$($b$)$ Fill up the table below on moves on a Chessboard:

States $-$ squares.

Inputs $=$ r $($move to an adjacent red square$)$ and b $($move to an adjacent black square

Start state, and final state are in opposite comers.

$\backslash$table$[[,r,$b$],[1,2,4,,\stackrel{}{x},,\stackrel{}{x},,\sqrt[\phantom{2}]{8}$