Alex's Adventures in Numberland - Alex Bellos [98]
In the mid nineteenth century American newspapers started to print chess problems. One of the first, and most precocious, devisers of these problems was Sam Loyd. A New Yorker, Loyd was just 14 when he had his first conundrum printed in a local paper. By 17 he was the most successful and widely celebrated deviser of chess problems in the US.
He moved on from chess to mathematically based puzzles, and by the end of the century was the world’s first professional puzzle-compiler and impresario. He published widely in the American media, and once claimed that his columns attracted 100,000 letters a day. However, we should take his figure with a pinch of salt. Loyd cultivated the kind of playful attitude towards the truth that one expects of a professional riddler. For a start, he claimed he had invented the Fifteen puzzle, which was taken to be true for more than a century until in 2006 historians Jerry Slocum and Dic Sonneveld properly traced its origin to Noyes Chapman. Loyd also revived interest in the tangram with The 8th Book of Tan Part I, a version of an ancient text about the supposed 4000-year history of the puzzle. The book was a spoof, even though it was initially taken seriously by academics.
Loyd had a unique brilliance at turning mathematical problems into entertaining, distinctively illustrated puzzles. His most genial creation was invented for the Brooklyn Daily Eagle in 1896. The ‘Get off the Earth’ puzzle widely i popular that it was later adopted as a publicity gimmick by several brands, including The Young Ladies Home Journal, the Great Atlantic & Pacific Tea Company and the Republican platform for the 1896 presidential election. (Although its message was not a manifesto pledge.) The puzzle is an image of Chinese warriors positioned around the Earth, which is on a disc made out of card that can be spun around its centre. When the arrow is pointing NE there are 13 warriors, but turn the disc so the arrow points NW and there are only 12. The puzzle is confusing. There really are 13 warriors, then – in a flash – just 12. Which man has vanished and where does he go?
The trick operating in this puzzle is known as a geometrical vanish. It can also be demonstrated in the following way. The image on chapter 6 shows a piece of paper with ten vertical lines on it. When the piece of paper is cut along the diagonal line, the two sections can be realigned so that only nine lines are created. Where has the tenth line gone? What has happened is that the segments have been rearranged to form nine lines that are longer than the original line. If the lines in the first image have the length 10 units, then the length of the lines in the second image is 11 , since one of the original lines has been equally shared among the nine others.
What Sam Loyd did with ‘Get off the Earth’ is to curve the geometrical vanish so it was in a circular form, and in place of lines put Chinese warriors. There are 12 positions in his puzzle, akin to the 10 lines in the example overleaf. The position in the bottom left corner, where there are originally two warriors, is equivalent to the end lines of the vanish. When the arrow is moved from NE to NW, all the positions gain a bit more warrior, apart from the position with two warriors, which shrinks drastically, giving the impression that a whole warrior has been lost. In fact, it has just been redistributed around the others. Sam Loyd claimed that ten million copies of ‘Get off the Earth’ were produced. He became rich and famous, revelling in his reputation as the puzzle king of America.
Geometrical vanish: ten lines become nine.
Meanwhile, in Great Britain, Henry Ernest Dudeney was acquiring a similar reputation. If Loyd’s capitalist chutzpah and gift for