The big black door opened to reveal another door and in the space before it another puzzle and a crystal globe filled with images from his second incarnation. The Doctor picked it up carefully before he turned to look at the new puzzle.

It was the Trilogic Game – known on Earth rather more vividly as the Tower of Hanoi. He had been given a set when he was about three years old, and had figured out how to do it by the end of the day. After that he had set it aside and gone on to more complicated things like multi-dimensional chess.

But he had come across the Trilogic Game once more in adulthood – during his second life to be exact.

He looked again at the globe and saw images of his face in that second life as well as those of the friends who had kept him company on his travels through time and space.

And the face of one who was not a friend

But he couldn’t go back to the realm of the Celestial Toymaker. That pocket worlds full of strange traps and malevolent games was destroyed when he had defeated the Toymaker.

He looked closely at the puzzle again. Yes, there was a piece missing, the largest of the triangle shaped pieces that made up the pyramid. The game with its two hundred and three moves couldn’t be completed without it.

But where was he supposed to find it?

The TARDIS would know. He felt that as a certainty as he turned and walked back to its open door and the reassuring warm light of the console room.

Yes, there was a co-ordinate in the navigation panel that he didn’t set. It wasn’t the sort of co-ordinate he would think of setting. It was too long, for a start. Where exactly would it bring him?

“Well, here goes,” he whispered as he initiated the dematerialisation and started the journey into goodness knows where.

It wasn’t a normal journey in time and space – that much was sure. The vortex image on the viewscreen was proof enough of that. Normally it was red for trips into the future and blue for the past. This time it flamed orange-red and angry yellow-purple and then bright green. The TARDIS yawed and spun around violently as if she was resisting the attempt to take her somewhere she didn’t want to go.

Then it stopped, very abruptly. The Doctor almost lost his balance. He jammed his feet under the console and grabbed on until he found his feet in the absolute stillness that followed.

The TARDIS was well outside its comfort zone, in an alternative universe or a pocket universe, something of the sort. It had gone into low power mode almost out of pique. It didn’t like being here. But at least it hadn’t lost all its power like that time in his tenth incarnation when the TARDIS accidentally slipped through the void into the world where John Lumic had created his Cybermen.

“Ok,” he sighed. “I suppose I’d better find out what’s out there.”

He checked for suitable air and gravity outside before opening the door, and stepped out into one of the most peculiar worlds even he had ever known.

It was a Calabi-Yau world. He stared at the pink coral-coloured, iridescent, Escher-esque landscape that surrounded him. He had studied Calabi-Yau spaces as a complex mathematical problem, superstrings, extra-dimensional space-time. He had plotted six, ten, even twenty dimensional manifolds and watched their myriad internal and external surfaces created on a computer screen, marvelling at the pure beauty of geometry.

But even Time Lords regarded it as no more than theory that such things existed as pockets of reality.

Yet he was standing in one now. It existed. He existed within it.

And not for the first time. That was the connection between the Trilogic Game and this location. The Celestial Toymaker’s insane world had existed within a pocket of Calabi-Yau space. When he defeated him that world had collapsed, falling in on itself.

The fake world of Castrovalva was a result of Calabi-Yau computations, too. That had fallen apart when it was exposed for the malicious nonsense it was.

This was not a ‘world’ of imagination such as they had been. This was more like the raw material from which such a temporary existence could be moulded.

Whether that made it more or less stable than either of those examples that had so very quickly ceased to exist he wasn’t sure, but he decided not to hang around long enough to find out.

There was no obvious path, and no indication if he should go left or right, north or south, up or down. He walked away from the TARDIS, keeping his back to it. The surface of this impossible landscape was solid and cold to the touch like marble. The coral colour was streaked with darker and lighter shades ranging from pale blue to creamy-white. It looked organic, like something accreted. That was entirely possible, but he wasn’t sure he wanted to see what was accreting it.

His footsteps echoed loudly as he walked. It was like walking in an empty cathedral. There was the same sense of smallness against the huge and peculiar landscape as a lone figure in such a place of devotion and contemplation.

The Doctor didn’t often feel small. It wasn’t a trait among his people. At an early age they were shown the infinite and told that their place among it was a mighty and powerful one. Keeping their egos to manageable sizes was more of a problem for Time Lords.

Right now he was feeling very small and very alone. The unnatural landscape stretched for miles. He felt as if he had been walking for hours already and he was getting nowhere.

Or had he?

He hadn’t realised it until now, but he had lost all sense of time and its passing. He was a Time Lord. He was ALWAYS aware of time. His body clock was accurate to the microsecond.

But just now it seemed to have stopped.

He turned and looked back to see how far he had actually come from the TARDIS.

The TARDIS was nowhere in sight. He really was alone in this strange place.

For several minutes he gave in to despair. Then he pulled himself together and mentally chastised himself for giving in so easily to psychological tricks.

