A geometric puzzle

To solve this problem, I looked at a clock with markings for minutes. Since there are 60 minutes in an hour, I said 7 would be where 14 is on the clock, and what's across from that? 44 was across, so 44/2 is 22, and so my answer is 22.

An extension could be to have 40 or 50 markings instead of 30, those numbers don't go as well into clocks, which is a circle with markings that we are the most familiar with, so the students might have a harder time visualizing the answer.

An extension that has no right answer would be for example 31. Because the number of markings is odd, there is nothing across from any number. A harder extension would be with a bigger odd number, where it might not be as easy to see that there are no markings across from each other.

I think that there is some value in giving students impossible questions. I did a lot of disproving in the first few years of my degree. I learned to think critically and trust my gut, and to apply logic to show why something wasn't possible. My favorite questions were the ones that gave a statement and said prove or disprove. I think it's important to learn not to take things at face value and challenge what you read and what people tell you. I think it's important to be curious and question everything, and that that will serve students well in the future.

I'm not too sure about what makes puzzles geometric rather than simply logical. If I had to guess, I would say that I think geometric puzzles have a visual aspect to them that logic puzzles don't necessarily have. For example, I think this is a geometric puzzle because to solve it, I had to either visualize the circle or draw it out. With logic puzzles, I often don't visualize anything, usually I jot down some ideas, let them stew in my brain, and come back to it a few days later and solve it.