Knight\u27s Tour Quotes (KTQs), also called Knight\u27s Tour Crypts, are a word puzzle enjoying a new vogue in the National Puzzlers\u27 League since David Silverman reintroduced them in 1973. Dmitri Borgmann presented some examples in  Chesswords  in the May 1974 Word Ways. A KTQ is a quote written out along a knight\u27s tour. It is a form, usually rectangular, with each square containing a single letter or punctuation mark. Stepping from letter to letter by knight\u27s moves (two squares horizontally or vertically, then one square perpendicular to that), visiting all letters once, one can spell out a message. To reduce the task from drudgery to pleasure, the starting letter is underlined and the word lengths and punctuation of the message are given

Cohen, Philip M.

English

Digital Commons @ Butler University

" i ~ 22 THEMATIC KNIGHT'S TOUR QUOTES PHILIP M. COHEN Aliquippa, Pennsylvania Knight's Tour Quote s (KT Qs), also called Knight I S Tour Crypts, are a word puzzle enjoying a new vogue in the National Puzzlers' League since David SilverITlan reintroduced theITl in 1973. DITlitri BorgITlann presented SOITle exaITlples in "Chesswords" in the May 1974 Word Ways. A KTQis a quote written out along a knight's tour. It is a forITl, usually rectangular, with each square containing a single letter or punctuation ITlark. Stepping froITl letter to letter by knight's ITloves (two squares horizontally or vertically, then one square per­pendicular to that), visiting all letters once, one can spell out a ITles­sage. To reduce the task froITl drudgery to pleasure, the starting let­ter is underlined and the word lengths and punctuation of the ITlessage are giv­ AAEE. ENR en. A sITlall exaITlple (" Even paranoids RDVNEASN can have real eneITlies." 4 9 3 4 4 7) is CHOAVIAE given at the right. IESMNLPE KTQs are fun to solve, but they are trivial to COITlpose. SiITlply take a knight's tour froITl a book and replace the nUITlbers in order with the characters of the quote. If none is available, one can very easily be constructed. The siITlplest way is to use Warnsdorf's rule: always ITlove the knight to the cell froITl which there are the fewest exits to un­occupied cells. If there is a choice, it can generally be ITlade at ran­dOITl, except SOITletiITles near the end of the tour. (It ITlay seeITl odd to always ITliniITlize one's choices, but this rule avoids the COITlITlonest error in constructing tours: absent-ITlindedly blocking all approaches to a square.) To add interest, and to challenge the constructor, I suggest adding the requireITlent that a line of the array spell out a word or words. AITlong other things, this can be used to produce personalized puzzles. I once sent a newlywed couple, both in the National Puzzle rs' League, a wedding card on which an epithalaITlial jingle was turned into a KTQ spelling out their NPL pseudonYITls. It is easy to blunder in producing a theITlatic TKQ; it took ITle hours to do ITly first few. I therefore show how to construct one, so that those interested will not have to reinvent the wheel. Step 1 Get a sheet of graph paper and a pencil with a good eraser. Step 2 Given the word that will appear in the final KTQ, you ITlust choose or write a quotation that includes the needed letters, properly placed. Fe joke from! Why did thE last rites. which willi knight's to' WORD WA' resulting 6 Step 3 In I far too con letters: th, is hard to I and so on. acters of tl and use the way is to " columns 01 Step 4 A ~ vice versa will have e versa. Tb odd-nuITlbe positions, ITlake a tab odd and ev, Letter , Even Odd will have t able quote ters confli Step 5 Ins For reaSOI an edge, 0 label the s f r OITl botto square is : corner is I tangle witt ner squarE 3 (Y) : knight rna. in a1. Fo policy is t, few knight bestweca (26,28), : ur Crypts, zlers I Dmitri ,e May ght's tour. ing a single ly knight's ~are per­out a mes­tarting let-NR S N AE FE Simply , order with ery easily ,Ie: always exits to un­de at ran­,ern odd to nmonest lproaches :est adding words. ,d puzzles. " League, ,to a KTQ k me one J so ~raser . ~ must properly 23 placed. For the words I will use WORD WAYS; for the quote, this joke from Son of Giant Sea Tortoise, edited by Mary Ann Madden: Why did the chicken cross the road? Because he was giving it the last rites. This contains 62 letters (60 if we omit punctuation marks), which will not make a suitable rectangle (the easiest shape for knight's tours). We want one side to be eight letters to accommodate WORD WA YS. So change" giving it the" to "administering"; the resulting 64 letters make a good eight- by-eight square. Step 3 In making the tour, it is 012 3 4 5 6 7 8 9 far too confusing to work with the WHYDIDTHE letters: there are duplications, it 10 CHI C KEN C R a is hard to recall what comes next, 20 SST HER a AD? and so on. So number the char­ 30 B E C A USE HEW acters of the quote in sequence, 40 A SADMIN 1ST and use the numbers. The easiest 50 E R I N G LAS T R way is to write the letters in ten 60 I T E S . columns on the graph paper. Step 4 A knight always move from a white square to a black one, and vice versa. In a tour on a checkerboard, therefore, all white squares will have even numbers and all black squares odd numbers, or vice versa. Thus. in WORD WA YS, the W, R, W, Y will have to occupy odd-numbered l'0sitlons in the quote and 0, D, A, Seven-numbered positions, or vice versa. To choose the proper letters from the quote, make a table of each letter's appearances in the quote, separated into odd and even. From the table given below, it is clear that W R W Y Letter W a R D W A Y S Even 26 18 4,6,28 40,42,56 ­ 20,48 Odd 1,39 19 25,51,59 43 1,39 27,33 3 21,35,41,57,63 will have to be odd; there is no choice for W W Y. An otherwise suit­able quote may have to be discarded at this stage if the no- choice let­ters conflict. Step 5 Insert numerical equivalents for the letters into the array. For reasons that become clear in Step 9, they must be inserted along an edge, or the task becomes too difficult. For reference purposes, label the squares of the eight-by-eight as follows: rows are 1 to 8 from bottom to top, columns are a to h from left to right, and a square is labeled by its column and row. Thus, the lower right hand corner is hI. We will insert WORD WA YS into aI-hI. (On a rec­tangle with an odd number of square s, like a seven- by- nine, all cor­ner squares must contain odd numbers -- remember this at Step 4.) 3 (Y) must go in gl, 26 (0) in b1. 1 (the first W) must be two knight moves away from 3, so it must go in e1, and 39 (the other W) in al. For the other letters there is a choice of numbers. The best policy is to bunch the numbers up so that they can be connected by a few knight moves. In this case, good bunching is not possible. The best we can do is: 3926 51 28 1 56 3 48 with four clusters: (1,3), (26,28),39, and (48,51,56). They will be hard to connect. 24 Now recheck the inserted nutnbers against the original quote! It is heartbreaking to cotnplete a KTQ and then find it doesn't spell out what it was supposed to. Step 6 Start connecting the nutnbers into a knight I s tour. Pencil in line s b3-a1-c2 and f2-h1-g3 as a retninder that these knight tnoves tnust be part of the final tour. Thus only 38 and 40 can go in b3 / c2; decide which goes 53 52 29 ~2b54 27 50 5128 55 1 249 56 58 4"f 3 57 48 where later. 26 and 28 can only be connected by a 27 at c3, so put that in; sitnilarly, 2 tnust be at £3. 48 can be connected to 51 via f2 / d3 or g3 / e2; let I s try the fortner. With 49 at f2, 47 tnust be at g3. Nowlookata2. Ithas'l-ccesstoonly2squares,c1andb4. 1£ we 1 re not to cut it off frotn the tour, we tnust connect it to c 1 (51) ; put 52 in a2, 53 in b4. Sitnilarly for h2. 