Oct 19 - Circle Puzzle

Numbers 1 to 30 on a Circle

1) Process

-> 30 segments, 15 per half of the circle

The number 7 is in the seventh slot, and because of circle symmetry the number opposite it will be 15 segments away, number 22

Can draw to check

 

 

https://www.blocklayer.com/circle-dividereng.aspx

2) One possible extension is to present this as a three-dimensional problem, perhaps split into 24 slices (to represent time zones), and ask students a similar diametric question. This would have a direct application when calculating time in various locations around the globe. I think its also kind of novel and entertaining to know which part of the world is opposite oneself. (Hello Oman)

One impossible puzzle/extension would be to split the circle into an odd number of segments, ask a similar diametric symmetry question, and only allow integer answers.

It is just as important to be able to recognize when a puzzle is unsolvable, as it is to be able to solve it. Recognizing a puzzle is unsolvable/impossible is effectively the same thing, since the solution is that there isn’t one. I think it can also lay the foundation for performing proofs by contradiction. If we only teach our students how to find the correct answer(s), it becomes harder for them to think about trying to get an incorrect answer (speaking from a bit of personal experience here).

3) I think to be truly geometrical a puzzle has to be spatial, possibly without known quantities. Once you add numbers, I think puzzles become more algebraic in nature.