Geometric/numerical puzzle

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

To solve this geometric/numerical puzzle, I drew a circle and made diametric lines across from numbers 1 to 30. Using my image, I find that the number diametrically opposite to 7 was 22. After drawing my image, I noticed that there are 15 ‘spaces’ between the starting number and the number diametric from it. 

Figure 1: My drawing 

A puzzle related to this can be to rearrange the numbers so that they are not organized in ascending order around the circle and ask students to find numbers diametric and next to a number, etc. If this were a word problem, it would be lengthy just to set up the problem alone. An extension of this is to use numbers 1-24 to correspond with letters of the alphabet and students can use it to create coded messages.

I feel like all problems can be logic problems, but a problem is considered “geometric” when there are aspects that allow for visualization of the problem geometrically. When I read this problem, I immediately thought of it as a geometric problem because I began visualizing a circle with the numbers arranged around it. I drew diametric lines to help me think of the solution and did not make the logical connection between half of 30 and properties of a circle.

I think there is more value to give students problems with no single correct answer (in an academia, these are considered wicked problems). This encourages discussion and conversation amongst students to share their reasoning and logic when arriving at their answer.