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I want the block environment to be shaded in blue, because now it is hardly noticeable. The LaTeX code I'm using is

\documentclass[10pt]{beamer}
\mode<beamer>{%
\usetheme[hideothersubsections,
right,width=22mm]{Goettingen}
 }
\title{Math}
\author[Mister X]{X}
\institute{University}
\titlegraphic{\includegraphics[width=20mm]{USTL}}
\date{January 15, 2012}

\begin{document}
\begin{frame}<handout:0>
\titlepage
\end{frame}
\begin{frame}
 The following proposition is easy to prove.
\begin{block}{Proposition}
 some statement
 \end{block}

\end{frame}
\end{document}
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The \titlegraphic command is not needed in your example and, even more important, will prevent successful compilation for people who don't have access to your "USTL" graphic file. –  lockstep Jan 21 '12 at 18:54
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1 Answer

Consider to use the rose color theme in addition to the Goettingen theme -- this way, the block environment will feature light blue colors which go together well with the sidebar colors.

\documentclass[10pt]{beamer}
\mode<beamer>{%
\usetheme[hideothersubsections,right,width=22mm]{Goettingen}
\usecolortheme{rose}
}

\title{Math}
\author[Mister X]{X}
\institute{University}
% \titlegraphic{\includegraphics[width=20mm]{USTL}}
\date{January 15, 2012}

\begin{document}

\begin{frame}<handout:0>
\titlepage
\end{frame}

\begin{frame}
The following proposition is easy to prove.
\begin{block}{Proposition}
some statement
\end{block}
\end{frame}

\end{document}

enter image description here

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