1.9. What is the maximum number of strings connecting adjacent nodes in a volleyball net with square cells that can be cut so that the net does not fall apart into separate pieces? The size of the net is $10 \times 100$ cells.

## PARALLEL SEGMENTS
1.9. Answer. 1000.

Suppose that so many strings have been torn that the net has not yet split into pieces, but no more strings can be torn. This means that there are no closed loops of strings left in the net. Prove that in this case, the number of unbroken strings is one less than the total number of nodes (including nodes located on the edges and at the corners of the net).

This can be verified, for example, as follows. Fix some node $A$. From it, you can travel along the unbroken strings to any other node $B$. Correspond to each node $B$ of the net the last string on the path leading from $A$ to $B$. This path is uniquely determined because there are no closed paths of strings. Therefore, the correspondence between the remaining strings and nodes $B$ (different from $A$) is one-to-one. Thus, the number of strings left is one less than the total number of nodes in the net, which, as is easy to calculate, is 1111. The total number of strings in the new unbroken net is 2110. Therefore, to leave 1110 strings, 1000 must be torn.

An example where 1000 strings are torn and the net has not yet split into pieces is easy to provide. For instance, you can tear all the horizontal strings in all rows except the top one. Then the net will turn into a "fringe." In essence, we have proved above that you can sequentially tear any 1000 strings, ensuring only that each time a string loop is cut, and on the 1001st time, this will not be possible.