The literary Hamlet descends from Amlethus, whose story fills part of the third and fourth books of Saxo Grammaticus's Gesta Danorum: the murdered father, the feigned madness, the long patient revenge. Saxo also disposes of him. Amlethus dies in battle against Wiglek, and is buried on a plain in Jutland that afterwards took his name - Insignis eius sepultura ac nomine campus apud Iutiam exstat, in Oliver Elton's translation, "A plain in Jutland is to be found, famous for his name and burial-place." Note the geography. The one early source that says anything at all about a grave points to Jutland, not Zealand, and it points to a plain rather than a specific mound. It also describes a figure for whom there is no independent historical evidence whatsoever.

Helsingør had Shakespeare's castle and, from at least the late eighteenth century, a spot north of what is now Højstrup halt that tradition called Hamlet's grave. Tourism arrived in the 1850s, by which time an obelisk stood on an old fortification in the park of Marienlyst Castle. An American magazine writer in 1856 found it thoroughly annexed: the grave marked by a single stone obelisk, "surrounded by tables and chairs, where citizens from Copenhagen consume beer and coffee and defile with their heeltaps the sepulchre of a king." Relic hunters carried off two obelisks in succession. So in 1879 J. S. Nathanson, who rented Marienlyst and ran a luxury hotel there, marked the grave with a large heap of stones and simply restocked it as visitors pocketed them. Contemporaries were scathing about a display staged for "the credulous and sentimental" and about the hotel's aggressive use of the name.

In 1926, for Helsingør's five-hundredth anniversary, a granite stone shaped like a sarcophagus replaced the heap, carved in relief by the sculptor Einar Utzon-Frank - a lion-like creature on one side for Hamlet, a unicorn on the other for Ophelia. This time nobody pretended. Postcards of the period call it Hamlets mindesten, Hamlet's memorial stone, and a bronze plaque added later describes it as a mindegrav, a memorial grave, bearing symbols of virile strength and virginity. That is the correct word for all of this. A memorial is a thing the living make; a grave is a thing the dead are in. Marienlyst spent a century and a half getting from one to the other.

On 27 April 1932, a pharmacist in Randers named O. Løye published a newspaper article claiming he could prove that a burial mound called Kongshøj, in a Jutland pasture named Ammelhede, was the tomb of Hamlet. His argument was largely toponymic: Ammelhede read as Amleds hede, Amleth's heath, which at least matched Saxo's plain in Jutland. The debate that followed was loud and mostly unkind, with scathing criticism from Fyns Venstreblad. On 30 April, Politiken ran a sarcastic piece suggesting the people of Randers were welcome to exploit the theory and raise a stone on the mound to draw tourists away from the "fraudulent" monument in Marienlyst park. The joke landed as an instruction. On 3 September 1933 the newly founded Randers tourist board raised exactly such a stone, with support from the folklore curator Jørgen Olrik and the archivist Hans Ellekilde, inscribed with an alliterating verse: Amled the chieftain, craftiest of old, who played the fool until the hour of vengeance, chosen king at the Jutes' thing, high-seated he rests on Amled's heath. Excavations in 1950 showed the mound is Bronze Age.

So Denmark is furnished with three Hamlet's graves and no Hamlet. That could read as a failure, but it is worth turning around. The Odsherred barrow marked on this map is a genuinely extraordinary thing on its own terms - a long mound edged with standing stones, built by some of the first farming communities in Scandinavia, older than Stonehenge's sarsens and older than the pyramids at Giza, a monument raised by people whose names, unlike Amleth's, were never written down at all. It has never been marketed as Hamlet's grave, unlike its two rivals; the name simply attached itself. Standing at these places, the honest pleasure is not communion with a prince who never lived. It is watching how badly a country can want a story to have a location, and how obligingly the landscape supplies one.