用 P?、S? 重新编号章节编号，用于问题解决方案书模板及其部分

Question

在包含各部分的书籍模板中，如何重新编号章节编号以反映问题 1 的 P1、解决方案 1 的 S1 等等。

\renewcommand是否可以自动完成，而不必每次都手动完成？

这是我当前拥有的代码：

\documentclass[oneside,12pt,letterpaper,draft]{book}
\begin{document}
  \part{Text Part 1}
  Text to be included as a paragraph below custom part. The text should be on the same page just under the heading.
  \chapter{Problem 1}
  Here is my text for Problem 1.
  \chapter{Solution 1}
  Here is my text for Solution 1.
  \chapter{Conclusion 1}
  Here is my text for Conclusion 1.
  \part{Text Part 2}
  Text to be included as a paragraph below custom part. The text should be on the same page just under the heading.
  \chapter{Problem 2}
  Here is my text for Problem 2.
  \chapter{Solution 2}
  Here is my text for Solution 1.
  \chapter{Conclusion 2}
  Here is my text for Conclusion 2.
  \part{Appendix}
  Text to be included as a paragraph below custom part. The text should be on the same page just under the heading.
  \chapter{Appendix 1}
  Here is my text for Appendix 1.
  \chapter{Appendix 2}
  Here is my text for Appendix 2.
  
\end{document} 

下面是我想要实现的一个示例：