestions about where to go next with the game?

Here we offer some suggestions about how you could take the Approaching Midnight game further.

Want a serious challenge? Have a look at these ideas for changing the Approaching Midnight game.