## Four and a Half …? by Sabre

### Puzzle explanation

The extra words in clues gave “the square root of half a number of bees”, which is the start of a riddle in Longfellow’s Kavanagh, given (in the Oxford Dictionary of Quotations) as “The square root of half a number of bees, and also eight-ninths of the whole, alighted on the jasmines, and a female buzzed responsive to the hum of the male inclosed at night in a water-lily. O, beautiful damsel, tell me the number of bees.” Algebraically, that can be expressed as n = √(n/2) + (8/9)n + 2, where n is the total number of bees. That can be rearranged as 0 = 2n2 − 153n + 648 = (n − 72)(2n − 9), so the two solutions for n are 72 and 4.5; but the number of bees must be a whole number (as all the bees in the riddle are alive), so 72 is the answer.

All of the grid clashes consisted of pairs of letters two apart alphabetically, to be replaced by B (the alphabetic difference), so that the grid contained 72 Bs to answer the riddle. The answer to 3dn could be BLOB or BLOT, but the former would have given 73 Bs in the grid.

### Clue explanations

Conventions: * = anagram, < = reversal

Across
1   ABBESS A + B + B ÈS S
6   BOBBLY BOBBY around L
11 the FINGER-AND-TOE IN in (OF GARDEN + E(ach) T(urnip)) *
13   UDOS DO in US
15   UNBELTED (E(mbarrass) + LT) in UNBED
16   BRAT BRA + T
17   BLUING (BUG IN + (wa)L(ls)) *
18 square DONE (knucklehea)D + ONE
19   SEEABLE SETTLEABLE − TTL
21   SLUBB BULBS *
23   H-BOMB (H + BOB) around M(alfunction)
25   OPORICE (USED + OPORICE) * = (ODIOUS CREEP) *
27   SCAB S(tore) + C + A + B
29   FIESTA (sancti)FIES TA(lk)
31   NAOI NAOMI − M’
33   BDELLIUM (MILD BLUE) *
34   SAIR AIRS with letters “cycled”
35   SNOWBALL TREE (SABRE NOT WELL) *
36   BENIGN BENI + (ri)G (remai)N
37   SULFUR SULU around F + R(eluctance)
Down
1   CHUBBS B in CHUBS
2   BIBBLE-BABBLE (B + BLEB + AB) in BIBLE
3   BLOT or BLOB B + LO + T/B (letter appearing twice in BATHTUB)
4   SEWEL LEWES <
5   SPLOG SLOG around P
6   BABBLER 2 meanings
7 root OPERAS O’ + PEAS around R(utabagas)
8 of BRRR BR + RR
9 half LOGANBERRIES (I + BARREL’S GONE) *
10 a WEBBED W(here) + EBBED
12   FLAB F + LAB
14 number QUICK 2 meanings
20   LOCKIAN A in LOCK-IN
22   J-PENS J + OPENS − O
23   HUBBUB HUB + BUB
24 of BLONDE (END + (e)LBO(w)) *
26 bees CARPET PET after CAR
28   BAJU B + A + JU(g)
29   DOWNS D(airymen) + OWNS
30   GOONS GO ON + S(creaming)
31   PEON PE(nsi)ON
32   BATH BATCH − C