Circle Puzzle

 1. My approach to this puzzle: 

2. Extension of the puzzle:

Possible one: Assume there are 32 dots on the circle, what's the one that is directly opposite to dot 5?

Impossible one: Assume there are 31 dots on the circle, what's the one that is directly opposite to dot 5?

I do think it is meaningful to give an impossible puzzle because this can train students to think critically and skeptically. An impossible puzzle also raises another question: why this puzzle is impossible? Which can guide students to have a better and deeper understanding of the concept. 

3. A truly geometric puzzle can be something like a tangram, where logical analysis can be more difficult to conduct compared to hands-on trial and errors.