Triumvirate by tnap

Puzzle explanation

The puzzle was based on the first three lines of an anonymous verse in the Oxford Dictionary of Quotations:

Multiplication is vexation,
Division is as bad;
The Rule of Three doth puzzle me,
And Practice drives me mad.

The letters missing from clue definitions formed MULTIPLICATION. The unclued entries were jumbles of US Army division nicknames, located at their division numbers, as given in Brewer’s Dictionary of Phrase and Fable under “Regimental and divisional nicknames”: 1 Big Red One, 2 Indianhead, 5 Red Diamond, 10 Mountaineers, 23 America, 37 Buckeye. The puzzle’s title referred to the third line of the poem.

Clue explanations

Conventions: * = anagram, < = reversal

No Missing letter Answer Explanation
Across
9 L(U)ing’s GUGA AGUE < with G for E
12   CEP (abundan)CE P(erhaps)
14   ONE-ER ON + E’ER
15   OURS (c)OURS(e)
16   NANNA ANNA(l) after (seaso)N
17 De(I)fy IDOLISE I DO + LISE (diminutive of Elizabeth)
18   ODIN O’ + DI + (dominio)N
19   OFFSET OFF + SET
21   BOERS BOWERS − W
22   UNLEAD JUNK-DEALER * − JERK *
25 ma(I)d SHES SMASHED * − MAD *
26 (A)Tom DOT 2 meanings
27   RECS homophone of WRECKS
29 S(T)ir DISTURB D(avid) + IS + BRUT(e) <
31   OPIATE O + PIA + TE
33   SMORE ’S + MORE
34   SINDHI IND in (SH + I’)
36   HOOT TOOTH < − T’
39 Cha(P)s ADMEN MADE * + N
40   OSSA O + ASS <
41   ANNIE (c)ANNIE(r)
42 s(L)ang TIN (castra)TI N(ever)
43 s(T)ay SIST ASSIST − AS
44   SASSENACH (AS CAITHNESS − IT) *
Down
3 fa(I)r BONNIEST B + (ISN’T ONE) *
4   INNS IN + N,S
6   GEIGER G + REGIE <
7 lan(C)e ORD O + RD
8   ROOFSCAPE (CAFÉ’S POOR) *
9   GULFY GUY around (L + F)
11   ARETHA (Marg)ARET HA(ll)
12   CHORUS C + HOURS *
13   PAINLESSNESS SPANIEL’S * + NESS
19   ORATORIANS A in (OR + TORII with ANS for I(ncantation))
20   ELECTRONIC (NOTE CIRCLE) *
21   BABUSHKAS (BACK + AS − C) around BUSH
24   IRISHMEN IN around RHEIMS *
28 bi(O)nt SESTON (SET + ON) around S
29 C(L)ubs DISCOS DISCUSS with O for US
30 me(N) BOSUNS BOSS around UN
32   ID EST (squal)IDEST
35   ADIE ADIE(u)
38 far(M) BAA B + À + A
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