Cross-number puzzle

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.

• what do you mean by "a square of ___" or "a power"?
– Alto
Sep 28, 2018 at 3:02
• @Alto "a square of G Across" means "(G Across) $\times$ (G Across)". "Power" means square, cube, etc. Sep 28, 2018 at 3:11
• Oh, then. "a power" could be any number! because in x^y, y can be anything. Yay! -edit Got that.
– Alto
Sep 28, 2018 at 3:15
• @Alto $y$ is an integer bigger than or equal to 2. Sep 28, 2018 at 3:17
• Nice puzzle! $(+1)$ $\color{darkorange}{\bigstar}$ :D Sep 28, 2018 at 5:36

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


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

I will definitely try to find a better answer though.

• 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.
– Alto
Sep 28, 2018 at 2:55
• @P.-S.Park Well when someone has more than 12K reputation, it's not really a surprise that he's a master :D Sep 28, 2018 at 4:11
• @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 Sep 28, 2018 at 5:40
• @El-Guest No problem. I said what was true :) Sep 28, 2018 at 9:27
• That comment was actually pretty funny, to be honest, hahah :P Sep 28, 2018 at 9:28