### 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.

# Getting Round the City

##### Stage: 3 and 4

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

The grid below represents a city laid out in "blocks" with all the roads running north-south, or east-west.
Imagine two friends live where the red and blue dots are on the grid.

The animation shows three paths that one friend could choose if he wanted to visit the other. He likes to find the shortest routes possible, so he always travels north or east, never south or west.

What interesting mathematical questions could you explore on a city grid like this one?

Click below for some ideas.

How many different paths are there from A to B?

If I know the coordinates of two points, can I quickly work out how far I will have to walk to get from one to the other?

Is there a quick way to find all the different paths from one point to another?
Is there a quick way to work out how many different paths there will be?

If I start at a point and only want to walk 6 blocks, how many possible places might I end up?