Geometric/Numerical Puzzle

I thought of this puzzle like a clock. So first we know 15 and 30 are diametrically opposite from each other, as 15 is the half way point between all the numbers between 1 and 30. Since 15 and 30 are 15 points apart, to find the point diametrically opposite to 7, we would add 15. So since 7+15=22, 22 is the number diametrically opposite to 7. 

Creating extended puzzles related to this one, to make it impossible there would have to be an odd number of points (ex: if asked to do this same puzzle with 25 points this is impossible as there is an odd number of points). I think a possible puzzle extending on this one could be asking a similar problem but with a different shape such as a square or oval.

I do think there is value in giving students impossible puzzles, as long as it doesn't take them too long to figure out it is impossible. I believe giving them an impossible puzzle would in the end allow for a deeper understanding of the methods behind solving it, as students would have to really understand the process of solving the puzzle to be able to recognize that it is impossible to solve.

I think what makes a puzzle truly geometric rather than simply geometric is having to draw it to solve it. Thus in the question it would have to ask you to draw something specific, in which the puzzle would be impossible to solve without the diagram. However, I do think there is logic in all puzzles to a certain extent.