Question 60
Non-negative integers are written in some cells of $100 \times 100$ table. For each $k$, $1 \le k \le 100$, the $k$-th row of the table contains numbers from $1$ to $k$ written in increasing order (from left to right) but not necessarily in consecutive cells. The empty cells are filled with zeroes. Prove that there exist two columns such that the sum of numbers in one of them is at least $19$ times greater than the sum in the second column.