Are We Nearly There?

Take some time to look at the route followed by the arrows in the diagram below:
Arrows following route (1,1) (1,2) (2,1) (3,1) (2,2) (1,3) (1,4)...

Look away and try to visualise the route.

Try saying out loud the coordinates that are visited in order. Notice any patterns?


Here are some questions you might like to consider:

If the pattern of arrows continues for ever, which point will be the 100th to be visited?

How many steps will it take to reach (60,40)? Where will the next step take you to?

Can you find a method to work out how many steps it takes to get to any point?

Are there alternative routes that visit all the points on a grid?




Hannah sent us a lovely solution, which you can see here.