a weblog of wordplay by Eric Harshbarger
Pangrammic Crosswords, Part 2A couple of weeks ago I wrote about pangrammic crosswords (a crossword of valid words which uses every letter of the alphabet exactly once*). The goal is to try to make the "tightest" grid of words so that the bounding rectangular box of the configuration has the smallest possible area.
Pangrammic crosswords have been toyed with since at least 1970 (the earliest reference I have seen of them). As far as I know, the final example I gave in that earlier LOGOLOG entry is the tightest created (an area of 44 = 4x11, using words from the third edition of the Official Scrabble Players Dictionary [OSPD3]).
That was the best answer known... until now. I have improved upon the solution.
My inspiration came from a different (but very reputable) word source: Merriam-Webster's Third New International Dictionary (MW3). Sometime last week it came to my attention that that lexicon includes "waqf" as a word (for these logological challenges I generally try to find single, non-hyphenated entries in boldface which are not abbreviations and are, at most, said to be "sometimes capitalized" -- words listed as slang and obsolete are acceptable).
Having been a competitive Scrabble player in the past I sort of had the OSPD3 list of "Q-without-U" words burned into my brain. I don't play Scrabble anymore, and I need to start making an effort to ignore that tunnel vision. It turns out that the MW3 has many, many more U-less Q-words than are afforded tournament Scrabble players.
"Waqf" happens to be a very useful one as far as pangrams go. "F", "Q", and "W" are all letters which often bedevil pangrammists, and to get them all collected into one word that uses only one vowel is a godsend.
It still took me several hours to improve upon my earlier 44-area crossword, however. Believe it or not, this is how I spent my New Year's Eve. Not partying until midnight, not watching television programs. No, I was shuffling a set of 26 letter tiles about on my desktop with the CD-Rom of my unabridged dictionary fired up on my computer.
Sometime late that night (very early in 2006, I guess), I created this gem:
WAQFS V L T UMP XI G Z C H JERK NOD Y B ALP, a high rugged mountain JERK, a foolish person JOB, a piece of work NOD, a sign of approval STICKY, being like an adhesive UMP, an umpire VUGH, variation of VUG, a small unfilled cavity in a rock WAQFS, multiple Islamic endowments XI, a Greek letter ZED, the letter "Z"
That's a 6x7 rectangle, for an area of 42. An improvement of two units!
As pleased as I was with that find, it seemed to only inspire me to look for an even better answer. The searches were geting tougher (there just wasn't a lot of room left for the letters to squeeze into a box), but I still thought smaller configurations might be possible.
I spent several more hours fiddling with combinations (and discovered several more 6x7 possibilities). Finally, I went back to the "long and narrow" strategy of rectangle formation and created this 3x13 wonder:
J ORB HM DE WAQF IVY X N G T Z PLUCKS BIZ, slang for BUSINESS DE, variant of DEE, the letter "D" ENS, more than one letter "N" HM, used to express thoughtful consideration [OSPD3] HYP, obsolete version of HYPOCHONDRIA IVY, ornamental vine JAG, to move in a jerky motion OFT, often ORB, a sphere PLUCKS, to pull or pick off WAQF, an Islamic endowment XU, a former South Vietnamese coin
Sadly (and oddly), "HM" is not in Merriam-Webster's dictionary other than as an abbreviation for "hectometer", so I had to revert to the Official Scrabble Players Dictionary (which also do not designate "BIZ" as slang). Both word sources are in quite good standing, however, so I don't mind using a hybrid of the two. Notice that this smaller area answer actually has more words stuffed into it.
The above solution yields an amazing area of 39 units. The grid has a "letter density" of exactly 2/3rds (0.666...). Can it be improved?
Well, I certainly know better than to say, "no". Maybe it can. But an improvement would certainly be a great accomplishment. Notice that in the 3x13 example every vowel (including "Y") is used in two words, and I then still have to resort to the vowel-less "HM" entry. There is a little bit of open area above "PLUCKS", and "IVY" uses two vowels at once, but I don't know if those things provide enough leeway to shuffle things around into a smaller rectangle. A 36-area solution does seem enticing, though... a 6x6?, 4x9? or 3x12?
I'll let someone else stay up until 4 o'clock in the morning to work on that...
* Technically, what I'm asking for in this article is a crossword grid of words that is both pangrammic and "heterogrammic", where the latter terms means that no letter is repeated. Generally speaking, a pangram uses all of the letters of the alphabet (possibly more than once), while an heterogram might have fewer than 26 letters, but none is repeated. In a word puzzle that is to use exactly 26 letters, it is really asking for a "perfect pangram", or alternately thinking, a "perfect heterogram". At 26 letters each, the two notions meet in perfection.
[2 January 2006]
Comments about this article:It is not an improvement to the 3x13 grid-size, but a variant to pangrammic and heterogrammic crossword:
Z OHM B GREX
WAQF IVY J L
P T D SNUCK
BYS - [n.] plural of by: a pass (in card games)
ELK - [n.] a large deer (Alces alces)
GJU - [n.] a type of violin used in the Shetland Islands of the United Kingdom
GREX - [n.] (botony) a category of cultivars from the same hybrid parent group; [v.] (dialectal) to grumble or complain
IVY - [n.] any of various climbing or creeping plants
MID - [prep.] amid, in the middle of, among
OFT - [adv.] often; frequently; repeatedly
OHM - [n.] an SI unit of electrical resistance
SNUCK- [v.] simple past and past participle of sneak: to go stealthily
WAQF - [n.] (Islam) the practice of property endowment to a religious institution
ZAP - [V.] to shoot or hit with an electromagnetic charge; to kill quickly
Posted by: Stuart M. Klimek
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