A Geometric Puzzle


If a circle is labeled with two numbers, then the degree between them is 180 degrees.
If a circle is labeled with three numbers, then the degree between any two numbers is 120 degrees.
If a circle is labeled with four numbers, then the degree between any two numbers is 90 degrees.
…
If a circle is labeled with thirty numbers, then the degree between any two numbers is 12 degrees.

Let’s define a function f(n) = 12*(n-1), where n is from 1 to 30.

Since, f(7) = 12*(7-1) = 72, we should find an n, such that f(n) = 72 + 180 = 252.

Solve for n:

12*(n-1) = 252

n = 22 (answer)

Extensions:
1.     What if the total number labeled on the circle is increased to 60?
2.     What if the total number labeled on the circle is odd, instead of even?

This puzzle is geometric, as students can easily visualize and identify the patterns to solve it.

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