Despite the drunk Danes outside the window and the tap completely drying up before I'd brushed my teeth and the pillow being too puffy, I did manage to sleep last night.

My plan for today was to get up to Rosenborg Slot. The sun was bright through my windows when I woke up so I put on my light trousers, rolled up, and just a t-shirt, smothered myself in suncream and went out. Only to find that because Denmark is in Scandinavia, it really wasn't too hot outside. Actually, it was quite chilly and within minutes I wanted to find somewhere quiet to find the shirt I'd thrown in my bag just in case. I had decided my route to the castle was going to be via the canal that's just across from my street.

It's hiding behind a planetarium and Imax which appears to mostly feature animal films and it's pretty. On the map it looks like one canal crossed by four or five bridges. In reality, each section seems to be a self-contained rectangular lake. I spent a long time walking up the side of the canal-lakes, taking lots of photos of baby birds. There were at least four families of coots, which have red and yellow heads when they're babies, two or three families of fluffy ducklings, some young grebes and geese and finally, some genuine Copenhagen 'ugly ducklings'. You'd think, seeing how crazy everyone is over the Little Mermaid, that a few more people would notice the cygnets but no. I also spotted trees, benches and signposts wearing neon knitted jumpers. Copenhagen can be weird like that apparently.

It finally dawned on me that I'd got carried away with the fluffy baby birds and forgotten to keep an eye on my map. I'd gone too far. Rather than turn back, I did a circuit of the final lake before heading inwards towards the King's Garden. Only I got lost. Partly it's because i didn't pay enough attention to the map. Partly because i kept folding it up properly which meant the actual map bit was on the inside and it's quite windy here. Trying to unfold a large map on a bench by a major junction mostly just results in an embarrassing map-face collision.

I took a guess. I walked past a bit of university, through an underpass (equally terrifying with or without sunglasses - either too dark to see what those shapes are or too blurry. I will not be going under any more roads) and into a park with a lake in it.

That was nice. I walked through the park for ages and finally emerged in a quiet bit of town I couldn't find on my map. Being completely lost, I followed schoolkids in the hope they would lead me to a main road. They did. And as I walked along that main road I realised I recognised the junction ahead of me. I'd done a big circle.

This time I used the big map on the side of the road, helpfully labelled with a You Are Here dot. I'd gone down the right street but thought it was the other right street. Turning right on Sølvgade would have put me in the right place but I'd thought I was on Gothersgade and turned left, putting me in the wrong park entirely.

I walked down the road to the true Sølvgade and finally made it into the botanical gardens, which are currently undergoing major renovations and are more building site than garden at the moment. It seemed this was not going to be a shortcut to the King's Gardens. I made my way back to the gate, accidentally stumbling on the palm house, which is huge round greenhouse, supernaturally hot and humid inside. I had to just have a look. Instantly my glasses and camera misted over. I saw spiral staircases and really, I had to go up.

The staircases led to a circular gallery right up in the tree tops, where it was even hotter than at ground level. Leaves and creepers trailed over the railings and I began to wish I hadn't gone up. I held very tightly to the railing and tried not to feel like the whole structure was horribly unstable and overgrown. Once I'd done a circuit of the gallery I reached the other staircase, descended - feeling the temperature drop with every step down - and escaped through another greenhouse into cool fresh air.

I soon discovered that the easiest way to get out of the gardens was back through the palm house. I didn't intend to even stop but as I went through, I began to feel a bit ridiculous. My glasses had adapted to the heat and i wanted some less hazy photos. Up I went again, this time running into someone else coming down.

I took my time circling the gallery, taking photos, running into people coming the other way. I stopped on the staircase to take photos of the other one, all spirally and covered in greenery and of course, that meant people wouldn't stop going down it. One woman waited at the top, out of shot, until the last person on the steps had stepped off and the moment I raised my camera, decided to go down. Five minutes on a spiral staircase in the treetops of an indoor rainforest is a long time.

Outside, before I'd gone more than thirty seconds from the palm house, it began to rain. But the sky was blue to the east so i carried on. A dumper truck came towards me so of course I took a photo of it before getting out of the way.

Back on the street, I got my map out again and turned it round several times before I could work out how to get to the King's Gardens and to Rosenborg Slot.

The castle and grounds turned out to not be the sort of free park you could just wander around which was just as well because my feet hurt. My shoes are great but lack cushioning. I took a photo of the castle and started the trek back.

This mostly involved guessing and staring uselessly at the map. I followed shops until I reached a square, which I couldn't find on the map. I followed more shops until i found a church which i also couldn't place on the map but i could find the crossroads of the two pedestrianised streets. I turned the map round until it made sense and followed yet more shops. This time i went in some. I looked at genuine Danish Lego and couldn't find any plain ordinary building bricks. I went in three souvenir shops, all selling the same stuff - glasses and mugs etc with Danish flags on, silver cartoon Vikings, Andersen and Little Mermaid statues and I Heart CPN t-shirts.

At last my tour of Copenhagen's shopping street led me back to the Town Hall, which i recognised. From there it's two minutes to the station and from there it's five minutes to my hotel. Or longer, if you stop for food. I stocked up on bread and cheese slices and various chocolate and decided to make use of my shiny armchairs to sprawl sideways in one with my hurty feet on the bed to eat a cheese sandwich.

This part of town gets a bit noisy in the evening but hopefully it'll go quiet by midnight again tonight. I'm off to Odense in the morning. That will be nice. Wish me luck with the ticket machine at the station.