Question

4. Consider a rook chess piece that is only allowed to move up by one square or to the right by one square. If we start it at the bottom left square of an 8 by 8 chessboard, how many different paths are there that the rook can take from the bottom left to the top right square?

0 0
Add a comment Improve this question Transcribed image text
Answer #1

Answer

Here we consider a rook chess piece that is only allowed to move up by one square or to the right by one square. Now if we start it at the bottom left square of an 8 by 8 chessboard, then in order to take the rook from the bottom to the left to the top right square, we have to proceed the rook 7 steps forward and 7 steps rightward ( here the position of the rook is at the 1st left most and 1st down cornered most position which in the concept of cartesian we can say as (1,1) , not (0,0), thats why to reach at the position (8,8) , the rook has to move 7 forward steps and 7 rightward steps).

So the total number different ways to reach such position be 7x7=49.

Hence the answer.............

Thank you.............

Add a comment
Know the answer?
Add Answer to:
4. Consider a rook chess piece that is only allowed to move up by one square...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • King in N moves. In chess, a king can move one space in any of the...

    King in N moves. In chess, a king can move one space in any of the 8 directions (2 vertical, 2 horizontal, 4 diagonals). Suppose our chessboard is infinite in every direction, and a king starts on a particular square. (a) How many different squares are possible locations for the king after N or fewer moves? (b) Answer the same question for a “crippled king” that can only move horizontally and vertically (no diagonal moves allowed). For both parts, show...

  • 4. Consider a chessboard, shown below. At starting at the square al (the lower right hand...

    4. Consider a chessboard, shown below. At starting at the square al (the lower right hand corner), you can go one step up or one step right at each move. The procedure stops until the point h8 (the upper right corner) is reached. a) How many different paths from al to h8 are possible? (b) How many differnt paths from al to h8 are possible if each path must pass through the square e4? 5. If 10 new teachers are...

  • Please write code in java You’re given a chess board with dimension n x n. There’s...

    Please write code in java You’re given a chess board with dimension n x n. There’s a king at the bottom right square of the board marked with s. The king needs to reach the top left square marked with e. The rest of the squares are labeled either with an integer p (marking a point) or with x marking an obstacle. Note that the king can move up, left and up-left (diagonal) only. Find the maximum points the king...

  • You're given a chess board with dimension n x n. There's a king at the bottom...

    You're given a chess board with dimension n x n. There's a king at the bottom right square of the board marked with s. The king needs to reach the top left square marked with e. The rest of the squares are labeled either with an integer p (marking a point) or with x marking an obstacle. Note that the king can move up, left and up-left (diagonal) only. Find the maximum points the king can collect and the number...

  • A robot is standing at the origin (0,0) of a square grid. The robot is programmed...

    A robot is standing at the origin (0,0) of a square grid. The robot is programmed to move exactly one unit at a time, in one of three directions: up, down, and right. The robot will never move left. For example, starting at (0,0), the robot will move either • one unit up, to (0,1), one unit down, to (0,-1), or • one unit right, to (1,0). . The robot is programmed to make exactly 5 moves, and then stop....

  • 5. Consider the grid shown below; one can imagine that it is a map of roads...

    5. Consider the grid shown below; one can imagine that it is a map of roads in a city. In this problem we consider the problem of moving from one corner of the grid to another. A B C 1 (a) Suppose that, starting at the point labeled A, you can go one step up or one step to the right at each move, as long as you stay on the grid. If you end up at the point labeled...

  • b+c ced in a 4x4 grid, as shown below left. A 12. Consider a puzzle consisting of fifteen numbered squares pla move consists of sliding a numbered square into the adjacent unoccupied square. 13 9...

    b+c ced in a 4x4 grid, as shown below left. A 12. Consider a puzzle consisting of fifteen numbered squares pla move consists of sliding a numbered square into the adjacent unoccupied square. 13 9 10 11 12 13 1514 13 1415 If we treat the unoccupied square as numbered 16, every configuration corresponds to a permutation in S16. For example, the initial configuration on the left corresponds to the identity, while the configuration in the middle corresponds to the...

  • Rooks can move any number of squares horizontally or vertically on a chess board. The n...

    Rooks can move any number of squares horizontally or vertically on a chess board. The n rooks problem is to arrange rooks on an n×n board in such a way that none of the rooks could bump into another by making any of its possible horizontal or vertical moves. For this problem, the variables are each column (labeled 0, 1, ... , n−1), the the domain consists of each possible row (also labeled 0, 1, ... ,n−1). In each column...

  • NEED HELP WITH DISCRETE MATH: . Consider the following game. Alice and Bob have a an...

    NEED HELP WITH DISCRETE MATH: . Consider the following game. Alice and Bob have a an infinite quarter chessboard in front of them. The chessboard has a left edge and a bottom edge. There is one checker on some square the chessboard. The player whose turn it is can move the checker down any positive number of squares, or can move the check one column to the left, but anywhere in that column. The game ends when a player cannot...

  • 5: Legend has it that the game of chess was invented for the amusement of a...

    5: Legend has it that the game of chess was invented for the amusement of a Persian shah - or an Indian maharajah, or a Chinese emperor - who became so enthusiastic that he wanted to reward the inventor, who desired only one grain of wheat on the first square of the chessboard, two grains on the second square, four on the third, and so on, doubling the number of grains for each successive square on the 64-square chessboard. (From...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT