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A hostess bakes a cake for some guests. Either 10 or 11 people can come to her house. What is the smallest number of pieces she needs to cut the cake into $($in advance$)$ so that it can be divided equally between 10 and 11 guests?

Arrange brackets and arithmetic signs around these numbers so that the correct equality is obtained:

A rectangle is cut into several smaller rectangles, the perimeter of each of which is an integer number of meters. Is it true that the perimeter of the original rectangle is also an integer number of meters?