TAPIR : TOPER MONAD : MINED CRONE : CLOSE MOVES : MAVIS PILER : POLAR BLAST : BRANT
Borgmann proposes several other conditions: the exchanged letters occur in every other position; the words in each pair share no letters; the words in each pair can be transposed to form a word (PALINDROME in the second example); the exchanged letters are consonants (tree in the third example). These conditions will be discussed further below.
In the nearly four decades since this challenge was laid down, few people have picked it up. The longest response in Word Ways was by Tom Pulliam, in the August 1976 issue (p 150). He listed 6-letter girders that satisfy Borgmann's first two conditions:
CUTLAS : COTMAN SUCLAT : SOCMAN CURPIN : CARBID BOGMEN : BUGLES BOGMEN : BUGLET LAMBED : LUMPEN BADGER : BUDLET COLIES : CULMEN METHOD : MATRON SUNLIT : SANGIR TUBMAN : TOBIAS CAPRIN : CUPRID
Pulliam concludes "Dmitri knew well what he was doing when he issued this challenge!".
If we had to guess why this logological form has received so little attention, it is probably because it is so difficult to find any examples. The problem seems to require a search nested within a search, which for a 100,000 word list blows up to 10,000,000,000 pairs. This blow-up in difficulty plagues any search for sets of words that together exhibit some property. Such problems are easy to state but potentially very hard to solve. Word girders are minimal examples of this type of problem, since two is the smallest set of words larger than a single word.
Any form of wordplay has external properties that are natural to it. Elucidating these properties is an esthetic issue, so tastes will vary. In the case of word girders, we are looking at external forms of letter exchange. One natural extreme is to mix the letters between words as thoroughly as possible. This leads to the condition:
1. The exchanges occur in every other position.
Since there are two exchanges, a second extremal condition is:
2. In the two exchanges, every letter is changed.
With these two natural external conditions, the word girder
word1: word2 word4: word3
leads to the diagram:
word1--all-odd-letters-changed [right arrow] word2 | | all-even-letters-changed all-even-letters-changed | | word3--all-odd-letters-changed [right arrow] word4
If we use a capital letter to represent any letter, and a lower case letter to represent any letter that is not equal to the letter represented by the corresponding capital letter, then we can write down a pattern for each of the words in a word girder formed with 5-letter words:
ABCDE [right arrow] AbCdE ABCDE : AbCdE | abcde : aBcDe aBcDe [right arrow] abcde
The resulting word girder is given above to the right. Thus we see that the words in each pair differ in every position; in other words, they do not crash. This condition was noted by David Morice in the February 1990 Word Ways (p 50).
We can form a 9/8-letter word girder satisfying these two conditions:
CAVATINAS : CIVETONES TIDERODE : TADARIDA
Unless otherwise noted, all words in this and subsequent girders will be found as closed compounds in Webster's Third. TIDE-RODE is hyphenated.
In his seminal article Borgmann added a third property:
3. The words in each pair have no letters in common.
If we impose all three of these conditions, we can form 7-letter or 7/6-letter word girders:
FINBACK : FUNPARK BURLAPS : BYROADS LANTUMS : LONGUES LUMPERS : LIMBECS CYTOID : CUTLIP PORGIE : PARTIM
CYTOID is in the OED. FUN PARK, PORGIE, and PARTIM are found in Chambers.
Borgmann considered two alternative fourth conditions, which in addition to the previous three are satisfied by the following 6-letter word girders:
4a. The letters in each pair can be transposed to form a word.
CAPRID : COPTIS (POMACENTRIDS) MILDER : MOLGES (PEAR MOLDINGS) MONTES : MANRED PONGAS : PINDAR
MANRED is found in Chambers.
4b. The exchanged letters are consonants.
GLACIS : GRAVID PROVED : PLOCES
If we drop the first two conditions and keep the third, but require there to be more than a single letter exchanged or the front and back halves switched, we can form the related 9/8-letter girders:
LAMPERING : LACKERING RAMPINGLY : RACKINGLY DUCKSHOT : DUMPSHOT DUCKSHOT : DUMPSHOT
DUCK SHOT and DUMP SHOT are open compounds.
If we require even more mixing, we can form several 8- and 7/9-letter girders:
BACKUPED : BOCKINGS BROCHING : BLACKEYS BLOCKED : BLACKINGS WORMINGS : WARMUPED FLATKEYS : FROTHING TRAMPINGS : TROMPED FLASHING : FLUSHBOX FLESHING : FLUSHBOX MILKWORTS : MULCHED TRUCKBOX : TRACKING TRUCKBOX : TRECKING PUNCHED : PINKWORTS SHACKLED : SHOCKING SHACKLED : SHUCKING TROMPING : TRAMPLED TRUMPING : TRAMPLED
BACK UPED, WARM UPED, FLAT KEYS, FLUSH BOX and TRUCK BOX are open compounds.
If we drop all the conditions but the first, and loosen the first to allow some letters to be left alone, we can form quite a few word girders. If we require that every word is unrelated to every other word, we can form several 9-letter girders:
BILLIKENS : BULKINESS CARMANIAN : CERTATION DUSKINESS : DISLIKENS TESTATION : TASMANIAN GUNRUNNER : GUNBURNER HEMATOSIS : HAMITESES OUTBARKED : OUTRANKED MALINESES : MELANOSIS MOSTLINGS : MISPLANTS PIEPLANTS : POETLINGS
OUTBARKED is in Funk & Wagnalls. HEMATOSIS is in Random House. MALINESES is in Chambers. MISPLANTS is in the OED. GUNBURNER is an open compound.
If we drop the restriction on related words, we can form a 10-letter girder that still exchanges every other letter:
SMELTERMAN : SWEETBRIAR SWEETBRIER : SMELTERMEN CHRIS COLE Milton, Massachusetts
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|Title Annotation:||word games|
|Date:||Nov 1, 2002|
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