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Letter sums and differences.

In the November 2004 Kickshaws, Dave Morice pointed out that the first two letters of HOW add to the third (8+15=23), and that the first two letters of WHO subtract to the third (23-15=8). This idea can be extended to longer words; any two consecutive letters in a word must add (or subtract) to the next letter, such as CADE, 3+1=4 followed by 1+4=5. To allow for sums greater than 26, use the circular alphabet: A=1, B=2, ... Z=26, A=27, etc. The same stratagem is used to create positive differences, such as SARI, 19-1= 18 followed by 27-18=9.

I further generalize letter sums and differences by offsetting the letters against their numerical values; for example, with offset 1, A=26, B=1, C=2, ... Z=25, leading for example to HELP, 7+4=11 followed by 4+11=15.

Letter Sums

Offset 0: cade howl msno orgy otic poet waxy

Offset 1: anna raft help lall sass mammy

Offset 2: boob booboo

Offset 3: ford hint pert quia tarp fords

Offset 4: cede cony glow meno rest

Offset 5: blip djin ells skye skyey varna

Offset 6: army clio feed jimp loud move ouds peon warm

Offset 7: dolt ques unbid

Offset 8: idea limn ruer situ snye sale limns

Offset 9: bibb inns phon zizz

Offset 10: cuny fawn grow ions jeez kabs milk odic pion wane pions

Offset 11: macs mega abri holp

Offset 12: dash eyre foil heat mops roux yerk

Offset 13: fled port raft ywis padri

Offset 14: clay code lect mono stye

Offset 15: dodd fard gums hunt loll odds hunts totty

Offset 16: chum epee ilea leap maxi poon

Offset 17: reft gese

Offset 18: gapy jump laud wine dwine

Offset 19: benz fred gyms indy pron libra

Offset 20: dish piel pier rust worm rust peals rusts sonic

Offset 21: gains hant herb lull mumm ogam rift suss herby miaou ogams rifted

Offset 22: cuba eire leud york sole

Offset 23: dahl kiwi olds told

Offset 24: eels fail genu maps meta pial soja

Offset 25: blob gems hent part

Letter Differences

Offset 0: alow bomb chum jeez sari tsar utas wave whos yips

Offset 1: anna awes erne owse pelt phiz yeuk yoke pelts verne

Offset 2: anoa boob cady deaf lamp life mano ohia sati yves booboo

Offset 3: dull pent prat

Offset 4: culm feed show

Offset 5: cagy halt koas lapp quay scum

Offset 6: ansa chain erse hush paul roil wong Paulo

Offset 7: anta bunn ciao hant idly meow mike pert trip aecia

Offset 8: apse atom awls mile pawl pest sloe wade yore pawls

Offset 9: caky mime quey roll smog syce nerve petti

Offset 10: ache awns coax chem etui mine tach whys khmer mines tache

Offset 11: burn elds hart ritz scare wage

Offset 12: hast king sadi kings

Offset 13: delf emeu fend mayo trop yowe delfs

Offset 14: auto feod mire poon rear slue yids autos slued

Offset 15: acme coca fill herb mise smug wake

Offset 16: acne crag coda gink inks mite pent shaw sizy wale codas ginks

Offset 17: fred jolt porn prot rotl syke wame

Offset 18: dual elks vein wane yelk yelks

Offset 19: ells epha inns odds saki

Offset 20: acre anga cavy elms feud hugh kops numb odes pail syne shew

Offset 21: eyas

Offset 22: duel erie irma kors ware aerie

Offset 23: beth koss lund pall soak

Offset 24: cola enow haet lout spam temp yerk yins clour tempus yerked

Offset 25: coma eyes haft mako mice sock trap jotty

And what about the question Dave raised in Kickshaws concerning HOW-WHO? This pair is matched by ENS-SEN, TAU-UTA and ODS-SOD, plus ABC-CAB if the former is admitted as a word (usually all caps, and spelled out by pronouncing the letters). If the circular alphabet is used, EVA-AVE, IRA-AIR, POA -OAP and OWL-LOW also qualify.

ERIC IVERSON

Eagan, Minnesota
COPYRIGHT 2005 Jeremiah Farrell
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2005 Gale, Cengage Learning. All rights reserved.

 
Article Details
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Author:Iverson, Eric
Publication:Word Ways
Date:Nov 1, 2005
Words:667
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