Knight's challenge answered.

Knight's challenge answered. Only one solution was received for the Five-Jog Knight puzzlecontest posed in the November Word Ways. Submitted in mid-December,editor Jeremiah Farrell's solution managed to achieve a 20/20Collegiate score, which is to say that every word in its 20-word wordset is an entry in Webster's New Collegiate Dictionary. Suchperfection had not been expected. Readers may recall that the object of this puzzle was to find aword for each of the 20 node circles in the knight's network suchthat each letter of that word would be shared with one of theneighboring node-words to which it was connected by a knight'smove. A further constraint was that each letter of the alphabet had toappear in the network at least twice and that no letter could appear init more than four times. (Or to put it another way, solvers were givenfour complete alphabets, two of them upper-case and two lower-case; all52 of the upper-case letters had to be used in the solution, as well asany 24 of the lower-case letters.) The solution containing the mostwords listed in the Collegiate was to be the winner. Shown at left below is a proof-of-solvability solution by theauthor in which 17 of the 20 words are listed in the Collegiate, theexceptions being feu, jynx and vac. The 12 lower-case letters it usestwice are a, e, h, i, l, n, o, r, s, t, u and y. To its right is theeditor's winning solution, in which, as mentioned, all 20 words areCollegiate entries. (Xed is the past tense of the verb "to x"[i.e., mark with an "x"], and is listed in boldface type underthe word X in the Collegiate.) The 12 lower-case letters it uses twiceare a, b, e, g, i, n, o, r, s, t, u and y. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] The reason for the Collegiate-score element of the contest, ofcourse, was to encourage solvers to search for the commonest words touse in their solutions. The Collegiate was not necessarily the bestdictionary that could be found to serve as the criterion of solutionquality ("quality," in this context, being taken to mean therelative commonness of a solution's word set), but its ubiquityrecommended it. An objectively better choice might have beenMerriam-Webster's next-smaller current dictionary, a tradepaperback entitled simply The Merriam-Webster Dictionary. This work,which is described as being "based on" the Collegiate,contains about 65,000 entries as compared to the Collegiate's165,000. When scored by this dictionary, my solution loses an additionalfive words (byre, crwth, dight, qoph and qursh), whereas Jerry'ssolution surprises again by losing only one word (qoph). Thus, while theCollegiate quantifies the quality difference between the two solutionsas 20 - 17 = 3, its smaller cousin makes it 19 - 12 = 7. Which of thesenumbers seems to better reflect the actual magnitude of the quality gap? An interesting, if perhaps irrelevant, aspect of solutions to thispuzzle has to do with their relative degrees of permutability. In thefirst solution above, for example, two of the words (six and nut) haveCollegiate-listed anagrams (xis and tun), meaning that it could havebeen expressed as any one of four different word sets. The secondsolution, on the other hand, with its Collegiate-listed anagramsbast/bats/stab/tabs, flogs/golfs and now/own/won, could have beenexpressed in no fewer than 36 different word sets. And had theCollegiate, as some other dictionaries do, chosen tav rather than tawfor the spelling of the Hebrew letter--thereby listing an anagram forvat--the number of different word sets that this solution could formwould stand at 72. Is it purely coincidence, I wonder, that the solutionwith the commoner words is also the more protean of the two? Although not interested in pursuing these puzzles to the Six-JogKnight's level, I was curious to see what its network would looklike and therefore constructed the following diagrams. They show thenetwork formed by a composite of all the routes that connect the centralsquares of the end rows of a 9 x 11 chess-board in six knight'smoves; grid lines are omitted for clarity. As a puzzle, the Six-Joglooks as though it might be solvable, depending on what, if any,restrictions were to be placed on the selection of the 184 lettersneeded to fill its 39 nodes. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] JIM PUDER Saratoga, California