Solve Checkers Problem: 8x8 Board, 7 Moves, Many Paths

  • Thread starter Chaotic Boredom
  • Start date
In summary, the conversation is about a problem involving a checker on a game board and finding the number of paths it can take to reach the top row after seven moves. The solution involves using numbers to represent the number of paths from the starting square to each square in the subsequent rows, eventually adding all the numbers to get the final answer of 41 paths. The person asking for help expresses their gratitude and excitement to solve the problem.
  • #1
Chaotic Boredom
13
0
All right...I've been at this all night, and any help whatsoever would be appreciated!

Problem-
An eight by eight square game board for checkers has a checker positioned in the fourth square of the bottom row. The checker is allowed to move one square at a time diagonally left or right to the row above. After seven moves the checker will be in the top row. How many different paths will lead to the top row?
 
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  • #2
Start with the first row. Write in each square the number of paths that lead from the starting position to that square. (there will be seven zeroes and one one)

Use the numbers in the first row to figure out the number of paths from the starting square to each square in the second row.

Use the numbers in the second row to figure out the numbers in the third row.

Keep doing this until you've filled the last row, then just add up the numbers!
 
  • #3
Danke! Very much! I owe you one! *runs off to solve problem*


EDIT: Final answer? 41 Wow...a lot smaller than what I was getting before...103...>_<
 
Last edited:

1. How many possible paths are there to solve the checkers problem on an 8x8 board with 7 moves?

There are approximately 2.5 trillion possible paths to solve the checkers problem on an 8x8 board with 7 moves. This number comes from the total number of combinations when considering all possible moves for each turn.

2. Is it possible to solve the checkers problem in less than 7 moves on an 8x8 board?

No, it is not possible to solve the checkers problem in less than 7 moves on an 8x8 board. This is due to the complexity of the game and the number of possible moves that need to be made in order to reach the solution.

3. How long would it take a computer to solve the checkers problem on an 8x8 board with 7 moves?

The amount of time it takes a computer to solve the checkers problem on an 8x8 board with 7 moves can vary depending on the speed and capabilities of the computer. However, it typically takes several hours to solve due to the large number of possible paths that need to be analyzed.

4. Are there any known strategies or techniques to solve the checkers problem on an 8x8 board with 7 moves?

Yes, there are several known strategies and techniques to solve the checkers problem on an 8x8 board with 7 moves. These include using algorithms, heuristics, and game tree search methods to analyze and narrow down the possible paths to the solution.

5. How does the difficulty of the checkers problem change with different board sizes and number of moves?

The difficulty of the checkers problem increases with larger board sizes and more moves. This is because there are exponentially more possible paths to consider, making it more challenging for a computer to solve. Additionally, the number of possible solutions also increases as the board size and number of moves increase, further complicating the problem.

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