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