Sam Loyd

In the nineteenth century, two important figures stand out in recreational mathematics : Henry Dudeney and Sam Loyd. Both were prolific compilers, though Dudeney is widely regarded as the better mathematician while Loyd is seen as the better puzzles promoter. The ingenuity with which Loyd presented his puzzles is unparalleled and no-one doubts the value of his contribution to recreational mathematics. But it has to be noted that despite his legacy, several of his claims to priority were unjustified. For example, one puzzle that is often credited to Sam Loyd is the cryptarithm or alphametic, where the digits in an arithmetic calculation have been replaced by letters, the aim being to recover the digits. However, an example appears in The American Agriculturalist of 1864 (Singmaster 1993a) and since the 23 years old Sam Loyd was still preoccupied with chess problems at the time, this example almost certainly predates his contributions. In order to assess his priority claims, though, we need to know what he claimed to have invented.

Trick donkeys puzzle

14-15 puzzle

His headed notepaper (shown right) dated 15 April 1903 presumes him to be the 'Author of the famous "Get Off The Earth Mystery", "Trick Donkeys", "15 Block Puzzle", "Pigs In Clover", "Parcheesi", Etc., Etc., ' (White 1914, Plate III). In fact, the "Get Off The Earth Puzzle" was a circular adaptation of linear disappearing objects puzzles (Gardner 1956, Chs. 7-8) and the Donkeys principle (shown left - cut along the dotted lines then seat the two jockeys on the two horses) had already been realised with dogs (Singmaster 1993b, p.222) around 1857, thirteen years before Loyd registered it. Headed notepaper

His biggest claim, though, is for the "15 block" puzzle and there are strong reasons for entertaining doubt as to Loyd's priority. Fifteen numbered blocks were randomly placed in a 4x4 grid with one vacant square. The aim was to use the vacant space to slide the blocks into serial order, leaving the space in the bottom right-hand corner of the grid. It was the greatest puzzle craze of the nineteenth century and occupied most of America and Europe from 1879 to 1881. The New York Times reported twice on the craze, on 22 March 1880 and again on 11 June 1880, and despite actually living in New York, Loyd curiously failed to receive credit. Other contemporary articles on the craze have also been found (Hordern 1986, p.20) and again Loyd is not mentioned. Given the master self-promoter that Sam Loyd was, his absence from publicity is uncharacteristic, especially since the puzzle attracted world-wide interest. It is possible that Loyd's notepaper refers to the "14-15" puzzle (shown above left), a special initial configuration of the "15 Block Puzzle", arrived at by placing all the blocks in serial order except the 14 and 15 which were juxtaposed. Loyd put up a prize of $1000, indicating it was his own invention. In fact, the inventor could have been just about anyone who attempted to solve the "15 Block Puzzle" as the New York Times of 22 March 1880 attests : "... At 8 o' clock the next morning Mr Schurz was taken home in a carriage completely exhausted, and leaving his blocks in the position 13,15,14 ...". Whoever reached this configuration first, Sam Loyd's son (Loyd 1928, p.1) did not think it was his father : "It was in the early 80s, when I had barely attained my 'teens, that the "14-15" puzzle flashed across the horizon, and the Loyds were among its earliest victims." So, it seems the "14-15" puzzle found Sam Loyd, not vice versa. In fact, to this day the real authors of the "15 Block Puzzle" and its insoluble derivative are unknown.

In our idealization of great achievers, they are often placed above human frailty. However, in the case of Sam Loyd, one must treat some of his claims to priority with caution. Even allowing for the inevitable unconscious borrowing that creativity is heir to, Loyd's borrowing was a little more conscious than most!

  2. Clarke, B. R. A history of recreational mathematics, Puzzles for Pleasure (Cambridge University Press : 1994)
  3. Gardner, M. Mathematics, Magic, and Mystery (Dover : 1956)
  4. Hordern, E., Sliding Piece Puzzles (Oxford University Press : 1986)
  5. Singmaster, D. Private correspondence, 17 July 1993, information originated from Will Shortz (1993a)
  6. Singmaster, D. Sources in Recreational Mathematics, An Annotated Bibliography, 6th preliminary edition, South Bank University, London, November 1993 (1993b)
  7. White, A. Sam Loyd and his Chess Problems (Leeds : 1914)