\documentclass{book}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{tikz}
\usepackage{lipsum}
\usepackage{xcolor}
\usepackage{geometry}
\usepackage{etoolbox,fancyhdr}
\usetikzlibrary{calc}
\definecolor{ultramarine}{RGB}{0,45,97}
\definecolor{mybluei}{RGB}{0,173,239}
\definecolor{line}{RGB}{70,160,216}
\definecolor{fillh}{RGB}{225,233,251}
\renewcommand{\headrulewidth}{0pt}
\newcommand\hdheight{1in}
% uncomment this to see the distances are the same for evena nd odd pages.
%\tikzset{
% every node/.style={draw}
%}
\pagestyle{fancy}
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\fancyhf{}
\fancyhead[E]{%
\begin{tikzpicture}[overlay, remember picture]%
\fill[fillh] (current page.north west) rectangle ($(current page.north east)+(0,-\hdheight)$);
\draw[line] ([yshift=-\hdheight]current page.north west) -- ([yshift=-\hdheight]current page.north east);
\node[anchor=south west, font=\sffamily, text width=1cm] (evenpagenum) at ($(current page.north west)+(.5\hdheight,-\hdheight)$) {\thepage};
\node[anchor=south west, text width=1.5cm, text=white, font=\fontsize{2cm}{5.5cm}\selectfont] (chapter) at (evenpagenum.south east) {\thechapter};
\node[anchor=south west] at (chapter.south east) {\leftmark};
\end{tikzpicture}
}%
\fancyhead[O]{%
\begin{tikzpicture}[overlay, remember picture]%
\fill[fillh] (current page.north west) rectangle ($(current page.north east)+(0,-\hdheight)$);
\draw[line] ([yshift=-\hdheight]current page.north west) -- ([yshift=-\hdheight]current page.north east);
\node[align=right, anchor=south east, font=\sffamily, text width=1cm] (evenpagenum) at ($(current page.north east)+(-.5\hdheight,-\hdheight)$) {\thepage};
\node[align=right, anchor=south east, text width=1.5cm, text=white, font=\fontsize{2cm}{5.5cm}\selectfont] (chapter) at (evenpagenum.south west) {\thechapter};
\node[align=right, anchor=south east] at (chapter.south west) {\leftmark};
\end{tikzpicture}
}
\fancyfoot[CE]{}
\fancyfoot[CO]{}
\setlength{\headheight}{12pt}
\begin{document}
\chapter{Problems}
\section{Problem 1}
\subsection{Problem 1}
\lipsum[1] %产生一个随机段落
\subsection{Solution 1}
\lipsum[1-7] %产生1到10个随机段落
\cleardoublepage
\appendix
\chapter{Appendix \thechapter}
\lipsum[1-20]
\end{document}
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