## 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 = 2*n*^{2} − 153*n* + 648 = (*n* − 72)(2*n* − 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

No |
Extra word |
Answer |
Explanation |

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 |

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