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23D = 99
12D = 179 (the other two options give a result too large for 23D)
37D = 14949
8A = 100
3D = 10
4D = 1111 (it can't be 2110 because the last digit would make the geometric mean of 13A 0)
3A = 1111111111
2D = 11111
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Wow, that is one mean puzzle.
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welcome back stranger!
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All interior digits (ie, not first or last) of 38A must be
8.The mean of the digits of 31D must be 4.
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36A has to be even (being equal to twice 6D), which means the only way to satisfy 19D with its even sixth digit is for it to be 9876543210.
(Indeed, since 6D ends with 2, 36A has to end with 4.)The first digit of 36A has to be 2: the digits that satisfy the clue for 36D are 1,2,4,5,6,7,9, and 2 is the only one that allows 6D to start with 1. (The other digit of 36D is either 0 or 8. Edit: Following what @dkf says, it's 8, and ditto for the first digit of 38A)
The third or fourth digit of 35D is a zero.
1D is 1111111111; starting with 1, and having so many digits that must be nonzero (the fifth, seventh, eighth, and tenth), that's the only sequence of digits that fits.
Which incidentally makes 14A 11111.
13D is a square number, two digits, ending with 1. There's only one candidate for that: 81.
44A has to be 8888888888; the third to last digit is 8, so the digits to either side must be either 8 as well or 7,9; but in the latter case you then have 89x and there is nothing for x to be.
43A has to be either 234 or 364, but only 234 allows 43D to work (28).
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@r10pez10 Fourth digit of 35D is
0as it is otherwise undetermined. Which doesn't help for 40A, but that's this puzzle all over...
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@r10pez10 Remaining digits of 13A are
8999in an undetermined order.
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@r10pez10 Which determines 13A.
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The remaining digits of 15D have to be some mix of 1,2,4,8 to get a geometric mean of 2.
Assuming that the "multiple" in 32A means "integer multiple" (otherwise it's pointless to mention) ... long story short, the multiple is 9, and
33A = 18
33D = 888With 40A starting with either 7,8, or 9 (because of 40D), that narrows 40A to either 88888 or 98765 (and 40D to either 888 or 978). Since 3D says the mean of the digits of 40A has to be 7, it's the latter:
40A = 98765
40D = 978
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I think there's a problem: 36A is supposed to be twice 6D;
2(1a592)=281b4which means200×a=b+692and there's no way to do that with single digitaandb.I think you mean
2b184? Thenais less than 5 andbis odd.
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