Probability Level 5

Assume you are trapped in the honeycomb at place "A" shown in the picture above.

There are six doors in each of the the rooms.

You know that on the border of the honeycomb there are Red death rooms (marked "X"). As soon as you enter into one of those rooms your game is over.

Also on the end of honeycomb there is one green room (marked "1") entering into which will make your life safe.

You have been informed that the smallest distance from your room to the green one is of 5 rooms, but on which direction it is located is a mystery.

You cannot enter the same room twice during your escape.

Your chances of selecting the shortest path to the green room and successfully escaping can be expressed as 1A.\frac{1}{A}. Find A.A.



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