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They drew up chairs and sat down facing each other across the board.

'Five seconds per move,' said the Doctor. 'First person to predict the precise number of moves to the first possible checkmate wins.'

Kadiatu nodded and opened with a queen's pawn advance.

The first game lasted twenty-eight moves and ended when the Doctor held up his hand and said: 'Mate in six.'

Kadiatu frowned at the board. 'Yes,' she said finally, 'mate in six.'

They turned the board around and set up the pieces again, the Doctor playing white. Chris and Dep watched as the two players slapped down the pieces with such speed that it was almost impossible to follow the course of the game.

Again the Doctor held up his hand. 'Twelve,' he said.

'Never,' said Kadiatu. 'You couldn't possibly force a mate in twelve.'

'Not me,' said the Doctor. 'Twelve moves until you beat me. I said the first possible checkmate, regardless of who's in check.'

'But that's stupid,' said Kadiatu. 'If we do it like that, it means either of us can deliberately play to lose in order to make the correct prediction.'

'Yes,' said the Doctor. 'Interesting concept, isn't it?'

'If you say so,' said Kadiatu. 'Are you implying that losing is as important as winning?'

'What I'm saying,' said the Doctor, 'is that you have to know by which set of rules you're playing the game.'

Kadiatu leaned back in her chair and folded her arms. 'Is this going to get needlessly philosophical?'

The Doctor said nothing as he replaced the pieces on the board and turned it around.

'What if I don't want to play?' said Kadiatu.

'Too late,' said the Doctor. 'You sat down at the table and now you have to play.'

Kadiatu smiled. 'All right then,' she said, 'but this time we make it two seconds a move.'

The sharp sounds of the pieces hitting the board was like the report of a clockwork machine-gun. Kadiatu sat hunched over the table, her hands moving so fast that they were almost impossible to see. Chris noticed that although the Doctor appeared to move far slower he none the less seemed to be placing his pieces, if anything, faster than Kadiatu. The game was over in less than two minutes.

'You cheated,' said Kadiatu. 'You played to win this time.'

'Again,' said the Doctor.

Another flurry of movements. Less than a minute.

'Twelve,' said the Doctor.

Kadiatu frowned and bit her lip. She replaced the pieces slowly, turned the board around and glanced down.

'Fifteen,' said the Doctor.

'Hey,' she said, 'I haven't even moved yet.'

'You were going to open with King's pawn,' said the Doctor, 'weren't you?'

'Yes.'

'Mate in fifteen then.'

Kadiatu stared at the Doctor, her eyes narrowed, then opened wide in understanding. The Doctor smiled smugly back at her.

They stopped moving the pieces. After another twelve 'games' they stopped looking at the board at all.

Chris and Dep watched on in fascination as the Doctor and Kadiatu faced each other across the table, the chessmen standing forgotten between them.

And the Doctor was still winning, rattling off his predictions before Kadiatu could open her mouth.

'Twenty-one,' said Kadiatu.

The Doctor hesitated and actually glanced down at the board. 'You beat me,' he said, 'I don't believe it.'

'Cheer up, Doctor,' said Kadiatu. 'It was bound to happen sooner or later.'

'Not to me it doesn't,' he said. 'You just said the first number that came into your head.'

'Ah,' said Kadiatu, 'but it was the right number.'

Muttering, the Doctor swept the chess pieces into the case and closed the board. 'Right,' he said, rolling up his sleeve and thumping his elbow down on the table. 'Arm wrestling, best of five.'

'The Doctor beat Kadiatu at arm wrestling?' said Bernice.

'That's what I said,' said Chris. 'Three falls to nothing.'

'I don't believe it.'

'That's what she said.'

The sky over the aerodrome had been overcast until saRa!qava had a little chat with God; after that the clouds simply evaporated in the space of ten minutes.

The ornithopter