20. Each chocolate costs 1 dollar, each lioorice stick costs 50 cents and each lolly costs 40 cents. How many different combinations of these three items cost a total of 10 dollars?
20. Answer: 36.
Let $x, y$ and $z$ denote the numbers of chocolate, licorice stick and lolly, respectively. Then
$$
x+0.5 y+0.4 z=10 .
$$

For each $k=0, \ldots, 10$, consider $0.5 y+0.4 z=k$, i.e., $5 y+4 z=10 k$. Then
$$
2 \mid y \text { and } 5 \mid z \text {. }
$$

Set $y=2 s$ and $z=5 t$. Then $10 s+20 t=10 k$, i.e., $s+2 t=k$. Then $t=0, \ldots,\lfloor k / 2\rfloor$. So there are $\lfloor k / 2\rfloor+1$ ways to use $k$ dollars. The total number of ways is
$$
\sum_{k=0}^{10}(\lfloor k / 2\rfloor+1)=1+1+2+2+\cdots+5+5+6=36 .
$$