12. Find the number of integer solutions ( $x ; y ; z$ ) of the equation param 1 , satisfying the condition param 2.

| param1 | param2 |  |
| :---: | :---: | :---: |
| $60^{x} \cdot\left(\frac{500}{3}\right)^{y} \cdot 360^{z}=2160$ | $\|x+y+z\| \leq 60$ |  |
| $60^{x} \cdot\left(\frac{500}{3}\right)^{y} \cdot 360^{z}=12960$ | $\|x+y+z\|<71$ |  |
| $60^{x} \cdot\left(\frac{500}{3}\right)^{y} \cdot 360^{z}=6000$ | $\|x+y+z\| \leq 102$ |  |
| $60^{x} \cdot\left(\frac{500}{3}\right)^{y} \cdot 360^{z}=36000$ | $\|x+y+z\|<87$ |  |

![](https://cdn.mathpix.com/cropped/2024_05_06_7d808265bf88383c5674g-1.jpg?height=593&width=151&top_left_y=840&top_left_x=1815)
12. Find the number of integer solutions ( $x ; y ; z$ ) of the equation param 1 , satisfying the condition param 2.

| param1 | param2 | Answer |
| :---: | :---: | :---: |
| $60^{x} \cdot\left(\frac{500}{3}\right)^{y} \cdot 360^{z}=2160$ | $\|x+y+z\| \leq 60$ | 60 |
| $60^{x} \cdot\left(\frac{500}{3}\right)^{y} \cdot 360^{z}=12960$ | $\|x+y+z\|<71$ | 70 |
| $60^{x} \cdot\left(\frac{500}{3}\right)^{y} \cdot 360^{z}=6000$ | $\|x+y+z\| \leq 102$ | 102 |
| $60^{x} \cdot\left(\frac{500}{3}\right)^{y} \cdot 360^{z}=36000$ | $\|x+y+z\|<87$ | 86 |