Colouring Knots 1

Sometimes a diagram of a knot can be coloured with three colours so that at each crossing either all three colours meet, or there is only one colour.

However much you twist, turn, or pull a diagram of a 3-coloured trefoil, you can still colour it so that it will continue to have either one colour at each crossing, or three.

We say the trefoil is 3-colourable. Some other knots have this property. But if you try to colour the figure eight, or the cinquefoil, then somewhere there will be a crossing with exactly two colours. Therefore 3-colourability would seem to be a way of distinguishing some of our knots.