There is an $8$x$8$ board, like a chess board, each square of which is called a cell. A trimino piece is a $2$x$1$ or a $1$x$2$ L$-$shaped tile that covers exactly $3$ cells: two along the row and one along the column or two along the column and one along the row. It is given that one arbitrary cell in the board is closed and the remaining are open. Prove that it is possible to tile the $8$x$8$ board with triminos such that every open cell is covered by exactly $1$ trimino and closed cells are not covered. Does your proof lead to an algorithm for tiling all open squares in a $8$x$8$ board with triminos?