# Problem 45389. Knight's Watch

```"Night gathers, and now my watch begins"
```

A knight is placed on an n-by-n sized chessboard at the position x. Find the probability that after k steps, the knight will remain within the chessboard.

Any knight's move that places him outside the board should be considered invalid.

``` For simplicity, the knight's position on the chessboard is defined with the numeric
notation instead of algebraic notation. so 'Ka1' is represented as (1,1).```

Brief explanation:

```Say the knight is placed in pos-(1,1). A knight has 8 possible moves. So in the next move,
the Knight can go to 8 different positions in the chessboard. But among them, only 2
positions are valid i.e. the knight remains within the chessboard and they are -
(3,2) & (2,3). So the prob. is 2/8 after 1 move. What will be the probability after k moves?
```

### Solution Stats

30.3% Correct | 69.7% Incorrect
Last Solution submitted on Jun 06, 2024

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