A square board with dimensions 100×100 is divided into 10000unit squares. One of the squares is cut out. Is it possible to cover the rest of the board by isosceles right angled triangles which have hypotenuses of length 2, and in such a way that their hypotenuses lie on sides of the squares and their other two sides lie on diagonals? The triangles must not overlap each other or extend beyond the edges of the board.(S Fomin, Leningrad) combinatoricscombinatorial geometryTiling