回複：Round table problem

There are 5 operations:

1. flip 1
2. flip adjacent 2
3. flip diagonal 2
4. flip 3
5. flip 4

There are 6 states:

0. all 4 are off.
1. 1 is on
2. adjacent 2 are on
3. diagonal 2 are on
4. 3 are on.
5. all 4 are on.


We start from the possibility set {0,1,2,3,4}, and want to reach {5}, where
the transition rules are:

0 --5--> {5}

1 --1--> {0, 2, 3}
1 --2--> {1, 4}
1 --3--> {1, 4}
1 --4--> {2, 3, 5}
1 --5--> {4}

2 --1--> {1, 4}
2 --2--> {0, 3, 5}
2 --3--> {2}
2 --4--> {1, 4}
2 --5--> {2}

3 --1--> {1, 4}
3 --2--> {2}
3 --3--> {0, 5}
3 --4--> {1, 4}
3 --5--> {3}

4 --1--> {2, 3, 5}
4 --2--> {1, 4}
4 --3--> {1, 4}
4 --4--> {0, 2, 3}
4 --5--> {1}

5 --*--> {5}

We can find a transition:
{0, 1, 2, 3, 4} --5-->
{5, 4, 2, 3, 1} --3-->
{5, 1, 4, 2, 0} --5-->
{5, 4, 1, 2} --2-->
{5, 1, 4, 0, 3} --5-->
{5, 4, 1, 3} --3-->
{5, 4, 1, 0} --5-->
{5, 4, 1} --1-->
{5, 2, 3, 0} --5-->
{5, 2, 3} --3-->
{5, 2, 0} --5-->
{5, 2} --2-->
{5, 0, 3} --5-->
{5, 3} --3-->
{5, 0} --5-->
{5}

Thus, the operation sequence we want to apply is:

5, 3, 5, 2, 5, 3, 5, 1, 5, 3, 5, 2, 5, 3, 5