Word ladder
Word ladder (also known as Doublets,[1] word-links, 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.[2]
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History [edit]
Lewis Carroll says that he invented the game on Christmas day in 1877.[2] 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.[2] Carroll published a series of word ladder puzzles and solutions, which he then called "Doublets", in the magazine Vanity Fair, beginning with the March 29, 1879 issue.[2] Later that year it was made into a book, published by Macmillan and Co.[3]
J. E. Surrick and L. M. Conant published a book Laddergrams of such puzzles in 1927.[1]
Vladimir Nabokov alluded to the game using the name "word golf" in the novel Pale Fire, in which the narrator says 'some of my records are: hate—love in three, lass—male in four, and live—dead in five (with "lend" in the middle).'[1]
Rules [edit]
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.[2] For example, the following are solutions to the word ladder puzzle between words "cold" and "warm".
COLD → CORD → CARD → WARD → WARM
COLD → CORD → CORM → WORM → WARM
COLD → WOLD → WORD → WARD → WARM
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).
Variations [edit]
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This section may contain original research. (April 2013) |
By using additional rules there are arising special variations of the wordladder. Examples of this variations are the "diagonal" and the "sandglass".
In a "diagonal", the player change the letters in a fixed sequence from the left to the right. In the first move the first letter is changed, then the second, then the third, and so on. Letters cannot be added or removed. The charm of the diagonal is that the end word becomes visible step by step from the first letter to the last. The obliged order of changing makes it difficult to find diagonals. At first only diagonals with three, four or five letters were known. Recently diagonals with six letters are discovered. The search for diagonals with seven or more letters is continuing.
In a "sandglass", letters cannot be changed. From the start word at every turn a new word is formed by removing one letter, until the shortest word of the sandglass is reached. On subsequent turns, one letter is added each turn until an end word is reached.
SEVERE → SEVER → EVER → EVE → EVEN → EVENT → EVENTS
The end word of a sandglass must have as many letters as the start word. When written one word below another, this forms a symmetrical hourglass shape. The intention is to find a sandglass with the largest number of steps.
Five-letter word ladders [edit]
Donald Knuth used a computer to study word ladders of five-letter words. He believed that three-letter word ladders were too easy (although Lewis Carroll found six steps were required for APE to evolve into MAN),[1] and that six-letter word ladders were less interesting, since relatively few pairs of six-letter words could be connected with a word ladder.[2] Knuth used a fixed collection of 5,757 of the most common English five-letter words, excluding proper nouns. He determined exactly when two words of the collection had a word ladder between them via other words in the collection.[2] Knuth found that most words were connected to each other, and he also found that 671 words of the collection did not form a word ladder with any other words. He called these words "aloof", because "aloof" is itself an example of such a word.[2]
Notes [edit]
- ^ a b c d Augarde, Tony Oxford Guide to Word Games Oxford University Press, 2nd ed. 2003 p.216 ISBN 0-19-866264-5
- ^ a b c d e f g h Deanna Haunsperger, Stephen Kennedy (July 31, 2006). The Edge of the Universe: Celebrating Ten Years of Math Horizons. Mathematical Association of America. p. 22. ISBN 0-88385-555-0.
- ^ Charles Lutwidge Dodgson (1879). Doublets, a word-puzzle, by Lewis Carroll. Macmillan and Co.
External links [edit]
- The longest word ladder puzzle ever Computer analysis to find long word ladders
- Doublets, a word puzzle, by Lewis Carroll
