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The annual fair at Wittering Feebleigh is a major event in the life of this little-known Grotswold village, and no event is awaited with greater expectancy than the Pageant of Pulchritudinous Pigs. Each of the ten judges awards the contestants a whole number of points between 0 and 9, based on a broad range of criteria such as size, odour, twirliness of tail, and resonance of grunt.
The points are displayed on a board, maintained especially for the purpose. It consists of ten nails in a row, upon which hang painted cards bearing the numbers of points awarded by the ten judges. A typical score is thus a row of ten digits 0-9, such as 1-2-1-3-3-3-7-8-0-6. In fact, that was the series of points scored by Larry Trotter’s prize porker Desdemona. Larry was an accomplished amateur mathematician, and he suddenly turned to his neighbour.
“Wilf? Do you see the pattern in those numbers?”
“The leftmost digit is 1, equal to the number of 0s in the row. The next digit is 2, equal to the number of 1’s in the row. The next digit is 1, equal to the number of 2’s in the row. The digit after that is 3, equal to the number of 3’s in the row!”
“Yup, true,” said Wilf, unimpressed, but Larry was getting quite excited. Would the pattern continue?
“Let me see... the next digit is another 3, so there ought to be three 4’s in the row—oh, buttercups!” Or words to that effect. “The pattern stops.”
Larry and Wilf watched as the scores for the next pig went up on the board. And, by a strange coincidence—
“Wilf! Look! The pattern keeps going all the way!” yelled Larry. “The successive digits are equal to the numbers of 0’s, 1’s, 2’s, 3’s, and so on in the row, all the way to the number of 9’s!”
What was the row of digits?
Ian Stewart writes a monthly Enigma and Puzzle column for Prospect Magazine