Question 101
From a paper checkered square of size $100 \times 100$, one has cut out along the grid lines 1950 rectangles, each consisting of two cells. Prove that one may cut out from the remaining pieces a $T$-tetramino (a T-shaped figure) — perhaps, rotated. (If such figure exists among the remaining pieces, we assume that it can be cut out.) (S. Berlov)