A wordy digression: the game of HIPE.

A wordy digression: the game of HIPE. In Mathematical Mind-Benders, Peter Winkler. Wellesley, MA: A KPeters, 2007. Reprinted by permission of A K Peters, Ltd(www.akpeters.com). How every fool can play upon the word! --Lorenzo, in Shakespeare's The Merchant of Venice This is a free chapter--my publisher assures me that the book wouldbe the same price without it. Think of it as an intermission, anon-mathematical break. Many mathematicians do love word games, though,and (in my experience) this one in particular. You may have heard the following puzzle: what English word containsfour consecutive letters that are consecutive letters of the alphabet?Answer: undeRSTUdy. Inspired by this and other word puzzles, I and threeother high-school juniors (6) at a 1963 National Science Foundationsummer program began to fire letter combinations at one another, askingfor a word containing that combination. The combination had to appear in that order and with no otherletters in between. Example: WKW = aWKWard, NSW = aNSWer. Some were onlytwo letters, e.g., HQ = eartHQuake; ZV = rendeZVous (or another borrowedword, mitZVah). Try BV yourself (hint: this one is obvious). Double letters (WW, VV, HH) can be fun too; but the most deadlycombinations we found were three or four letters, as in GNT, PTC, THAC,HEMU--answers at the end of the chapter. We named, the game after one ofour favorite combinations, HIPE = arcHIPElago (despite later discoveringthat "worshiper" can be spelled with one "p"). Ofcourse, HIPE has no doubt been invented and. reinvented thousands oftimes over history, and you are under no obligation to use our name--butit's helpful to call it something. In devising a HIPE, a naturalobjective is for it to be artfully concealed in the solution; andit's additionally satisfying for the solution to be a common wordthat's hard to think of. For example, ONIG has a solution that isamong the most common words in the language: can you find it? And whatfun it is to stump a friend with a HIPE like LYLY, then tell them theyhave to add only one more letter. Ideally, you'd like the solution to be unique (among, say,Scrabble[TM]-eligible, non-capitalized words), but insisting on thisleads to unnecessary quibbling. Still, a really good HIPE should haveone standout answer. Back in 1963 we agreed on the following HIPEetiquette: when your victim produces a valid solution to your HIPE, hisor her obligation is fully discharged. In particular, you are notallowed to ask for the solution you had in mind. During the summers of 1967 and 1968 I gave a HIPE a day to all the(supposedly) gifted kids at Science and Arts Camps, in Port Ewen, NY.Here are some of their favorites: SPB, RAOR, XS, DQ, HCR, UDU, YEB, YNG,TIK, XOP, and BEK--answers at end of chapter. Rarely do good HIPEs of more than four letters arise, since theytend to give away too much information. Two cute ones, notable for theirpleasing repetitiveness, are ACHACH and TANTAN (solutions at end). Who is good at solving HIPEs? Over the years, I have made aninformal study of this question. Of course, as with mathematicalpuzzles, you never know until the game is played. People you think wouldbe terrific fall flat on their faces, while others shock you by spoutinganswers you haven't even thought of. There are some interesting tendencies, though. Once I found anexcuse to introduce the game while teaching a class on automata aboutcontext-free languages; one student proved tO be better at it than therest of the class put together. She was the first educated person in herfamily and was a voracious reader who could spell many more words thanshe could pronounce. Naturally, she was less likely to be misled bytricky HIPEs; she knew words by their appearance. How, indeed, do we "know" a word? Is it primarily by theword's meaning, by the word's sound, or by the word'sappearance? Would you believe none of the above? My psychologist friendstell me that