14
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enter image description here

ACROSS:

A. a square

C. a multiple of N Across

E. (C Down) $\times$ (I Across)

G. a square root of A Down

I. a square root of D Down

J. (J Across) $\times$ (K Across) = (F Down) $\times$ (M Down)

K. (J Across) $\times$ (K Across) = (F Down) $\times$ (M Down)

L. a divisor of H Down

N. a divisor of O Down

P. a divisor of I Down

R. a multiple of P Down

S. a square of Q Down

DOWN:

A. a square of G Across

B. a square

C. not a square

D. $1000-$(A Across)

F. a power

H. (L Across) $\times$ (N Across)

I. a multiple of P Across

L. (P Down) $\times$ (Q Down)

M. a power

O. a multiple of N Across

P. a divisor of R Across

Q. a square root of S Across

Edit:

No numbers begin with digit 0 and all numbers are different. So the correct answer should contain twelve distinct 2-digit numbers and twelve distinct 3-digit numbers.

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  • $\begingroup$ what do you mean by "a square of ___" or "a power"? $\endgroup$ – Alto Sep 28 '18 at 3:02
  • $\begingroup$ @Alto "a square of G Across" means "(G Across) $\times$ (G Across)". "Power" means square, cube, etc. $\endgroup$ – P.-S. Park Sep 28 '18 at 3:11
  • $\begingroup$ Oh, then. "a power" could be any number! because in x^y, y can be anything. Yay! -edit Got that. $\endgroup$ – Alto Sep 28 '18 at 3:15
  • $\begingroup$ @Alto $y$ is an integer bigger than or equal to 2. $\endgroup$ – P.-S. Park Sep 28 '18 at 3:17
  • $\begingroup$ Nice puzzle! $(+1)$ $\color{darkorange}{\bigstar}$ :D $\endgroup$ – Mr Pie Sep 28 '18 at 5:36
6
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I found an answer:

I didn't really use a whole lot of logic to solve this. It was mostly a couple educated guesses and a whole lot of trial and error.

324 376
6 988 7
19 1 26
 48 54 
20 3 47
9 122 9
781 729

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4
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Technically, I think I have a cheaterpants solution to this:

enter image description here

I will definitely try to find a better answer though.

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  • 1
    $\begingroup$ NOOOOOO!!! I have to solve this! Fast!!! [jk, but you're so fast! how do you do it?] Good job, nice. Also, there's no rule against it, so you're good to go. $\endgroup$ – Alto Sep 28 '18 at 2:55
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    $\begingroup$ @P.-S.Park Well when someone has more than 12K reputation, it's not really a surprise that he's a master :D $\endgroup$ – Kevin L Sep 28 '18 at 4:11
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    $\begingroup$ @KevinL El-Guest is indomitable; unbeatable; undefeatable; invincible; unsurpassable; unassailable; unstoppable; etc. Know why? Because all those words end in le. Put it backwards and you get el for El-Guest :P $\endgroup$ – Mr Pie Sep 28 '18 at 5:40
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    $\begingroup$ @El-Guest No problem. I said what was true :) $\endgroup$ – Kevin L Sep 28 '18 at 9:27
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    $\begingroup$ That comment was actually pretty funny, to be honest, hahah :P $\endgroup$ – Mr Pie Sep 28 '18 at 9:28

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