A clock face has 18 evenly spaced LEDs positioned around its circular edge. By connecting any three of these LEDs, how many distinct equilateral triangles can be formed?
(a) 8
(b) 6
(c) 10
(d) 9
Explanation
To form an equilateral triangle on a circle with 18 equally spaced points, the spacing between chosen points must be equal.
This occurs when the step size is a multiple of 18/3 = 6.
So valid triangles are formed with step sizes of 6 and 12.
Total positions: 18
Each triangle appears 3 times by rotation ⇒ divide by 3:
18/3 = 6, so total 6 triangles will be formed.
Hence, correct option is b.
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