AFTER becoming the world champion, Grandmaster Vishwanathan Anand is relaxing in his Chennai house when the doorbell disturbs him. A bearded man in magician’s robes with eyes hidden behind shades is at the door.

"Mr Anand, it is said that you are the best chess player in the world," he says. "I am only a humble student of this game, but who are you and what is your business with me?" says Vishy. "You can call me the Knight of Mathland, but what’s in a name. I have brought you a chessboard and a little mind game. Would you play it?" the man replies.

"The world championship match was exhausting and I would rather not look at another chessboard for some time," Vishy says. "This is not another chessboard and this is not an ordinary chess game," the man replies and takes out a 3x3 chessboard from his bag. Then he takes out four knight pieces (two black and two white) from it. These are put on the four corner squares on the board, the white ones in the top row and the black ones in the bottom row, while Vishy observes.

FIGURE1

"The white knights are to be swapped with the black ones by using only legitimate chess moves for knights (two ahead or down and one to the left or right). It means that two knights cannot occupy the same square. I forgot to mention that there would be no opponent. You will be on your on. I like if chess games are short, so, you will have to finish in the minimum number of moves. Of course, you can quit if you are scared. Nice guys don’t stay at the top, but mad men do, like the champion of 1972."

Vishy’s eyes twinkle for a moment. The gentleman accepts the challenge and his mind becomes a calculator. He says, "Leaving out the middle square, let me arrange the rest of the eight in a sequence, beginning from the top left square and proceeding towards the right. There is a relation between these squares and the knights."

Anand draws a picture to show all the legitimate knight moves. There is no way to reach the middle square. From all the other squares, there are exactly two legitimate moves. This observation helps Vishy unfold the moves into a sequence of eight squares. He shifts the knights in a selected direction one after another and solves the puzzle in the minimum number of moves. "I could have moved the knights in any direction and won. Gentlemen do win, Sir, if they know how to calculate," says Vishy.

He says, "I remember the words of Norbert Wiener. He said mathematics was a field in which one’s blunders tended to show very clearly and could be corrected or erased with a stroke of the pencil. Mathematics has often been compared with chess, but differs from the latter in the sense that it is only one’s best moments that count in mathematics and not one’s worst. A single inattention may lose a chess game, but a single successful approach to a problem, among many that have been relegated to the wastebasket, will make a mathematician’s reputation. I am sure that you will agree with me on this one, Bobby."

"Bobby who?" says the man. "Stop being fishy. I know that you are Bobby Fischer who won the world chess title in 1972. No one else believes that you have to be mad to win in chess. It is my honour to receive you," Vishy replies. "I was wrong. Gentlemen do win," says Bobby and shakes the hand of the champion.

— Aditya Rishi

— Godfrey Hardy