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XYZ = 100x + 10y + z
Is it something related to this?

Could be, my approach is somewhat different.

100x + 10z + y + 100y + 10x + z ...... = 3024

let me think

122x + 212y + 221x = 3024
I can't go any further :?

need Permutation?

Nope

what is permutation

Hmm...I'm not sure which permutation to use here.

Number of arrangement.

Number of arrangements if order matters.

As far as I know, you used permutations only to arrange xyz in different ways

i think im gettting to it!!

wait..whats the permutation formula?

Permutations formula:
\(\Large \color{Black}{\Rightarrow _nP_r = {n! \over (n - r)!} }\)

... this is not a straight forward permutation problem.

can u give me a hint..

I like this question when i am unable to solve it......

is the answer:\[x\times y\times z = 126\]?

Yes, approach? :)

very weird, im pretty sure its nowhere near the best way to look at this.

222 * 18 - 3024 = 972 --- Whose sum of digits = 18 too.

Interesting approach can we generalize it?

Why do you choose divisibility by 9 in the first place?

where k is the remainder of the sum after division by 9.

So the answer is ?
126?