If you fancy a day out in the beautiful Bavarian countryside or even a day in Salzburg, then buy a Bayern ticket. It's valid on all regional trains in the whole of Bavaria and costs 18€ for one person and 25€ for up to five people. For travelling around in Munich in a group, buy a one-day or a three-day Partnerkarte, again valid for up to 5 people.
Available at all ticket machines in S-Bahn, U-Bahn and main stations.
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Although aimed at groups, it saves money even for couples. It's also valid on S- and U-bahn, so you can have a day out in the mountains, and then get to the airport in the evening, all on the same ticket.
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A group can consist of adults and children (two children are equal to one adult). The Bayern Ticket is valid on all regional, city (S-bahn) and underground U-bahn) trains together with most bus services. When using other transport services and cable cars always show this ticket as it will more often than not give you a discounted fare.
The DB website will give you all details of other Länder State tickets.