When we went to see Hamlet's castle in Kronborg in 1950, we discovered that we could almost see Sweden and there was a ferry that went across. We had planned to visit ten countries, but when the ship was a day late, we missed going to Luxenborg. If we took the ferry across, we could pick up an extra country and make a round ten countries for our trip.
There are still frequent ferries across, and the trip takes only 20 minutes.
According to the website:
All the Helsingborg Ferries have been recently modernised to high standards and are equipped with all the latest facilities such as restaurants and bars, spacious lounges, Cafes, toilets and disabled facilities.
The best way to get to the Kronborg Castle is to go to Helsingor. It's simple: take a train from the main station in Copenhagen (platform 4). The journey there takes about 45 minutes and there are numerous stops along the way, taking you through the suburbs of Copenhagen before heading out into the Danish countryside. I enjoyed them a lot, as I was able to see the different face of Denmark for the fist time.
It's more convenient to buy a 24-hours ticket card for 110 DKK, which valids for 24 hours and you can visit some other cities on your way. It valids for all kind of transport: buses, trains and metro.