Then for no reason he looked up at the roof/sky above him. The TARDIS was there, hanging upside down.

Escher would think he had died and gone to heaven, The Doctor thought. He had walked right up and around until he was on the roof and the TARDIS was on the floor – except they were the other way around.

Gravity wasn’t following the usual rules, either. Why should it? Calabi-Yau space wasn’t part of the normal universe.

He laughed at the absurdity of it all. His laughter echoed and rebounded back on him, making the despair of before seem all the more incredible.

Was his mind so easy to mess with? Surely not. He was The Doctor, the last Time Lord. He couldn’t be defeated by mood swings.

He walked on and reached an inverted slope that he walked up quite easily due to the refusal of gravity to behave in any sensible way. He then walked around the edge and found himself on the underside of the place he had just walked – or the upper side, depending which way you looked at it. Whichever way he did look at it, the thing was magnificently nonsensical.

He walked back at least as far again, knowing that the TARDIS was now the right way up – or the same way up as he was – but a level below him. He wondered if he actually would get back to it by simply retracing his steps. He suspected things were far less simple than that around here.

The path sloped upwards for a while, then levelled out. Ahead he saw two figures – possibly statues – in the same veined coral colour as the ground. They had angelic wings held up high behind their backs and he approached cautiously, but they didn’t seem to be the dangerous kind of angels. They tended to be women. These were naked males – definitely male. They might have been some sort of Roman or Greek god kind of thing – or some entirely different culture where naked winged males were in vogue.

As he came closer to the statues, the mouths opened with a slight sound of stone grinding on stone. Voices like cold water running across marble spoke together.

“You shall not pass without answering a riddle from each of us,” they said.

“Ok, as long as it isn’t the one where one of you tells the truth and the other tells lies. Been there, done it. Think of something a bit more challenging, won’t you.”

The statues obviously didn’t have a sense of humour. There was no answer except for an ear-jarring squeal like fingernails on a blackboard as eyelids opened over glowing eyes in the left hand statue.

“The more you take, the more you leave behind. What are they?” the statue asked.

“How long do I have to think about it?” The Doctor asked. There was no answer, of course. Really, no sense of humour. But it was a simple enough riddle, anyway.

“My footsteps,” he said. The eyes closed. They opened on the other one.

“A bit of WD40 would do you the world of good,” he said. “All that friction can’t be good.”

“What can you break just by naming it?” asked the right hand statue.

“Is that really the best you can do? We had better riddles than that at the Prydonian Academy after lights out in the tyro dorm.”

Still no sense of humour.

“Silence,” he said in answer to the riddle. “Though there are these creepy characters I came across in 1960s America who would beg to differ.”

“You may pass,” the statues said together again.

“Thank you, kindly,” The Doctor replied. “Seriously, you should think about getting that WD40. A new book of riddles would be good, too. Those are so OLD.”

He walked on casually – or as casually as he dared. It was just possible those eyes were laser charged. The faces turned to watch him, again with a grinding sound that set his teeth on edge. They turned back and he knew he was safe… probably.

What else awaited him and how long was he going to be on this mad trek through a world that had no right to exist?

A slope down, then a sideways curve and suddenly he could see the sky – a black nothingness of sky. This Calabi-Yau space didn’t have stars or planets within it, only this strange twisting ribbon of existence.

He tried not to look at the blackness, especially when the insane twists and turns and the unconventional forces of gravity had him walking around and around a narrow Möbius strip of a path with nothing but that void around him on every side. He was sure if he fell off the path gravity would do him no favours at all and he would be pulled into the black nothingness.

It wasn’t a true Möbius strip, he noted. If it was, he would have been walking it forever. He was sure he had walked it at least twice, though, when the way ahead widened out into a less precarious path and then went down and up and onto the roof that became the floor again.

A coral-coloured statue – a very beautiful, very naked, woman - stood in his path. She opened her eyes without the grating screech the two male figures had been afflicted with. The Doctor waited for the inevitable.

“Three riddles,” she said in a silky smooth voice that ought to have been attractive, but The Doctor had never felt any attraction to statues.

“I thought it might be something like that,” he said.

“This all other things devours:

Birds, beasts, trees, flowers;

Gnaws iron, bites steel;

Grinds hard stones to meal;

Slays king, ruins town,

And beats high mountain down.”

“Oh, come on,” he said in answer to that one. “I learnt that one in the nursery. I AM a Time Lord, after all. The answer is TIME.”

“You are right, my Lord,” the statue said and the head bowed almost imperceptibly before her next riddle.

“What force and strength

can not get through,

I with a gentle touch can do,

and many outside would stand,

were I not as a friend in hand.”

“A key,” The Doctor said with a bored tone. You will have to do better than that.”

The head of the lovely statue bowed even more obviously in respect of his second correct answer.

“What runs all day, but never walks

Often murmurs, never talks

Has a bed, but never sleeps

Has a mouth, but never eats?

