Honeycomb
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 A 1 . Find A .
The answer is 3750.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
@Aaditya Bhatt I'm wondering about this answer. My approach was to first identify the possible shortest paths. There are 5 that I can see, namely [A,21,13,7,3,2,1], [A,21,13,7,4,2,1], [A,21,13,8,4,2,1], [A,21,14,8,4,2,1] and [A,22,14,8,4,2,1].
Each one of these 5 paths occur with a probability of
6 1 ∗ ( 5 1 ) 5 = 1 8 7 5 0 1 ,
so the probability that one of the shortest paths is taken is
5 ∗ 1 8 7 5 0 1 = 3 7 5 0 1 , thus resulting in 3 7 5 0 being the solution.
Log in to reply
Thanks. I have updated the answer to 3750.
Log in to reply
the smallest distance from your room to green one is of 5 rooms.
Aren't there 6 steps to get to the safe green room?
Log in to reply
@Guiseppi Butel – Yes there are 6 steps but difference of A to 1 room is of 5 rooms.
Firstly i forgot to multiply by 5 hence that mistake occured. But now it looks ok.
I don't quite get what the problem is asking. I have a strategy that guarantees 1 out of 6 chance of succeeding.
For the first door, pick any of the doors. Next, pick the door to the front-right (60 degrees clockwise from your current direction). Lastly, just go straight for the remaining doors.
3750