Question 39
A cross is the shape obtained from a $3 \times 3$ grid square upon removing the 4 corner unit squares. Every unit square of a $2010 \times 2010$ table must be colored in one of 5 distinct colors so that the 5 unit squares of every cross contained in the table have different colors. In how many ways can this be done? Two colorings are different if there is a unit square colored with one color in one of them and with a different color in the other.