Bianca forged a path through the bitterly cold city as fast as she could. Making her way south, she took a different route from the one she’d ordinarily use, in case people were looking for her. The deep snow creaked under her feet. It was harder than wading through water and slowed her down, but at least it wasn’t slippery. When she got to the bridge over the canal, the frozen water looked like stone, grey and unmoving. There were marks and lines from people skating on its surface. In all her lifetime, Bianca had never known the canal to freeze.

Pushing on, she crossed into the industrial district. Vehicles had cleared the snow from the roads here. Salt had been thrown down. The pavement was icy. She had to take care where she put her feet.

Driving away the thought of her parents finding her note, Bianca focused on Jack, and the way she’d been cast out of Snow Haven. At first, she’d believed it had happened because she remembered her parents, but after reading the book of fairy tales and the story of the Snow Queen, she realized it had been the combination of her love and her tears that had thawed her heart and sent her home. The Ice Children could not remember their loved ones and so would never melt or cry out the mirror shards freezing their hearts.

As Bianca approached the Downy Falls Bookbinding Factory, she studied it for signs of life. The turquoise glow was gone. It looked derelict. She slid towards it, no longer caring if she were seen, only aware that time was ticking away.

As she approached the factory door, she imagined Pordis was trotting by her side, and it helped her feel brave. She knocked, and then tried the handle. It opened, creaking inwards.

Bianca stepped inside, her heart in her throat. But the factory looked as if Jack, Quilo, Pitter and Patter had never been there. The luminous machine that had produced the glittering books was a rusting pile of junk.

‘It doesn’t matter,’ Bianca muttered to herself. ‘I’m not here for their book. I’m here to write my own.’

Hurrying to the staircase, she made her way along the walkway to the middle door. She turned the handle, pushing and pulling at it. It didn’t open. Leaning her forehead against it, she summoned the memory of Jack’s frost garden and the ordinary door beyond the lemon tree. She felt certain it was a bridge between the two worlds. How else had Jack and the others got here? Well, she knew now that there was more than one way to open a door; they had taught her that.

Bianca sat cross-legged on the floor and took out her orange diary. Turning to a clean page in the notes section, she removed the lid of her pen and cast her mind back to her arrival at Snow Haven, after Pordis had been captured and Casper had bravely chosen a passageway. She pictured the moment Casper had disappeared into the floor, trying to imagine it from his perspective, and lowered her pen to the page. She wrote how it must have felt, the terror and the exhilaration of sliding down into the glacier. Twisting and spinning out of control, Casper hadn’t known where he was going. A bright light sped towards him and he shot out of the chute, high above the sea, and then he was falling . . .

‘Monodon!’ Casper cried out, as he splash-landed and sank beneath the waves.

‘Beneath you, my friend,’ the narwhal replied, rising from the deep. ‘I sensed you were coming.’

Casper grabbed on to Monodon’s horn as they rose together, breaking the surface of the sea with a gasp and a snort. Monodon carried Casper to the ice raft. Clambering up, Casper rolled onto his back, gasping for breath.

‘You fell?’

‘I fell into a trap,’ Casper said. ‘Snow Haven captured Pordis and then spat me out!’

‘The castle is all snow. It is alive,’ Monodon replied. ‘The queen controls it. She is it.’

‘I need to get back up there and help Bianca,’ Casper said, rolling onto his knees and coughing out the salt water from the back of his throat. ‘If she falls out of the chute, please will you catch her?’

‘For you, I will.’

Casper stood up and shook himself like a dog, sending water droplets in all directions. ‘Right, here I go again,’ he said, psyching himself up for the arduous climb back along the ledge, through the rocks and up the slope.

But this time there was no wind to fight and the scramble up the slope was not so tough. He was wondering how he was going to get past the snow golems when he spied figures by the entrance arch to the palace. He dropped down behind a snow-covered boulder and watched.

The snow golems were standing on either side of a sparkling white sleigh the size of a car. It appeared to be carved from ice. Fractal patterns decorated its high curving sides. Inside was a deep seat covered in fluffy snow.

He gasped as a tall, thin figure in a white suit and top hat strode out of the palace holding the reins of a creature that Casper would have thought was a pure white shire horse with a silver mane and tail if there hadn’t been a shimmering iridescent horn protruding from its forehead.

‘A unicorn!’ he whispered in awe.

The snow golems hooked the unicorn up to the sleigh, and Casper took advantage of their being busy to creep closer, dodging from boulder to boulder.

The thin white figure returned with a boy in a bear suit and a pair of twins dressed in grey.

The boy in the bear suit climbed into the driving seat of the sleigh and took the unicorn’s reins. The other three children lined up as a beautiful wraithlike girl glided out of the palace in a dress of snowflake lace, wearing a crown of diamonds. She was clutching the hand of a little blond boy dressed in navy starred pyjamas. He was accompanied by a bouncing snow hare.

Casper swallowed. He was almost certain he was looking at Bianca’s little brother. But where was she?

Taking the white-suited child’s hand, the girl climbed into the sleigh. Bianca’s brother got in and sat next to them with his snow hare. The grey twins clambered into the seat in front, sitting either side of the boy in the bear suit.

The golems collapsed into heaps of snow that rippled like a wave to raise the sleigh, as the boy in the bear suit blew a great gust of wind under the hooves of the unicorn, lifting it into the air as it trotted forward.

Casper watched in wonder as the sleigh flew up and away from Snow Haven.

Remembering his mission, he sprinted towards the giant archway, expecting that at any second a golem would rise up in front of him and bar his way – but he made it.

‘Pordis?’ he called out, looking up at the cage suspended in the porch roof. ‘You still up there?’

Hearing the clatter of hooves above him, Casper went back outside and looked around. He found a big rock that he could just about move, and rolled it into the porch until it leaned against the wall to which the chain was attached. Climbing onto it, he was able to reach the wheel that held the chain. He yanked at it and pushed it, but it didn’t move. Jumping down, he ran back outside, searching for something that would help, and spotted a sharp-edged flint. He grabbed it and ran back to the rock. Clambering up, using both hands, he brought the sharp edge of the flint down on the chain with all his strength, again and again, until the ice link shattered, and the cage dropped. It made a terrible racket as the chain spooled down. The ice cage hit the floor with a bang!, shattering and falling apart.

Pordis snorted as she jumped free, giving him an accusatory look.

‘Sorry.’ Casper shrugged apologetically. ‘It was the only thing I could think of.’

Pordis shook her antlers, and Casper wasn’t sure whether she was cross or forgiving him.

‘Bianca’s in here somewhere. We must find her.’

But Pordis was already trotting towards the passageway that Casper had first chosen.

‘No, not that way. It’s a trap.’

Pordis ignored him, prancing over the hole that Casper had fallen into and continuing up the hall. Casper had no choice but to follow the reindeer.

When they arrived in the frost garden, Casper gazed around in amazement, but Pordis took the edge of his pyjama top between her teeth and pulled him through the garden until he stood beside a lemon tree in front of an ordinary-looking door.

The reindeer pawed her hoof against the door.

‘Is Bianca behind this door?’ Casper asked.

Pordis nodded.

‘Then we’d better work out how to open it.’ Casper ran his hands over its surface. There was no handle or lock. It felt like a sheer rectangular wall of ice.

Casper took a step back, studying the door. He fancied he could see a dark shape through it. The harder he looked, the clearer the shape became, until he could see it was Bianca, in her purple jumper and coat, sitting cross-legged on the other side of the door, writing in a small orange book. He focused his attention on her, and the image grew sharper until the door was as transparent as water. Following a sudden instinct, Casper reached both his hands through the glassy surface and made a grab for her.