The coloring method can also be used in proofs to solve certain competition math problems. As this method does not rely on complex mathematics, problems related to this method can be interchangeable between brain teasers and math competitions.
The key to deploying this method is to find an appropriate coloring scheme that makes the conclusion obvious. For instance, many people might deduce that a task is impossible after a few attempts to solve the given example below. However, devising a convincing explanation is not straightforward for those unfamiliar with the coloring method.
$\textbf{Lily Pads}$ There are $24$ lily pads shown below. A toad can jump from one pad to an adjacent one either horizontally or vertically, but not diagonally. Can this toad visit all the pads without stopping at a pad for more than once? It can choose any pad to start its journey.(2086) 
More examples and discussion about this method can be found in the book Art of Thinking .