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How many non-negative integer solutions are there to x+y+z = 30 such that each of x, y, z is divisible by 3?

It is simple if it does not have to satisfy the divisible by 3 condition. However with that condition in place, I can't seem to figure out how to solve this. Please help, Thanks!

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    $\begingroup$ How many non-negative integer solutions are there to $x+y+z=10$? $\endgroup$ – Lord Shark the Unknown Jul 10 '17 at 3:46
  • $\begingroup$ Yes. That's better. Forgot that we can transform variables too. $\endgroup$ – Dhruv Kohli - expiTTp1z0 Jul 10 '17 at 3:48
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    $\begingroup$ @Lord Shark the Unknown thank you! $\endgroup$ – Kevin Jul 10 '17 at 4:22
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If $x$, $y$, and $z$ are all divisible by 3, then $\frac{x}{3}$, $\frac{y}{3}$, and $\frac{z}{3}$ are all non-negative integers and $\frac{x}{3} + \frac{y}{3} + \frac{z}{3}=10$.

Can you see where to go from there?

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