53 can now be connected to 56 in only one way. This leaves 28 only one exit, so put 29 at b2. The first connections are done, and appear in the above array. Nowuilderline, all .active nutnbers - - those still lacking at least one connection. Run through the fragtnents of the tour thus far (1- 3, 26­29, 47-58) for errors, and tnake sure no active nutnber is walled in. Make such checks frequently, or you will tnake errors, and waste a lot of titne. It looks OK, so save this diagratn for reference (in case later tnis­takes force us to retrace our steps) and copy it elsewhere. Step 7 Continue to connect the scat­ 23 54 46 5 tered chains. In doing so, there are 3053244136435845 three itnportant principles to follow: ""Z5382750TI 2474 52 29 40 37 42 49 44 57 ( 1) The still-unused squares tnust 39 26 51 28 1 56 3 48 always be 1<ept in as neat and rectan­gular a group as possible, to ease later work. Here, the isolated squares in the second row and the protrusion at a4/a3/b3 should be filled in as soon as possible. (2) Keep an eye on all active nutnbers to tnake sure they are never cut off. 1£ you fill in the next-to-last exit on an active square, like 28 in Step 6, itntnediately extend its portion of the tour to the last exit, and circle the extension to tnark it as a new active nutnber. (3) Watch for squares with only two exits; new ones will constantly be fortned as you go. It is a good idea to tnark a two-exit square by pencilling in lines frotn it to its exits, as was done at the corners in Step 6. Otherwise you will forget, block one off, and have to retrace. Suppose we connect 39 to 47 first. Observe how 40-44 fill in the second row. Note that placing 42 forces us to extend 3 to 4, and 43 forces extension of this to 5. 38 tnust go in b3. Now extend the 26-29 and 38-58 chains to stnooth out the left side. Now check once again: are all active squares tnarked and not blocked? Are all chains legal so far? All Step 8 Wit and care -­ly. We no~ sweat-and­last connec ing area th< ing rootn. nutnbers at reach this I nections to The quote v It'shar to get one (] ever space It's short, its ends ar' because on! At this thetn spidel the retnaini and retnOVE We also ext Step 9 At draw the ot '!quare s sel ity, and wo bers are w: nutnbers (t ing chains I trial-and-e this square new one -­To put ions for aw knight I s t01 can be com quires an e have to bac one active I our 5-23 c~ tnove along that, at 6, the present expect one of the loop If not, tink, back to Stel quote! It : spell 58 47 -- 57 348 , so put 51 via lst be at ~d b4. If el(51); mnected to I at b2. , array. ~ast one (1-3, 26­walled in. 'I waste a e later =is­5 5845 47 4 44 57 348 .olated hould be are never re, like le last nber. constantly quare by >rner s in to retrace. 'ill in the , and 43 dthe 26-29 ce again: ins legal 25 so far? All is well, so save this and copy it over elsewhere. Step 8 With just a little practice -­ 32 and care - - the above steps go quick­ 33 ly. We now approach the blood­ 34 31 sweat-and-tears stage: =aking the 23 35 54 59 46 5 last connections in a s=all re=ain­ 30 53 24 41 36 43 5"B 45 ing area that leaves little =aneuver­ 2538275055 247 4 ing roo=. With properly- bunched 52 29 40 37 42 49 44 57 nu=bers at the start, we should 39 26 51 28 1 56 3 48 reach this stage with only two con­nections to interweave, but here we have three: 5-23, 30-36, 58-64. The quote was not obliging. It' s hard to juggle three chains in this tight space; it see=s best to get one out of the way so=ehowand put =ost effort into filling what­ever space this leaves. The clear choice is the 30-36 connection. It's short, leaving =ore roo= to work with than 5-23 would, and both its ends are constrained. We'd rather save 58-64 for the final crunch, because only the 58 end is tied down; the 64 can stop anywhere. At this stage, two-exit squares grow thick, and the lines fro= the= spiderweb the edges. In connecting 30 to 36, we can try to keep the re=aining area rectangular by hugging the edge s, or charge in