### 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.

# Find the Robber

##### Stage: 3 and 4

This resource is part of "Dotty Grids - Exploring Distance"

Can you help the police locate the robber?

The robber is hiding at a crossroads in a modern city, where the roads are all at right angles and equally spaced.

Choose coordinates where you think the robber might be hiding. The interactivity tells you the shortest distance to the robber, travelling along the roads.

Try to find the robber using only a few guesses.

This text is usually replaced by the Flash movie.

Can you guarantee to always find the robber in less than five guesses? Can you do better than this?

How would your strategy change if the robber were allowed to move 1 block after each guess?

Can you think of any other mathematically interesting variations of the game?

To play a similar game in three dimensions, take a look at Find the Metagiff.

Want to share what you've done? Got any interesting questions or ideas?