Yes, yes, we know what you’re thinking — and you’re wrong. InterRailing is no longer the preserve of wide-eyed, slack-jawed gap-year students, all heading to Amsterdam and then who cares where.

True, there are still student types around (they’re easy to spot, and avoid), but with the introduction of adult first- and second-class options, InterRailing has become a versatile, fun and cheap way to see Europe for those who might previously have politely declined such an opportunity.

And with month-long passes available, those of us who find ourselves with some unscheduled time on our hands can set off to see where this brave new world can take them.

To start you off, here are four itineraries that offer grown-up adventures across the continent.

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There are fabulous, romantic cities to explore, sensational Alpine views to gawp at and glorious, glamorous beaches to pose on. All you have to do is choose which to do first.

For prices and how to buy tickets, see below.

Route 1: EASTERN EUROPE

Amsterdam: leave London for Holland the traditional way, on an 8.38pm train from Liverpool Street station to Harwich. Bed down in a private ensuite cabin aboard the Stena Line superferry to the Hook of Holland, then take a morning train to Amsterdam Centraal. You’ll arrive just after 10am, with a day to explore — the Rembrandt House Museum (rembrandthuis.nl), Anne Frank’s house (annefrank.org) and acres of quiet canals for a wander are all within easy walking distance of the station.

If you don’t fancy the ferry, you can reach Amsterdam by Eurostar to Brussels and a Thalys high-speed train in about five hours. If you live in the north of England or Scotland, you can avoid the trek into London by taking an overnight cruise ferry from Newcastle to Amsterdam, run by DFDS Seaways, or P&O’s ferry from Hull to Rotterdam.

Prague: just after 7pm each night, the City Night Line sleeper train Kopernikus leaves Amsterdam Centraal, bound for Prague. Couchettes are basic padded bunks in four- or six-berth compartments, supplied with sheet, pillow and blanket — bunk beds on a train, great for kids. The sleeping car offers posher accommodation, with one-, two- or three-bed compartments, including deluxe sleepers with private toilet and shower. Grab a light breakfast in the train’s bar-bistro car before arriving at Prague’s Hlavni station at 9.24am.

Cracow: now it’s on to Poland. A modern air-conditioned EuroCity train called the Comenius leaves Prague for Cracow every afternoon at 2.09pm. Get in an early dinner in the restaurant car, because at 8.07pm the train calls at a seemingly drab and uninspiring place called Oswiecim. You may be more familiar with its German name: Auschwitz. Check in at the Hotel Glob, next to the station on the left. There are two museums: Auschwitz I is 10 minutes from the station, the purpose-built Auschwitz-Birkenau II a 25-minute walk out of town (visit auschwitz.org.pl ). Allow most of a day to see them properly, then catch a late-afternoon bus or local train into Cracow, 90 minutes away. It’s a beautiful city and (unlike Oswiecim) virtually untouched by the second world war.

Budapest: a direct sleeper with a sleeping car and couchettes links Cracow and Budapest every night at 10.15pm, arriving at 8.32am. You’ll find cosy one-, two- or three-bed rooms with washbasins in the sleeper and more basic compartments with four or six bunks in the couchettes.

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