Question

Fool's problem of the day,

\((1)\) There are \( N \) equidistant light poles around a circular garden. If every three light poles which form either an acute angled triangle or an obtuse angled triangle are fixed with same shape of light, find the number of different shapes of bulbs can be used.

**NOTE**: Please don't post the solution here, instead use this thread for clarification of problem statement discussing strategy and checking the answer. The reason for this is once a solution is posted it act as a spoiler for others. At-least wait for a day before posting a solution. And If you are really confidant about your solution send my via private message.

Good luck!

Regards,
Fool/FFM!

Answer 1

i cant send u private msg it says "user accepts message from only people he has fanned"

Answer 2

I realized that and have changed my settings :)

Answer 3

If I think there's a finite number of possibilities of shapes, could I check if I have the right number of possibilities in this thread?

Answer 4

King, i am sure that you won't post a spoiler :)

Answer 5

I think there are three different cases of N we have to consider. In those three, we get different numbers of possibilities for the number of shapes.

Answer 6

Interesting, what does your hypothesis give answer for N=20 (say)? ;)

Answer 7

Just 1.

Answer 8

If it helps that's not the right answer :)

Answer 9

I shall continue thinking about this problem in that case.

Answer 10

One more question: Can we re-use the vertices to form multiple triangles or not? Such as Do I have to count all the acute/obtuse triangles formed here? or do only distinct triangles count?