### 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 Taking it Further

##### Stage: 2 and 3

If you are fascinated by the structure of the Approaching Midnight game, you could look at what happens if you use numbers or counters instead of a clock.

Can you generalise the structure of this game?

 What did you have to do to be able make connections between the clocks, counters and numbers? What did you have to do to be able to generalise? What was it about 'playing around' that helped you to generalise?

Let us know your thoughts here.

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