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Chess distances

By David, 20 February 2013 Activity

You might think you’ve got a good handle on distance. But not all things measure distance the same way – what if you were a chess piece?

You will need

What you will need.

What you will need.

  • Graph paper – larger squares are better. You can draw your own, or download some graph paper here [PDF, 3kB].
  • Coloured pencils or textas
  • Black marker

What to do

  1. Arrange your pencils or textas in rainbow order – red, orange, yellow, green blue, purple.
  2. Count out a square on your grid paper that is 4 boxes tall and 4 boxes wide. Draw a border around the square with the black marker.
    These are all the moves that a knight can make.

    These are all the moves that a knight can make.

  3. Colour the top left box black. We’re going to be looking at how the knight moves in a game of Chess and this is where the knight will start from.
  4. A knight moves in a sort of ‘L’ shape. It moves two boxes vertically (either up or down) then one box horizontally (left or right). Alternatively, it can move two boxes horizontally then one box vertically. Take the red pencil. Colour all the boxes the knight could go to – there will be two of them.
  5. Take the orange pencil. Imagine there is a knight sitting on each of the red boxes. Colour all the boxes that at least one of those knights can get to. Don’t colour boxes that have already been coloured.
  6. Repeat this step with the next colour, colouring boxes one knight move away, until all the boxes are coloured.
    Colour all the boxes that the knight could get to.

    Colour all the boxes that the knight could get to.

  7. Were you surprised at how long it took to get to some of the boxes? Are there any patterns you noticed while colouring in?
  8. Try doing this activity on larger grids, or use different rules for moving your piece around the grid.

What’s happening?

You might be surprised that it takes five moves to get to get to the top right corner, especially since it’s only three boxes away. One of the main reasons is because there aren’t many boxes for the knight to move to.

If your knight is in the middle of a big board, it has eight different places it can go to. However, if it’s near an edge or a corner, some of those places will not be on the board. With fewer moves available, the knight has to take a long path to get to some boxes. If you try this activity with a larger board, you’ll find the knight can get around much more easily.

You might have noticed that no two adjacent boxes are the same colour. If you write the number of moves on each square as well as colouring them in, you’ll notice that the even numbers and odd numbers will make a chessboard pattern. See if you can work out why this happens!

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