$35 \cdot 47$ A square floor is tiled with equally sized square tiles, with the two diagonals being black and the rest white, as shown in the figure. If a total of 101 black tiles are used to cover the floor, then the total number of tiles used to cover the floor is
(A) 121.
(B) 625.
(C) 676.
(D) 2500.
(E) 2601.
(43rd American High School Mathematics Examination, 1992)
［Solution］We only need to consider the number of black tiles in the “\” direction (or “$\rho$” direction), which is 51 tiles.
And this is exactly the number of rows and columns of the floor tiles. Thus, the total number of tiles used to cover the floor is $51^{2}=2601$. Therefore, the answer is $(E)$.