{{Short description|Word game}} {{Use dmy dates|date=April 2025}} [[File:head_to_tail_word_ladder.svg|thumb|upright=0.5|Lewis Carroll's ''doublet'' in [http://gutenberg.org/files/35418/35418-h/35418-h.htm Vanity Fair, March 1879] changing the word "head" to "tail" in five steps, one letter at a time]] '''Word ladder'''{{efn|Also known as '''Doublets''',<ref name=Oxford/> '''word-links''', '''change-the-word puzzles''', '''paragrams''', '''laddergrams''',<ref>{{cite web|url=http://www.laddergrams.com |title=Laddergrams |publisher=Laddergrams |date= |accessdate=5 March 2016}}</ref> or '''word golf'''.}} is a word game invented by Lewis Carroll.<ref>{{Cite web | url=http://www.lewiscarroll.org/news/times060298.html | title=Lewis Carroll books are much in demand by collectors | access-date=4 November 2025 | archive-date=23 November 2008 | archive-url=https://web.archive.org/web/20081123033218/http://www.lewiscarroll.org/news/times060298.html | url-status=dead }}</ref> 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 exactly one letter.<ref name=Edge>{{cite book|title=The Edge of the Universe: Celebrating Ten Years of Math Horizons|author=Deanna Haunsperger, Stephen Kennedy|publisher=Mathematical Association of America|page=22|date=31 July 2006|isbn=0-88385-555-0}}</ref>
==History== Lewis Carroll says that he invented the game on Christmas in 1877.<ref name=Edge/> Carroll devised the word game for Julia and Ethel Arnold.<ref>{{Cite book|last=Cohen|first=Morton N.|url=https://books.google.com/books?id=a-8NBQAAQBAJ&q=doublets+julia+arnold&pg=PT347|title=Lewis Carroll: A Biography|date=9 April 2015|publisher=Pan Macmillan|isbn=978-1-4472-8614-1|language=en}}</ref> The first mention of the game in Carroll's diary was on 12{{nbsp}}March 1878, which he originally called "Word-links", and described as a two-player game.<ref name=Edge/> Carroll published a series of word ladder puzzles and solutions, which he then called "Doublets", in the magazine ''Vanity Fair'', beginning with the 29{{nbsp}}March 1879 issue.<ref name=Edge/> Later that year, it was made into a book, published by Macmillan and Co.<ref name=CarrollBook>{{cite book|url=https://books.google.com/books?id=JkQCAAAAQAAJ|title=Doublets, a word-puzzle, by Lewis Carroll|author=Charles Lutwidge Dodgson|publisher=Macmillan and Co|year=1879|authorlink=Lewis Carroll}}</ref>
J.{{nbsp}}E. Surrick and L.{{nbsp}}M. Conant published a book titled ''Laddergrams'' of such puzzles in 1927.<ref name=Oxford/>
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).'<ref name=Oxford>Augarde, Tony ''Oxford Guide to Word Games'' Oxford University Press, 2nd ed. 2003 p.216 {{ISBN|0-19-866264-5}}</ref>
The game was revived in Australia in the 1990s by ''The Canberra Times'' as "Stepword".<ref>{{cite news |url=http://nla.gov.au/nla.news-article129095312 |title=Cold Heat |newspaper=The Canberra Times |volume=65 |issue=20,392 |location=Australian Capital Territory, Australia |date=10 February 1991 |accessdate=18 September 2017 |page=3 |via=National Library of Australia}}</ref>
Word ladders are often featured in the ''New York Times'' crossword puzzle.<ref>{{Cite news|last=Amlen|first=Deb|date=21 February 2017|title=Quite Enough|language=en-US|work=The New York Times|url=https://www.nytimes.com/2017/02/21/crosswords/quite-enough.html|access-date=22 August 2020|issn=0362-4331}}</ref><ref>{{Cite news|last=Amlen|first=Deb|date=13 June 2018|title=Way to Go on Record|language=en-US|work=The New York Times|url=https://www.nytimes.com/2018/06/13/crosswords/daily-puzzle-2018-06-14.html|access-date=22 August 2020|issn=0362-4331}}</ref><ref>{{Cite web|last=Gaffney|first=Thomas|date=19 June 2013|title=Climb the Ladder|url=https://wordplay.blogs.nytimes.com/2013/06/19/climb-the-ladder/|access-date=22 August 2020|website=Wordplay Blog|language=en-US}}</ref>
==Rules== The player is given a ''start word'' and an ''end word''. In order to win the game, the player must progressively change the start word into the end word, creating an existing word at each step. Each step consists of a single letter substitution.<ref name=Edge/> For example, the following are the seven shortest solutions to the word ladder puzzle between words "cold" and "warm", using words from Collins Scrabble Words.
:{| style="text-align:center;" |COLD||→||CO'''R'''D||→||COR'''M'''||→||'''W'''ORM||→||W'''A'''RM |- |COLD||→||CO'''R'''D||→||C'''A'''RD||→||'''W'''ARD||→||WAR'''M''' |- |COLD||→||CO'''R'''D||→||'''W'''ORD||→||W'''A'''RD||→||WAR'''M''' |- |COLD||→||CO'''R'''D||→||'''W'''ORD||→||WOR'''M'''||→||W'''A'''RM |- |COLD||→||'''W'''OLD||→||WO'''R'''D||→||WOR'''M'''||→||W'''A'''RM |- |COLD||→||'''W'''OLD||→||WO'''R'''D||→||W'''A'''RD||→||WAR'''M''' |- |COLD||→||'''W'''OLD||→||W'''A'''LD||→||WA'''R'''D||→||WAR'''M''' |}
As each step changes only one letter, the number of steps must be at least the Hamming distance between the two words – four in the above example.<ref>{{cite book |last1=Waggener |first1=Bill |title=Pulse Code Modulation Techniques |date=1995 |publisher=Springer |isbn=9780442014360 |page=206 |url=https://books.google.com/books?id=8l_o6kI3760C&pg=PA206 |access-date=13 June 2020}}</ref> 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).
==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.<ref name=Edge/> 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.<ref name=Edge/> 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.<ref name=Edge/>
== See also == * Paronym
== Notes == {{Notelist}}
== References == <references/>
==External links== * [http://blog.wolfram.com/2012/01/11/the-longest-word-ladder-puzzle-ever/ The longest word ladder puzzle ever] Computer analysis to find long word ladders * [https://books.google.com/books?id=JkQCAAAAQAAJ&dq=charles%20dodgson&pg=PP1 Doublets, a word puzzle, by Lewis Carroll] * [http://ceptimus.co.uk/wordladder.php An on-line word-ladder solver for English]
Word ladder Category:Semantic relations