and re=ove a few two-exit squares at any cost. Here we try the latter. We also extend 58 to 59 to s=ooth out the outline. Step 9 At this stage. I generally draw the outline of the re=aining "quares separately for greater clar­ity, and work with that. No nu=­bers are written except the active nu=bers (to show where connect­ing chains =ust attach). Now it's trial-and-error ti=e. "Well, this is a dead end, but suppose I link this square to this one instead, erase this other link, and draw this new one -- oops, that's a dead end, too". To put so=e sy~te= in the trials, I generally ignore the connect­ions for awhile and try to link all the unfilled squares in a single closed knight's tour (a closed tour is one in which the start and end squares can be connected by a knight =ove to for= a closed loop). This re­quires an even nu=ber of squares. We have 22 here: otherwise we'd have to backtrack or advance a bit. When the loop is done, choose one active nu=ber and try to connect it to another along the tour. In our 5-23 case, We would enter fro= 23, put a 22 on the tour, and =ove along it (trying both directions) to 21, 20, 19, ... and hope that, at 6, we would find ourselves a knight's =ove away fro= 5. In the present case -- two entry points for 23, three for 5 -- we could expect one or two successes. For each, see, if the re=aining portion of the loop can serve as a connection for the re=aining nu=ber( s) . If not, tinker with the tour and try again. It =ay be necess ary to go back to Step 8, or even Step 7, and rearrange things a bit. 26 In this case, luckily, the answer comes with a bit less work. At the stage shown, with a closed tour and two left-over three- square chains, I noticed that one of the left-overs could be eliminated by moving from 59 to c6-b8-d7. From there I tried moving to f6 and h5 (Warnsdorf rule). Could the tour of the remainder be juggled's into a route from 5 to 23? It could! I was done in forty minutes, well under par. Step 10 Run through the whole chain. If it's correct, replace num­bers with quote letters, and feel a glow of satisfaction. If not, groan and backtrack. 32 61 14 21 18 7 12 9 CTKSRTIE 15 22 33 62 13 10 19 6 ETAECCOD 34 31 60 1720 63 8 11 UEICSSHH 23 16 35 54 59 46 5 64 HNSGRNI 30 53 24 41 36 43 58 45 BNESEDTI 25 38 27 50 55 2 47 4 REAELHID 52 29 40 37 42 4944 57 I?AHATMS 39 26 51 22 1 56 3 48 WORDWAYS READ READ In the late 1920s, Allen Walker Read (now professor emeritus of English at Columbia) collected graffiti from the walls of rural outhouses in the western United States and Canada, later employing these as citations to illustrate the usages of various scatalogical and obscene words (in the spirit of the Oxford English Dictionary). His work was privately published in Paris in 1935, in an edition of only 75 copies. In 1977, Mal­edicta Press (331 S. Greenfield Avenue, Waukesha, WI 53186) reprinted it as Classic American Graffiti, an 83-page paper­back for $ 6. 00. Scanning Professor Read's several hundred examples, one is struck by how little the words and their usages have changed over the past half-century. Since he was not privy to the inscriptions in outhouses used exclusively by women, his work is necessarily biased; would different em­phases have been revealed in those pre-women' s-lib days? Despite the gamy nature of his material, Professor Read has written a text of impeccable scholarship and dignity. CUR II RICHARI Concord, In hi~ George S charactOl former VI as a wore icle in th magazine FAST to SCAN 0' PHEII til CLE), vi The idea book Play ally been verman ir liam in 11 Contrl Paradoxel Seven-Up evolutiona Silvermar Words: E In like vel nate and a antonyms, In thel Funt and I the First, Cathedral king told 1 Sir Christ as three h awe-inspil 

Thematic Knight\u27s Tour Quotes

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Thematic Knight\u27s Tour Quotes

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