the kinetic sense of how to produce a word dominates, atleast in some sense, the other aspects. Now, if that's really thecase, then people who can't hear well, especially those whocustomarily communicate in a sign language, might be expected to have anadvantage in playing HIPE. Their concept of a word might be expected tobe short on sound and production (with the mouth) and thus relativelylong on spelling. Resolved to test this hypothesis, I introduced HIPE to a group ofhearing-impaired employees at a government agency, who sat together andconversed in ASL daily at lunch. They found the game completely trivial;as fast as I wrote HIPEs on napkins, they wrote solutions around them.To them it was a mystery why anyone would think HIPE was any kind ofchallenge. Looking back on this episode, it occurs to me that the fact thatsome of the folks at this table were professional cryptanalysts shouldhave made me a bit hesitant about drawing conclusions. But is theconnection between hearing loss and code-breaking a coincidence? Myadvice is, if you need someone to (say) read a garbled telegram, tryyour hearing-impaired friends first. Here's a longer list of HIPEs, with no solutions provided. Ofcourse, you can find solutions for any of them easily on your computer,by downloading a word list from the web and searching for a given HIPEcombination by your favorite method. But I suggest trying out your brainfirst.BG CM FC FW GC GJKC GD GZ HK IJ KGKJ LJ LQ MD MQ PJTJ TK TV UH UQ XFXG XN XQ ZB ZK ZMZP ZWAFY AIE AIQ AKN AKTAMT ANW AOH AOT APKATG AWG BFR BOF BOJBPL BPO BTF CAQ CECCEK CHG CTY CYH CYOCZE DDB DDM DEK DEQDHP DSC DSK DTE DWRDYB DYG DYM EGW EKDEOI ETD EWG EZA FEGFEK FSA FSI FTB FTTGEC GEF GGN GGP GHGGNP GOC GSK HDI HDUHLR HMM HPL HPR HSHHSK HTC HTG HTM HYNIAI IAU IDP IEI IFAIJI IMF IOA IOE IOIIOV IPK IUT LYF IZUKAC KBL KCL KEB KSGKSK KSU KTR KUS KYCKYR LAL LCL LDB LDTLEK LEQ LPL LII LKHLML LNO LPF LPL LSCLTC LTP LYD LYF LYVMBB MBN MBP MCH MEUMKH MND MNL MPF MPGMPM MPP MSK MSM MSPMSU MVE MWI NDD NDJNDK NGN NKG NKM NNKNYH NYP OAB OAU OAVOEQ OEU OHO OHY OIEOKC OUA OUQ OWU OYHOYO OYR PEV PIP PIUPFR PPH PSF PSM PSPPYC PYW RDP RDV RFDRJU RLH RMC RMP RNHRPM RSB RTG RYD SDRSHH SIQ SKR SSK SUOSYW TBL THC THT TIWTMU TOZ TYD UAH UDBUEO UFA UMC UXU VEFVEP VEW VYH VYS WAWWPE WNC WNM WNP WNUWSB WSM WSW XAD XIBXTB XYE XYM XYS YAGYFR YHA YOE YRD YSCYSL YSY YUN YZY ZEFCEBE DROB ECIB ELELERYO EWHA FELE FRARGHAG GUAG FODI HA00HTEE KADA LECU LESLLSEL IKEA ITCA MECAMEON MELT MYRO NIKEOELA OFOL OFTO OOMMOORK OMUC OWAD OWNOPIOC PLEL PONR RESKROOR SPES TYPU UBBUUGUG ZIPA Promised solutions to earlier HIPEs: * gloWWorm, poWWow * saVVy, reVVing * hitcHHike, batHHouse * sovereiGNTy * bankruPTCy * tooTHAChe * chrysantHEMUm * raSPBerry * extRAORdinary * coXSwain * heaDQuarters * witcHCRaft * fraUDUlent * eYEBrow, eYEBall * larYNGitis * swasTIKa, baTIK * saXOPhone * unBEKnown * stomACHACHe * insTANTANeous I hope you've enjoyed HIPE (7) and will use the game to driveyour friends crazy. Now back to mathematical puzzles. (6) Richard Thurston, Robert Webber, and Robert Winternitz--yes,roommates were assigned alphabetically. (7) For those who think games like this are good for nothing,picture your author as a high-school senior trying to get into Harvard.He is asked to write about himself. He is from Fair Lawn, NJ, and isgood at math. He is competing with kids who were raised by monks inMandalay, played solo bassoon for the Queen of England, and cloned amoose at age 12. What can he say? Hoping to sucker the admissionsofficers into playing HIPE, he writes a light essay called "TheHIPE Story" in which he describes how he and his friends started alocal craze. Four years later, he is a senior at Harvard and overhears atutor who had served on the admissions committee torturing a colleaguewith HYPEs. What's more, the tutor is calling them HIPEs. So, Ifigure HIPEs got me into Harvard, and I owe them this chapter. PETER WINKLER Madison, New Jersey