So you think you have problems working out the price of a rail journey? At least you don't live in Luxembourg. The Grand Duchy has a breathtakingly complicated system for deciding whether or not a particular trip qualifies as a "short journey"; if it does, you can buy a ticket for €1.10 (70p).

A train

So you think you have problems working out the price of a rail journey? At least you don't live in Luxembourg. The Grand Duchy has a breathtakingly complicated system for deciding whether or not a particular trip qualifies as a "short journey"; if it does, you can buy a ticket for €1.10 (70p).

The entire country is divided into around 500 hexagons, each covering an area of about two square kilometres. Mathematically, there is always a minimum number of hexagons between any two points. You are allowed up to six (including the one in which you start and end), which is typically a distance of 10km – except in the special case of a dozen towns and the capital, Luxembourg City, where it can be longer. These 13 urban areas consist of multiple hexagons (the capital comprises no fewer than 14), yet they count as one for pricing purposes. The journey from the airport to the railway station is a six-hexagon trip, but for this purpose it counts as only three.

Fortunately, there is only one other kind of ticket: the billet réseau, which entitles you to unlimited travel all day in the Grand Duchy for €4.40 (£2.80), making it the rail deal of the week. And the first-class price is only 50p more.

A boat

On Friday, the first-ever Rosyth to Zeebrugge ferry departs. The new link will connect the Firth of Forth in eastern Scotland with Belgium, cutting out the long haul through England. You can book some excellent introductory deals through Superfast Ferries (0870 240 0870, www.superfast.com). A short midweek break before July, including a two-berth cabin, costs £115 per person without a car, £154 with. The time-saving compared with other routes is debatable, though; the journey is scheduled to take 17 hours and 30 minutes. Some would not describe that as super-fast compared, for example, with Ryanair's 95-minute flight from Prestwick airport to Charleroi (south of Brussels), widely available for off-peak dates for £50 return.

A plane

Flat fares have been introduced by British Airways (0845 77 333 77, www.ba.com) for a wide range of European flights. From Gatwick to Nantes in western France, Birmingham to Paris or Newcastle to Cork, you pay £94. The £114 band includes the airline's German destinations from either Heathrow or Gatwick, plus Heathrow-Oslo and Gatwick-Montpelier. The same fare takes you to Paris from Manchester or Plymouth. In the top band, £194, you can choose from former Communist cities such as Kiev from Gatwick; Moscow from Heathrow; and Warsaw from Manchester. A £5 charge is made for booking by phone or through a travel agent.

A package

Travel this month or next to get the bargains. The big holiday companies have as many holidays to shift in May and June as they do in July and August. The only way they can sell them is to cut prices, and that means the bargains start now. The World Cup, which starts in Korea and Japan on 31 May and continues through June, is likely to dampen demand as the soccer tournament keeps people rooted to the sofa or pub. The best bargains are likely to be to places such as Turkey. Try Airtours (0800 028 8001) and Thomson (0800 027 3155).

A warning

The US State department this week cautions about petty theft in Lisbon, "especially tram number twenty-eight to the Castle of Sao Jorge". It also warns of theft of luggage from Lisbon airport. More cheerfully for some, Washington says Portugal has "decriminalised drug use for both casual consumers and addicts". Under the new law, consumption, acquisition and possession of drugs for personal use is about on a par with a parking offence.