What are the word records for letter sum of equal-sized pieces equal?

language/english/spelling/alphabetical.order/entire.word/letter.sum.of.equal.sized.pieces New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

What are the word records for letter sum of equal-sized pieces equal?
(Spelling / Alphabetical Order / Entire Word)

  a.  numerical tautonym (two halves have same sum), longest
  b.  three equal-sized pieces have same sum, longest
  c.  four equal-sized pieces have same sum, longest
  d.  five equal-sized pieces have same sum, longest

[ Editor: question framed by the editor from the headings of the Taxonomy of Wordplay. ]

Show solution

[ Editor: from the Taxonomy of Wordplay, www.questrel.com, retrieved 28 Oct 2026. Classes (common, uncommon, hyphenated words, phrases), scores, ties (-t) and the source codes in brackets are explained in language/english/word.records.introduction. ]

Sources: [M186,3-10,4-185]

e.g., EXIT: E(5) + X(24) = 29 = I(9) + T(20)
a.  numerical tautonym (two halves have same sum), longest
        common words: vasoconstriction, conditionalities, whatchamacallits, unconventionally, persuasivenesses (16-t)
        uncommon word: dicyclopentadienyliron (22)
        phrase: laugh on the wrong side of one's mouth (30)
b.  three equal-sized pieces have same sum, longest
        common word: exterminator (12)
        uncommon word: microspectroscopes (18)
        phrase: reconnaissance in force (21)
c.  four equal-sized pieces have same sum, longest
        common word: underpayment (12)
d.  five equal-sized pieces have same sum, longest
        phrase: transfer payment (15)

-- Taxonomy of Wordplay, www.questrel.com

In article: 13609 of rec.puzzles, S.Procter@ee.surrey.ac.uk (Steve
Procter) asks

>a) what do the following four-letter words have in common:
>
>      thug    serf    gnat    robe

Where a=1, b=2, c=3, d=4, ..., z=26,

t+h=u+g, s+e=r+f, g+n=a+t,
r+b=o+e ("robe" doesn't fit the pattern of the other 3 words).

Further examples:
Following the "thug" pattern:
 heal (h+e=a+l), leap, pale, near, rein, peat, tape,
 dial, laid, tail, vain, tang

Following the "robe" pattern:
 fain (f+i=a+n)

Following another pattern:
 hale (h+e=a+l), wise

Six-letter words:
 murmur (m+u+r=m+u+r), cancan, tsetse, testes, muumuu, tartar,
 tertre, natant
 marram, redder, terret

-- Richard Sabey <rsa@swindon.gpsemi.com>