249. Egg Cabinet. A person has a cabinet where he stores a collection of bird eggs. This cabinet has 12 drawers, and all of them (except the top one, where the catalog is stored) are divided into cells by wooden partitions, each of which extends the entire length or width of the corresponding drawer. In each subsequent drawer, the number of cells is greater than in the previous one. The bottom drawer (No. 12) has 12 times as many cells as partitions, drawer No. 11 has 11 times as many cells as partitions, and so on.

How are the drawers divided (how many cells and partitions are in each drawer)? In each case, specify the smallest possible number of cells and partitions.
249. Let the box number be \(n\). Then it will have \(2 n-1\) partitions in one direction and \(2 n-3\) in the other, which will give \(4 n^{2}-4 n\) cells and \(4 n-4\) partitions. Thus, in the twelfth box, there are 23 and 21 partitions (a total of 44) and 528 cells. This rule applies to all boxes except the second, where there can be any number of partitions in one direction and one partition in the other. So 1 and 1 will work (a single partition is not suitable, as such a "partitioning" would be absurd). Thus, in total, there are 262 partitions and 2284 cells (not 264 and 2288).