The annual fair at Wittering Feebleigh is a big occasion in the life of this little-known Grotswold village, and no event is more eagerly awaited than the pageant of pulchritudinous pigs. Each of the ten judges awards the contestants a whole number of points from 0 to 9, based on a range of criteria such as size, odour, twirliness of tail, and resonance of grunt.
A board with ten nails in it serves as the scoreboard. From each nail hangs a painted card bearing the number of points. Scores are thus a row of ten digits, such as the 1-2-1-3-3-3-7-8-0-6 awarded to Larry Trotter's prize porker Desdemona.
On seeing the score, Larry, a keen amateur mathematician, turned to his neighbour. "Do you see that pattern of numbers?"
"What pattern?" said his neighbour Wilf.
"The leftmost digit is 1, equal to the number of 0's in the row. The next digit is 2, equal to the number of 1's. The next digit is 1, equal to the number of 2's. The digit after that is 3, equal to the number of 3's in the row!"
"Yup, true," said Wilf, unimpressed, but Larry continued. "Let's see, the next digit is another 3, so there ought to be three 4's in the row—oh. The pattern stops there."
As Larry and Wilf stood there, the scores for the next pig went up on the board. And, by a strange coincidence—
"Look! For this pig the pattern keeps going all the way!" said Larry. "The successive digits are equal to the numbers of 0's, 1's, 2's, 3's, and so on, all the way to the number of 9's!"
What was the row of digits?
Prospect invites you to solve the puzzle and send us the solution. Correct answers will be entered into a draw. The winner receives a copy of the book Flatland: The Movie Edition (Princeton University Press, £8.95), a special edition of the classic mathematical adventure novel Flatland by Edwin Abbott, plus a DVD of the animated short film Flatland: The Movie, starring Martin Sheen.
Send answers to info@prospect-magazine.co.uk by 10th April. The winner will be announced in our May issue.
