A Geometric Puzzle

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The number diametrically opposite to 7 on a circle of 30 numbers is 22.

I figured this out the old fashioned way of calculating the midpoint between 7 and 30.  I know that there are other, more creative mathematical ways of calculating this number.

I'm sure there are other extended puzzles that I could give related to this one.  I could use a different shape perhaps or add a triangle into the mix in some form.

We talked in class about giving students impossible puzzles.  My initial thought was that I would definitely give students impossible puzzles but after considering the comments of my classmates, I think it would depend on the mix of my class.  For a class of rather inexperienced math students (ie: grade 8 or 9), I would not give an impossible puzzle unless it was to some more of the advanced students.  Math is hard enough, I don't want to make it any more frustrating.  However, for students who have an interest, I think it would be challenging and exciting to give an unsolvable problem.

A puzzle is geometric when it involves shapes and space.  A logical puzzle involves some deductive reasoning.

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