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200 points are equally spaced on the circumference of a circle. How many squares can be formed with 4 of the 200 points as vertices?

tertre  Feb 18, 2018

Best Answer 

 #1
avatar+13621 
+1

Each square requires 4 points.....then you can rotate it by 1 point....then 1 point again.....

you can rotate 49 times before you start to repeat the square pattern.....the original square plus 49 more = 50 squares.

ElectricPavlov  Feb 18, 2018
edited by ElectricPavlov  Feb 18, 2018
edited by ElectricPavlov  Feb 18, 2018
 #1
avatar+13621 
+1
Best Answer

Each square requires 4 points.....then you can rotate it by 1 point....then 1 point again.....

you can rotate 49 times before you start to repeat the square pattern.....the original square plus 49 more = 50 squares.

ElectricPavlov  Feb 18, 2018
edited by ElectricPavlov  Feb 18, 2018
edited by ElectricPavlov  Feb 18, 2018
 #2
avatar+3270 
0

Yes, that's correct! Good job, EP!

tertre  Feb 18, 2018
 #3
avatar+3270 
+1

Solution

For any given one of the 200 points, we can find exactly one square with that point as one of the vertices---that point, the point diametrically opposite it, and the endpoints of the diameter that is perpendicular to the diameter formed by connecting the first two points. Each square then accounts for 4 vertices, so there are \(200/4=\boxed{50}\) squares.

tertre  Feb 18, 2018

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