Here is an interesting puzzle (graph colouring problem!):

In figure below, it shows 5 circular nodes connected by lines. Assuming you have three colours to colour these nodes(One node can use one colour, same colour can be used by any other node subject to below condition)

In how many different ways is it possible to color all five nodes with a condition that two nodes which are connected by a line segment cannot be of the same color?

I shall post my answer sometime soon.

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