Eckler is also a frequent contrbutor to www.wordways.com, which has some good web accessible articles I like this observation, also due to Eckler apparently, that the 26 neighbors of a lattice point in Z3 invite a person to assign letters to the directions and then start looking for knotted words. http://www.wordways.com/knotted.htm Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/ehome.htm ----- Original Message ----- From: "Michael Kleber" <kleber@brandeis.edu> To: "math-fun" <math-fun@mailman.xmission.com> Cc: "Andrew Bremner" <bremner@tulwar.la.asu.edu>; <bremner@asu.edu> Sent: Monday, August 11, 2003 8:30 AM Subject: Re: [math-fun] Words
On Monday, August 11, 2003, at 10:34 am, Richard Guy wrote:
I recently ran across a word problem, which I vaguely remember from years ago, and which (evidently) has the solution
S T A R T L I N G S T A R L I N G S T A R I N G S T R I N G S T I N G S I N G S I N I N I
The best source I know for such games is Ross Eckler's outstanding book _Making the Alphabet Dance_ (St. Martin's Press; paperback $14.95). Eckler is the editor of _Word Ways_, a quarterly publication dedicated to this sort of stuff, and MtAD is the highlights of decades of collecting.
The first section of Chapter 4, "Transforming one word into another", is on the above question. The book reports various length-record-holding sequences (depend on the dictionary you're using, of course):
M-W unabridged initially looks close to yours above, but goes off in a different direction with, shall we say, less familiar words: strangelings-strangeling-strangling-stranging-stanging-staging- saging-aging-aging-ging-gin-in-i. Definitions available at m-w.com, I suppose.
Pocket M-W, it claims, gives you: sheathed-sheathe-sheath-heath-heat-eat-at-a. Yours is length 9 and this is only 8, and I can't think of what word you used that wouldn't be in there, but I don't have a copy to check.
The OED has a length 14 chain starting with "strengthenings", but it passes through some pretty funny-looking territory (strenghing, streing) along the way.
The chapter goes on to describe the large connected component of the insertion-deletion graph for pocket M-W boldfaced main-entry words: it contains around 2800 words, including such 8-letter outliers as heathery, splutter, and wrangler; its diameter seems to be 34, the best known distance from DUD to MISERLY, and there is a length 14 path from LEATHERY to SOWING which is optimal (in that it could not be shorter even if we added extra words, since the words have no letters in common and their lengths total to 14 -- SNOWING makes this 15, but it's not a main entry word, only listed under SNOW).
That should give you a feel of what the book is like; really a pleasure...
--Michael Kleber kleber@brandeis.edu
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