### 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 the Ultimate

##### Stage: 2 and 3
What would happen if we introduced further complexity to the Approaching Midnight game, such as players get to pick which steps they use from a pool and then that step cannot be used again? Would this make a good game?

You may like to explore this idea or one of your own.

If you would like to see other ideas we have thought of to explore, click below:

2D – could you play a version of the game going down a staircase rather than on a straight line?

Try playing a sequence of games with different start times (pre-declared) and the loser of each round gets to pick who goes first in the next round.

A random number is added to the step that you choose.

 What do you think is an effective way to introduce further complexity that makes for a good game? How do you define a good game?

Let us know your thoughts here.