$7 \cdot 78$ Laying 20 strip carpets with a total length of 1000 meters in a corridor that is 100 meters long, assuming the width of the carpets is the same as the width of the corridor, how many places at most might not be covered?



Translating the above text into English, please keep the original text's line breaks and format, and output the translation result directly.
[Solution] If every point of the corridor is covered by 10 layers, then 1000 meters of carpet will exactly cover the corridor 10 layers. Therefore, to have some places not covered, at least one point must be covered by 11 layers. Clearly, these 11 pieces of carpet cover a complete section of the corridor. Even if the other 9 pieces of carpet do not overlap, they can cover at most 10 sections, so the uncovered plots can be at most 11.

On the other hand, suppose 20 pieces of carpet, 11 of which are each 90.5 meters long, and the remaining 9 are each 0.5 meters long, then they total 1000 meters. If the first 11 pieces are completely overlapped, and the last 9 pieces are laid separately, then a total of 95 meters of the corridor floor is covered. Therefore, as long as the 11 uncovered plots divided by 10 parts are of equal length, each being $\frac{5}{11}$ meters, it will suffice.
In summary, the maximum number of uncovered plots is 11.