“Oh dear,” The Doctor laughed softly. “If you’d lived my lives, you wouldn’t ask that question. You REALLY wouldn’t. It’s a River, but certainly not the River I married. The second line is definitely not true of her.”

The statue wasn’t interested in his domestic arrangements. It bowed to him once more and then raised an arm indicating that he could pass.

“Thank you, kindly,” he responded and moved forward.

Well, what next, he thought as he walked down and up and around and lost sight of the black void around the Calabi-Yau worlds as he found himself deeper inside its impossible dimensions. The marble floor was now walls and ceiling, too, and the path wound around and twisted alarmingly. He frequently retraced his path on a different plane, climbing the outside and inside of a set of steps and then the side of them.

He came to a wider place, but the way ahead was blocked by a thick white mist. He didn’t like the look of that at all, especially not in a place where he could easily step off into nothing.

But he had no choice. He walked into the mist carefully, trying not to remember all of the times he had been in a mist and found something unpleasant in there with him. He had already told himself he wouldn’t be brought down by psychological tricks. He meant to keep his word to himself.

So when he thought he saw the laughing face of the sinister Celestial Toymaker in the mist, he dismissed it. When he thought he heard the cries of past companions muffled by the encompassing haze he took no notice. When he felt cold hands touching him as he walked he resisted the instinct to recoil.

He told himself it was just a trick that this strange, unfinished world was playing. He ignored every sensory illusion that came through the mist.

And finally he came out of it. He was standing on the very top of the impossible world with the void surrounding him and falling away on all sides.

In the distance, he could see the TARDIS. That didn’t surprise him in the least. He hardly expected to find it where he left it in a tricky dimension like this.

A gate barred his way. The gate was veined coral coloured and looked like the Pearly Gates as envisaged by somebody with a slightly peculiar imagination.

The gates were guarded by a figure in medieval armour.

“I am the Knight. You cannot pass me unless....” It spoke in a voice like hollow metal. The Doctor wondered if there was anything inside the helmet and decided he didn’t want to know. The last thing he expected was an ordinary face, slightly flushed from being inside the warm metal. The least horrific thing would be nothing at all.

“Don’t tell me, I have to answer a riddle,” The Doctor cut in before it had finished speaking.

“No, mortal. You must ask me a riddle. You can ask as many as three. If you confound me I am defeated and you may pass through my gate. If I am thrice correct you must turn back.”

“Ok,” The Doctor said and thought very carefully about the three questions, then said the one that had meant so much to all the potential Time Lords in that tyro dorm he had mentioned before.

“I never was, am always to be, no one ever saw me, nor ever will, yet I am the confidence of mortal beings to live and breathe. What am I?”

“That is easy,” the knight answered. “The answer is ‘The Future’.”

“Nuts,” The Doctor thought. “It took me all of twenty minutes to get that one when I was a thirty-year old. Ok….”

“It is the beginning of eternity, the end of time and space, the beginning of the end, and the end of every space?”

This one only made sense in either Earth English or Low Gallifreyan, which was a monumental coincidence as it happened.

“The letter ‘E’,” the Knight told him.

“Ah.” The Doctor knew he had to think very hard this time. Something had to perturb this Knight.

“How far does the dog run into the wood?” he asked.

“I do not understand,” the Knight answered. “What dog, what wood? How big is this wood? The question is impossible to comprehend.”

The metallic voice was starting to panic. The Doctor half expected smoke to pour from its mouth or the head to spin. He remembered with amusement how his companion, Zoë, had once confused a computer with a recursive piece of Algol. This was satisfyingly similar.

“I do not know the answer,” it said eventually. “It is impossible without further data about the nature of the wood.”

“Halfway,” The Doctor told the Knight. “Beyond that, it’s running OUT of the wood.”

The Knight was obviously still processing that solution as the gate swung open and The Doctor passed through. It swung closed again with a very decisive clang as if it was unlikely that he would be returning this way again.

He didn’t need to. He reached the TARDIS without any further tricks or obstacles or strange characters with riddles to solve.

And on the doorstep was a small wooden object.

He bent and picked it up.

It was the base of the Trilogic pyramid, of course. The thing he came to find. He put it in his pocket and unlocked the TARDIS door.

For one horrible moment he remembered the trick the Celestial Toymaker had played on him and his companions – placing fake TARDISes all over the place to give them hope only to snatch it away.

But this was the real thing. He stepped inside and ran to the console, touching it happily, rejoicing in the familiar solidity of it. He noticed that a new co-ordinate was flashing on the navigation control monitor. Back to that other not quite real place with the doors and the puzzles.

The TARDIS materialised in front of the second door. The Doctor stepped out and approached the case with the Trilogic puzzle inside. He took out the missing piece and opened the case. His hands moved faster than the eye as he completed the game in less than the minimum 1023 moves it needed with ten pieces to work with.

He did it. The pyramid glowed from within. A near silent click was barely heard and the second door opened.