### 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 Metagiff

##### Stage: 3 and 4 Challenge Level:

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

You may wish to try Find the Robber before exploring this problem.

In a three dimensional city on a distant planet, the metagiff has escaped from the zoo!
Can you help the sheriff locate the metagiff?

The metagiff is hiding at a point on the three dimensional grid, so his location is specified by three coordinates (x,y,z).

Choose coordinates where you think the metagiff might be hiding. The interactivity tells you the shortest distance to the metagiff, travelling along the grid lines.

Try to find the metagiff using only a few guesses.

This text is usually replaced by the Flash movie.

Can you guarantee to always find the metagiff in less than six guesses? Can you do better than this?

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

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

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