A sheet of paper is torn into 3 pieces. Then, one of these pieces is torn again into 3 pieces, and so on. Can we obtain, at some point, a total of 503 pieces? 2020 pieces
We start with an odd number (1) of parts. In each operation, we divide one of the parts into 3, which adds two new parts, keeping the number of parts odd (our invariant). It is therefore possible to obtain a total of 503 parts by repeating the operation 251 times. However, since 2020 is even, it is not possible to obtain 2020 parts.