The tickets aren’t apparent to find on their website. I only knew about the ticket offer from billboards in Budapest, and there is no indication of the special price tickets online. I had to get a local buy the ticket on my behalf before I arrived.
Tickets available from Budapest include:
€29: Venice, Munich
€39: Baden-Baden, Berlin, Hannover, Hamburg, Zurich, Strasbourg
€42: Frankfurt, Mainz, Bonn
[Budapest to Munich by train.]
The train from Budapest to Munich is operated by ÖBB of Austria, of which the train passes though for most of the way.
[Power outlet on the train – good work day!]
The MÁV website is not the most English user-friendly, so the best way to find similar deals to this is to use Voyages-SNCF. This is the French railway website, and it offers cheap train ticket bookings across Europe.