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Suppose we have a numbered circle. We want to go from point A to point B but we don’t know if we should go to the left or to the right. How would you, using numbers, calculate in which direction you should go?
Example:
We are currently on 1. We want to go on 5. I can see vissualy that 5 is closer so we go to the right. Also note, that you are always facing inwards.
First make sure that every calculation you do is modulo 6 (or
n). That means -2 modulo 6 = 4. Then you can calculate once a clockwise trip and one counter clockwise. The clockwise trip is B-A, counter clockwise A-B. Then compare those two results, the lower one wins.Example:
A = 1, B = 5
clockwise move: B-A = 4
counter cw move: A-B = -4 = 2
Example 2:
A = 5, B = 1
clockwise move: B-A = 2
counter cw move: A-B = 4