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). Five-letter word ladders 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. See also Paronym Notes External links The longest word ladder puzzle ever Computer analysis to find long word ladders Doublets, a word puzzle, by Lewis Carroll An on-line word-ladder solver for Afrikaans, English, Esperanto, German and Spanish (requires login) An on-line word-ladder solver for English Lewis Carroll Resources On-line facility giving Carroll's original puzzles with hints and solutions and tool to help solve and compile puzzles Word ladder Semantic relations