### Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

### Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

### Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

# Approaching Midnight Get Started

##### Stage: 2 and 3
Have a go at this game using the full screen version.

 Full screen version Want to see part of a game being played? This text is usually replaced by the Flash movie.      Full screen version

Can you find a winning strategy?

Have a go yourself, or if you'd like some ideas, click below.

How can you be sure you can always win?

How elegantly can you explain your winning strategy to someone else?

 What is it about this game that you've enjoyed? What elements of the game do you find engaging? What do you think makes a good game?

Let us know your thoughts here.

What next?