A Bishop And A Rook Puzzle
A white rook and a black bishop of a standard chess set are randomly placed on a chessboard
What is the probability that one is attacking the other?
ANSWER – 0.3611
EXPLANATION-
The probability of either the Rook or the Bishop attacking the other is 0.3611
A Rook and a Bishop on a standard chess board can be arranged in:
= 64P2 (64 Permutation 2)
= 64*63
= 4032 ways
Now,
There are 2 possible cases – Rook attacking Bishop and Bishop attacking Rook.
As we know that the Rook and the Bishop never attack each other simultaneously. Let’s consider both the cases one by one.
Case I – Rook attacking Bishop
Rook can be placed in any of the given 64 positions and it always attacks 14 positions.
Hence, total possible ways of the Rook attacking the Bishop
= 64*14
= 896 ways
Case II – Bishop attacking Rook
View the chess-board as a 4 co-centric hollow squares with the outermost square with side 8 units and the innermost square with side 2 units.
If the bishop is in one of the outer 28 squares, then it can attack 7 positions.
If the bishop is in one of the 20 squares at next inner-level, then it can attack 9 positions.
If the bishop is in one of the 12 squares at next inner-level, then it can attack 11 positions.
If the bishop is in one of the 4 squares at next inner-level (the innermost level), then it can attack 13 positions.
Hence, total possible ways of the Bishop attacking the Rook
= 28*7 + 20*9 + 12*11 + 4*13
= 560 ways
Thus, the required probability is
= (896 + 560) / 4032
= 13/36
= 0.3611
Your Answer
More puzzles to try-
Magical circle trap puzzle
Suppose you are trapped by a witch in a magical circle of radius 100 feet. Whenever you try to move ...Read More »NDA Exam-II 2012- Which number replaces the question mark in the square?
Made from Egg
He is live, can sizzle like bacon, made with an egg, Have plenty of backbone, but lack a good leg, ...Read More »Journey to Treasure Island Puzzle
Harry Potter with his friends plans to go to the Treasure Island. It needed six days to reach there. One ...Read More »Points on a circle
Given N points randomly distributed around the circumference of a circle, what is the probability that all N points lie ...Read More »What kind of bird is it?
A man leaves his cabin and travels 100 meter north, 100 meters west, and 100 meters south just to arrive ...Read More »The Peculiar Number
There is a number which is very peculiar. This number is three times the sum of its digits. Can you ...Read More »Car selling in silent auction puzzle
You are hosting a silent auction to sell your antique car. The rules are: (1) prospective buyers bid for your ...Read More »How does he know what is inside the box?
A man walks into a completely dark room. There is a box on a table at the other end of ...Read More »Reading without Light
Jessica is telling her friends this story and asks them to guess if it’s the truth or a lie: “There ...Read More »Mystery in selling marbles riddle
Two women were selling marbles in the market place- – One at three for a paisa and – Other at ...Read More »Measure the Water
Suppose you are sitting in an interview and the interviewee asks you an aptitude question. You have three buckets with ...Read More »Vacation at cousin’s place puzzle
It was vacation time, So I decided to visit my cousin’s home. What a grand time we had! In the ...Read More »What was the statement the young man had given?
A young man walks through the forest. He comes to a bridge. In front of the bridge is a large ...Read More »Four Nines Equal Hundred
Can you make four (4) nines (9) equal 100?Read More »Average speed of train riddle
A train is going at a speed of 60kmph towards Delhi and returned back at a speed of 30kmph. What ...Read More »It’s pretty hard to give up
It’s pretty hard to give up. If you remove a part of it, you will be left with a bit. ...Read More »Ring to Girlfriend Riddle
A King wants to send the diamond ring to his girlfriend securely. He got multiple locks and their corresponding keys. ...Read More »Personality Rebus Puzzle
What does this below rebus puzzle mean?Read More »Who is Youngest
Kareena is older than Katrina and younger than Karishma. Isabelle is younger than Bipasha and Karishma. Bipasha is older than ...Read More »