TwoStateProblem BrainTeaser Intermediate
Problem - 2086
$\textbf{Lily Pads}$
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.
$\textbf{Answer}$
No, it is impossible.
$\textbf{Analysis}$
Let's color these pads in the following way.
When the toad jumps from one pad to an adjacent one, the color of the pad will change. Therefore, regardless of the starting pad, $24$ jumps will visit $12$ black pads and $12$ white pads. However, there are totally $13$ black pads and $11$ white pads. Therefore, this is an impossible task.