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HIGHLINE SCHOOL DISTRICT  MATH OLYMPIAD

March 25, 2000

 

The Circle Problem

                                                                                                                                                                                                                       

 

If you draw 4 dots equally spaced on the circumference of a circle, you can draw 6 lines connecting them all.

 

 

 

 

 

 

 

 

If you draw 5 dots equally spaced on the circumference of a circle, you can draw 10 lines connecting them all.

 

 

 

 

 

 

 

 

If you draw 6 dots equally spaced on the circumference of a circle, you can draw 15 lines connecting them all.

 

 

 

 

 

 

 

How many lines can you draw by connecting 20 dots on a circle? 

 

 

 

Your response should be made on the Response Sheet.  You may use both sides of the sheet.  Be sure to describe any patterns you see in this problem, and your strategies for solving it.