Word ladder

Word game

Word ladder (also known as Doublets, or word golf) is a word game invented by Lewis Carroll. A word ladder puzzle begins with two words, and to solve the puzzle one must find a chain of other words to link the two, in which two adjacent words (that is, words in successive steps) differ by one letter.

Lewis Carroll says that he invented the game on Christmas in 1877. The first mention of the game in Carroll's diary was on March 12, 1878, which he originally called "Word links", and described as a two player game. J. E. Surrick and L. M. Conant published a book Laddergrams of such puzzles in 1927. The game was revived in Australia in the 1990s by The Canberra Times as "Stepword". Word ladders are often featured in the New York Times crossword puzzle.

The player is given a start word and an end word. In order to win the game, the player must change the start word into the end word progressively, creating an existing word at each step. Each step consists of a single letter substitution. Lewis Carroll's example has an extra fifth step as the third letter changes twice. Often, word ladder puzzles are created where the end word has some kind of relationship with the start word (synonymous, antonymous, semantic ). This was also the way the game was originally devised by Lewis Carroll when it first appeared in Vanity Fair. Some variations also allow the player to add or remove letters, and to rearrange the same letters into a different order (an anagram).

Donald Knuth used a computer to study word ladders of five letter words. He felt that three and four were too easy and six was too hard. Knuth used a collection of 5,757 common English five letter words, excluding proper nouns. He wrote a program which showed the steps connecting any two words, or noted that no connection was possible. He found that many word pairs were connected, but that 671 words were not connected to any other word, i. e 'had no neighbours', as he put it. He called these words "aloof", and noted amusingly that "aloof" is itself such a word.