20
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Police officers entered the home of Dr. Erwin Schrödinger. The neighbours had reported that the doctor had locked his cat in a box and was subjecting it to "particle physics", whatever horrors that may mean. As there were lives at stake – nine, potentially – the department had obtained a speedy search warrant and officers had rushed to the scene, sirens blaring. Dr. Schrödinger was shocked to see officers of the law barging into his house. The box was located in no time. It was placed in plain sight. Prepared for the worst, they opened it…

Down clues are presented in alphabetical order (by clue, not answer) and are not numbered. Solvers must choose one of the given clues for each down entry, noting that the same clue may be used multiple times. Word lengths have been omitted to avoid showing which clues correspond to which entries; instead, the enumerations indicate whether the clues have one-word answers, two-word answers, or both.

Furthermore, ten across clues can be solved in two ways, one of which results in an answer containing one extra letter. Find the position of the first instance of that extra letter in the clue, and select a letter in the same position when counted from the end of the clue backwards. (For example, if the extra letter is B and the first B in the clue is its third letter, select the third-last letter of the same clue.) The letters so selected, in clue order, reveal what the police discovered in the box in Dr. Schrödinger's house.

enter image description here

Across
1. Assignment getting a Biblical gent (3)
3. Fateful entrance at a hotel party (5)
6. Impromptu sailing vessel almost drowned in current (2,3)
9. Lara 4 down scored #2 spots spinning frequently (5)
10. "You fools!" shouted to Henry and Pascal, perhaps (5)
11. In the protection of historic empire, it's sometimes "black" – usually, though, it's not (3)
12. Patriarch's fifth convoying extremists in libertine capital, in Iași (3)
13. Winding-up of filming, in audition, hip hop music (3)
14. Position of opportunity to turn in rebel leader (5)
17. Solar system's component is without resistance, female caretakers (3)
18. Maybe Stuart and 4 down backed Arab country, having lost one man (5)
19. Rings shown all around the bounds of Seoul, a former Olympic host city (4)
21. A couple of imbeciles broke sofa (4)
23. Secret place to hide stuff: tree at the end of street (5)
24. Prog rock chanter Anderson overheard The Beatles member (3)
26. Standing in front of wretch, regardless of the odds? No point (5)
28. Take a role leading, smear with sticky, oily substance (3)
29. Oscar's held hostage by the man producing a tool with gardening use (3)
31. A little Bacardi's Howard's portion (3)
32. Capital's cover up in replacing article (5)
33. Child working for Mossad department (5)
34. Woman from America surrounded by Poles (5)
35. 1–0 with a single attempt (2,3)
36. A long time hiding last of elitist college in Berkshire (3)

Down
A. Extremities – one left and one right – below female chin? Funny term for birds (1 wd.)
B. Future millionaire? Banks fortune, ultimately having become central in testament… and primarily humorous animated series (1 wd.)
C. King in Ecuador's capital, during the common era, to get one respected Native American tribe? (1 wd.)
D. South Armagnac's borders enclosed by beer and wine region in eastern France (1 wd.)
E. Storm's centre is coming in, hon, 'kay? It regularly devastated a city in Asia's east (1 or 2 wds.)
F. 20th-century entertainer Kennedy has one wing of mansion duplicated in Mexican city (2 wds.)
G. US president Tyler, devoid of entrails – initially unidentified male person (1 or 2 wds.)

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  • 1
    $\begingroup$ "Down clues are presented in alphabetical order" - of clue, right, not of answer? $\endgroup$ – Vicky Sep 21 at 11:22
  • 2
    $\begingroup$ @Vicky Good point, I've clarified that they're alphabetized by clue. $\endgroup$ – jafe Sep 21 at 11:58
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    $\begingroup$ @jafe rot13(Fzvexvat ng gjb qbja...) $\endgroup$ – Gareth McCaughan Sep 21 at 12:04
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    $\begingroup$ ooh, this is exciting! $\endgroup$ – Deusovi Sep 21 at 12:40
  • 1
    $\begingroup$ @GarethMcCaughan and some others! $\endgroup$ – Vicky Sep 21 at 13:37
11
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The grid:

enter image description here

Clue explanations:

enter image description here
In Down clues, definitions have been underlined, and any linking words have been bracketed and italicized.

And, from the 10 ambiguously-solvable Across clues, we can see that

the police discovered that THE CAT IS OK!

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  • $\begingroup$ Not happy posting a partial answer this close, but I just can't seem to get that last clue, and I've been staring at it for over half an hour. I think it's most likely another A -- I thought TIPS / HIPS / RIBS / LIPS could work for "extremities", but couldn't parse any wordplay there. C also seems like it could potentially have another parsing. $\endgroup$ – Deusovi Sep 21 at 14:50
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    $\begingroup$ I think 30D is Rot13(GVGF). $\endgroup$ – Vicky Sep 21 at 15:01
  • $\begingroup$ @Vicky Ah, of course - I'm not sure how I missed that for so long. Thanks! $\endgroup$ – Deusovi Sep 21 at 15:20
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    $\begingroup$ Nice solution. I had it all apart from 11A, but that was mainly because I had Rot13(UBBGREF) at 7D so had the wrong first letter! $\endgroup$ – Vicky Sep 21 at 15:29
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    $\begingroup$ I was tempted to say "I have got 30D Rot13(GVGF)... literally" but that might have been too puerile for this august site (and anyway it's not technically true, although it could have been). :-D $\endgroup$ – Vicky Sep 21 at 15:31

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