Christmas 2015 – a doublet

christmas treeCharles Lutwige Dodgson, alias Lewis Carroll, did not just write Alice in Wonderland, but also books on Mathematical subjects and puzzle books. The story goes that Queen Victoria, who reigned Britain during Charles live, was so enchanted by ‘Alice in Wonderland’, that she wrote the author and asked him to send her a copy of his next book. Charles dutifully did sent her his next book – on a mathematical subject.

Charles was also the inventor of a type of puzzle where one word has to be changed into another word by changing one letter at a time.
cot (replace ‘a’ with ‘o’)
cog (replace ‘t’ with ‘g’)
dog (replace ‘c’ with ‘d’)
Lewis Carroll says that he invented the game on Christmas day 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. Carroll published a series of word ladder puzzles and solutions, which he called “Doublets”, in the magazine Vanity Fair, beginning with the March 29, 1879 issue. Later that year it was made into a book, published by Macmillan and Co.The one which Charles originally used was the problem to change HEAD into TAIL:
heal (Replace ‘d’ of ‘head’ to ‘l’)
teal (Replace ‘h’ of ‘heal’ to ‘t’)
tell (Replace ‘a’ of ‘teal’ to ‘l’)
tall (Replace ‘e’ of ‘tell’ to ‘l’)
TAIL (Replace ‘l’ of ‘tall’ to ‘i’)
The puzzles have been called Doublets, Word-links, Laddergrams, Word-golf, and Word-ladders.

At this time of the year, a Christmas puzzle seems appropriate. Over the past century, attention at Christmas seems to have shifted from Mary and her Baby to the christmas tree.

Try to change the word MARY into TREE in the fewest number of steps. Or, if you prefer that, you can change the word TREE back to MARY.

Marcel Danesi, Ph.D., on, believes that ‘solving them will give the verbal areas of the brain a veritable workout. The reason I believe this to be the case is that a solution entails knowledge of both word structure and semantics. The main semantic process involved is word association and, thus, recall, which is a powerful form of brain-activating thinking, at least as I read the relevant research. We are of course faced with the usual problem of trying to understand or explain how the research translates into benefits through puzzle-solving. The way I look at it is that puzzles such as the doublet can only be beneficial to overall brain health. As one’s semantic memory begins to wane through the aging process, giving the semantic parts of the brain a puzzle workout can only be advantageous

You can check your solution here

You are welcome to remark on the puzzle: its wording, style, level of difficulty. I love to read your solution times. Please do not spoil the fun for others by listing the solution. Solutions will be posted after one or more weeks.

Sources and further reading: The Levehsteind distance between two words is the number of operations that is needed to change one word into another by adding a letter, removing a letter or replacing a letter. The Damerau–Levenshtein distance is identical, but also allows the transpostion of two adjacent characters.
The distance between two words in a doublet as used by Dodgson is a special case of the Levenshtein distance: inseryion and deletion are not allowed, while all intermediate words must appear in a dictionairy. doublets as a complex network


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