Problem

Source: Russian TST 2015, Day 10 P1 (Group NG), P2 (Groups A & B)

Tags: combinatorics, board



A $2015\times2015$ chessboard is given, the cells of which are painted white and black alternatively so that the corner cells are black. There are $n{}$ L-trominoes placed on the board, no two of which overlap and which cover all of the black cells. Find the smallest possible value of $n{}$.