Numerical Puzzle

My solution for the given puzzle :

30 is an even number, so I put 30 numbers into two rows. 

1,    2,  ….  ,  15

16,  17, … ,   30

1 is diametrically opposite to 16, 15 is diametrically opposite to 30. 

Since 7 is 6 more than 1, so its diametrically opposite number is 6 more than 16 which is 22. 

Answer is 22. 

An extended puzzle:

48 points are labelled on the 4 sides of a square in order. Each side of the square has same number of points, and the points should not be placed on the vertices. The distance between any two adjacent points including vertex is equal. Which number is opposite to 15?

In my puzzle, the total number of points should be the multiple of 4, otherwise it is impossible to solve this puzzle. 

What makes a puzzle truly geometric, rather than simply logical?

A more geometric puzzle should involve elements of geometry and geometric relationships. Take the first puzzle as an example, circle and point are elements of geometry, "equally spaced" and "diametrically opposite" tell us the geometric relationships among these elements. So the first puzzle is an more geometric puzzle. I think most of the students will choose drawing a picture to solve it.   

Impossible puzzle:

I believe both impossible puzzles and possible puzzles are valuable to be given to our students to work with. Firstly, because the process is more important. The problem solving process could bring us closer to the truth. This truth could also be " no solution". Secondly, I think impossible puzzles could promote inventions. For example, space travel, aviation, mobile communications, etc. most of them were deemed impossible. We keep working on these impossible puzzles until one day we find a way to work out. Working on impossible puzzles doesn't mean we will get stuck somewhere, but learn something new to us.