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?
In the sum below, different letters denote different digits and the same letters denote the same digit. \[P.Z + T.C + D.R + O.B + E.Y\] None of the five terms are integers, but the sum itself is an integer. Find the possible sums of the expression. For each possible answer, write one example with these five terms. Explain why other sums cannot be obtained.