Geometric Puzzle

Thirty equally spaced points on the circumference of a circle are labeled in order with the numbers 1to 30? Which number is diametrically opposite to 7?

Answer: let suppose that diagonal line between 7 and n(number)is the diameter of the circle.
that means 180 degrees.

30/2= 15 (because of 30 equally spaced points on the circumference of a circle)
Therefore, n=7+15=22.

The extended puzzles are:
1. possible solution:
21 equally spaced points on the perimeter of the equilateral triangle are labeled in order with the numbers 1to 21? Which number is diametrically opposite to 7?

The one possible answer is: 14 & 21                         

2. Not possible puzzle: 
Thirty unequally spaced points on the circumference of a circle are labeled in order with the numbers 1to 30? Which number is diametrically opposite to 7?

Answer: The puzzle does not have only one answer because if we enlarge the circumference of a circle then the diametrically opposite to 7 number is the different number than the reduce circumference of a circle has. The answer does not remain the same number as we reduce or enlarge the circumference of a circle then the diametrically opposite to 7 number.

• What process did you use to work on and solve this puzzle?

I drew the circle and 30 equally spaced points on the circumference of a circle are labeled in order with the numbers 1to 30, and I have realized that if I draw the large circle and label the number 1 to 30 then I have 15 number which is diametrically opposite to 7 but if I draw the small circle and label the number 1 to 30 then I have 22 number which is diametrically opposite to 7. I have noticed that if I change the circumference of a circle then my answer is also changed.

I think that there is no value to give the students impossible puzzles. It does not make sense for them to spend so much time behind the unsolvable puzzle.

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

The puzzle has mentioned the circle shape instead of any other geometric shapes and that makes a puzzle truly geometric, rather than simply logical. In other words, if we change the shape, our answers also change.