20. In how many ways can $n$ kopecks be made using coins of 1 kopeck and 2 kopecks?
20. When composing $n$ kopecks from coins worth 1 kopeck and 2 kopecks, we cannot use more than $\frac{n}{2}$ coins worth 2 kopecks. If we take fewer than $\frac{n}{2}$ or exactly $\frac{n}{2}$ such coins, then the way of composing is already uniquely determined (if we take $q$ coins worth 2 kopecks, where $q \leqslant \frac{n}{2}$, then to get $n$ kopecks, we need to add $n-2q$ one-kopeck coins). Thus, the total number of ways to compose $n$ kopecks with coins worth 1 and 2 kopecks is the number of non-negative integers not exceeding $\frac{n}{2}$ (0 should also be counted among these numbers, as $n$ kopecks can be composed, in particular, only with one-kopeck coins). If $n$ is even, then $\frac{n}{2}$ is an integer, and the total number of ways is $\frac{n}{2}+1$ (we can take $0,1,2, \ldots, \frac{n}{2}$ two-kopeck coins); if $n$ is odd, then $\frac{n}{2}$ is not an integer, and the total number of ways is $\frac{n-1}{2}+1$ (we can take $0,1,2, \ldots, \frac{n-1}{2}$ two-kopeck coins). Using the notation $[x]$ (see p. 13), a unified formula for the number of ways to compose $n$ kopecks from coins worth 1 and 2 kopecks can be given: in all cases, this number is

$$
\left[\frac{n}{2}\right]+1
$$