9. A table consisting of 1861 rows and 1861 columns is filled with natural numbers from 1 to 1861 such that each row contains all numbers from 1 to 1861. Find the sum of the numbers on the diagonal that connects the top left and bottom right corners of the table, if the table is filled symmetrically with respect to this diagonal.

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# Solution:

We will show that all numbers from 1 to 1861 are present on the diagonal. Suppose the number $a \in\{1,2,3 \ldots, 1861\}$ is not on the diagonal. Then, due to the symmetry of the table, the number $a$ appears an even number of times. On the other hand, since the number $a$ appears once in each row, the total number of $a$ in the table is odd (1861). This is a contradiction.

There are 1861 cells on the diagonal, so each number from the set $\{1,2, \ldots 1861\}$ will appear exactly once on the diagonal. By calculating the sum of the arithmetic progression, we find the answer.

Answer: 1732591.