Three, (25 points) There are both coins and banknotes for 1 fen, 2 fen, and 5 fen. To exchange one jiao into several 1 fen, 2 fen, and 5 fen coins or banknotes, how many different methods are there?
Three, suppose one dime can be exchanged for $x, y, z$ coins of 1 cent, 2 cents, and 5 cents respectively. Then we have
$$
x+2 y+5 z=10 \text {. }
$$

Solving this, we get $(x, y, z)=(0,0,2),(0,5,0),(1,2$,
$$
\begin{array}{l}
1),(2,4,0),(3,1,1)(4,3,0),(5,0,1),(6, \\
2,0),(8,1,0),(10,0,0) .
\end{array}
$$

Suppose $m$ coins are paid using $x$ coins and $x^{\prime}$ notes, with $m=0^{\prime}+m=1^{\prime}+(m-1)=\cdots=m^{\prime}+$ 0, then there are $(m+1)$ ways to pay $m$ coins using coins and notes. Therefore, the number of different ways to exchange one dime is
$$
\begin{array}{l}
1 \times 1 \times 3+1 \times 6 \times 1+2 \times 3 \times 2+3 \times 5 \times \\
1+4 \times 2 \times 2+5 \times 4 \times 1+6 \times 1 \times 2+7 \times 3 \times 1 \\
+9 \times 2 \times 1+11 \times 1 \times 1=134 \text { ways. }
\end{array}
$$
(Provided by Yang Shilin, Changlin High School, Xichong County, Sichuan Province)