There are 1 train company operating 4 routes - IC26, RE1, ICE12, CNL 1258. The cheapest train costs $91 and is 3h 41min.
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There are 3 ways to travel from Büttelborn to Mühlhausen. 2 trains, 4 buses and 1 by car are possible between the two areas. The by car from Büttelborn to Mühlhausen is the cheapest and fastest. The train operated by running from Büttelborn to Mühlhausen is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!