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Randy plots a point A. Then he starts drawing some rays starting at A, so that all the angles he gets are integral multiples of 10◦. What is the largest number of rays he can draw so that all the angles at A between the rays are unequal, including all angles between non-adjacent rays?

This is Problem 3 of AHSMC 2013. The solution is: Problem 3

I understand the argument, however, I am unable to see how to come up with the arrangement of the 6 rays. I started bashing by guessing and checking, but I was unable to come up with arrangement and I was wondering if there is a way to solve it systematically.

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