Knock, Knock by Karla

Puzzle explanation

The clashes were resolved by choosing the letter that made real words in both directions. The extra letters in clues gave a list of characters, “asterisk, p, e, l, i, c, equal”. Combining these with letters in the resolved clash cells produced the six terms of the Drake equation for estimating the number of detectable extraterrestrial civilisations in the Milky Way. The equation is

R* × fp × ne × fl × fi × fc × L = N
where R* is the number of stars formed in the galaxy per year that are suitable for the development of intelligent life; fp is the fraction of those stars that have planets; ne is the number of planets, per solar system, with an environment suitable for life; fl is the fraction of suitable planets on which life actually appears; fi is the fraction of life-bearing planets on which intelligent life emerges; fc is the fraction of civilisations that develop a technology that produces detectable signs of their existence; L is the average number of years for which such civilisations produce such signs; and N is the number of such civilisations that are currently detectable.

In the grid, the N was changed to O, indicating that there are no such civilisations, and forming PARADOX to be highlighted in the bottom row. This related to Enrico Fermi’s argument that reasonable supposition suggests that Earth should have been visited by aliens but there’s no reliable evidence of that, in relation to which he asked “Where is everybody?”. The grid’s unclued sides contained FRANK DRAKE, ENRICO FERMI and WHERE IS EVERYBODY. The curve drawn through the equation’s terms formed a question mark, using the final O to represent the dot. Curves extending into cell containing “=” or not were both accepted. Lower- or upper-case letters for the equation’s terms were accepted.

Clue explanations

Conventions: * = anagram, < = reversal

No Extra letter Answer Explanation
Across
10 (A)isle NARRATE (vo)TE(rs) after ARRAN <
11   UNHIVE UN + IV in HE
12 (S)hack FUMED FUM + ED
14 Close(T)’s EBB (clos)E + BB
15   INTER NOS INTERN + SO <
16   KISSERS KISS + ERS
19   IN TUNE TUN in (l)INE(r)
20 gam(E) ADOPTEES A + POD < + TEES
21   RORTS RO + R(u)T(h’)S
24   PENCE PEN + EC <
27   LIFE PEER LIF(ted) + ÉPÉE + R(iposte)
29   KORORA R in (A + ROOK) <
30   FARADAY RADA in FAY
32   NEATENED E in (NEAT + END)
35 B(R)eak LIB BIL(l) <
36   GLAIR homophone of GLARE
37   RACEME RACE + M(aiz)E
38 fin(I)al AMENDED END in DAME *
39 (S)talk PARA RAP < + A
40 sun(K) X-RAYS X + R(adar) A(fter) Y(acht) + S
Down
1 (P)article IAMBI (A + MB) in II
2 Woo(E)d CRIB BIRC(h) <
3   ORFE ((re)EF RO(cks)) <
4 c(L)ue FAUCETS F + (SAT + CUE) *
5 ru(I)ns REEN R + E’EN
6   MUDFISH D(a)F(t)I(e) in MUSH
7   INVEST VEINS with IN moved higher + T
8   WHIRTLE WHIRLE(d) around T
9 un(C)ited EVZONE E + V + Z + ONE
13 re(E)d INURNED (RED NUN + I) *
15   IDE (acc)IDE(nts)
17 FA(Q) SORORAL SO + R + ORAL
18   SERIN RINSE with letters cycled
22 ro(U)t TROTTER (cover)T ROT TER(rified)
23   CLANGED CLANGE(r) + D
24   FERNIER ERNE split in FIR
25 Be(A)st TOECAP TOP around ACE <
26   BREGMA B + GAMER *
28   CAD 2 meanings
31   AIDES ASIDE with S moved to the end
33   EOAN (NA + OE) <
34   ARNA AR(e)NA
35 P(L)ea LADY DAL < + Y
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