Geometric puzzle

It was a little hard for me to draw 30 equally spaced points. So, I thought of visualizing a clock that has 12 equally spaced points and matched the numbers diametrically and found that 1 is opposite to 7, which means 1 matches with ((half of 12) +1)= 7. Similarly, Considering 30 equally spaced point on clock, then matching the numbers which are diametrically opposite to each other, I found that 1 is diametrically opposed to (half of 30) + 1= 16, hence drawing and generalizing , I found that 7 is opposite to (( half of 30) + 7) = 22.
Therefore, the formula becomes, A number diametrically opposite to x in evenly spaced points on circle= (half of evenly spaced points) + x.


This problem can be extended to figure out what if the number of evenly spaced points is odd, how would the formula change.
The value of giving an impossible puzzle is that while solving the puzzle they might get introduced to new insights of math, which did not think before. But on the contrary, it can be sometimes a bit time consuming and frustrating as well for some kids who just want to focus on the curriculum.

I believe if the puzzle has some kind of geometric figures attached, I tend to solve it by actually drawing it out and then inferring the logic behind it and then generalizing it if possible.