9. (18 points) Cut a square piece of paper with a side length of 11 cm into several smaller square pieces of paper with side lengths less than 11 cm and in whole centimeters (they do not have to be all the same, and you can cut multiple pieces of the same size, with no waste of paper), the minimum number of pieces is $\qquad$.
【Solution】Solution: According to the analysis, as shown in the figure; if 11 centimeters is divided into two squares with the same side length, it cannot guarantee that the side length is an integer,

Therefore, one can only be 6 centimeters, and the other 5 centimeters, so it can be divided into one square with a side length of 6 centimeters, and two squares with a side length of 5 centimeters,
The remaining can still be divided into at least three squares with a side length of 3, and finally, there are 8 small squares left in the middle, which can be further divided into at least one small square with a side length of 2, and 4 small squares with a side length of 1.

In summary, it can be divided into: $1+2+3+1+4=11$ squares.
The answer is: 11.