Imprima todo el recorrido de Knight posible desde un punto de partida en el tablero de ajedrez NxN

Dado un tablero de ajedrez N x N con un caballo inicialmente parado en la ^fila X y ^la columna Y , la tarea es imprimir todos los caminos posibles de modo que el caballo deba visitar cada casilla exactamente una vez.

Ejemplo:

Entrada: N = 5, X = 1, Y = 1
Salida:
1 6 15 10 21
14 9 20 5 16
19 2 7 22 11
8 13 24 17 4
25 18 3 12 23
1 6 11 18 21
12 17 20 5 10
7 2 15 22 19
16 13 24 9 4
25 8 3 14 23

… 302 más
Explicación: Inicialmente, el caballo está en (1, 2) ^la celda. Según el 1er camino, el caballero visitará las celdas en el siguiente orden: (1, 1) -> (3, 2) -> (5, 3) -> (4, 5) -> (2, 4) … y así.

Entrada: N = 3, X = 1, Y = 3
Salida: -1
Explicación: No existe una secuencia válida de caminos para que el caballero visite cada casilla exactamente una vez.

Enfoque: el problema se puede resolver con la ayuda de recursividad y retroceso generando todos los recorridos posibles uno por uno y verificando si cumple con las condiciones dadas. Una explicación más completa del enfoque similar se discute en el Problema de la Gira del Caballero . A continuación se detallan los pasos a seguir:

Cree una función recursiva para iterar sobre todos los caminos posibles que puede seguir el Caballero.
Mantenga el número de casillas visitadas por el Caballero utilizando una variable visitada .
Cree una función isSafe() que tome las coordenadas de un cuadrado como argumento y devuelva si el cuadrado es válido para el próximo movimiento del Caballero.
Repase todos los 8 movimientos posibles del Caballero y verifique si es seguro visitarlos. Si lo son, llama recursivamente al siguiente movimiento hasta que el número de cuadrados visitados sea igual al número total de cuadrados.

Complejidad del tiempo: O(8 ^N*N )

Espacio Auxiliar: O(1)

A continuación se muestra la implementación del enfoque anterior:

C++

// C++ program of the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Stores the 8 possible combinations of
// moves that the knight can follow
int DirX[] = { 2, 1, -1, -2, -2, -1, 1, 2 };
int DirY[] = { 1, 2, 2, 1, -1, -2, -2, -1 };
 
// Function to find if (i, j) is a valid
// cell for the knight to move and it
// exists within the chessboard
bool isSafe(int i, int j, int n,
            vector<vector<int> >& Board)
{
    return (i >= 0 and j >= 0 and i < n and j < n
            and Board[i][j] == 0);
}
 
// Stores whether there exist any valid path
bool isPossible = false;
 
// Recursive function to iterate through all
// the paths that the knight can follow
void knightTour(vector<vector<int> >& ChessBoard, int N,
                int x, int y, int visited = 1)
{
    // Mark the current square of the chessboard
    ChessBoard[x][y] = visited;
 
    // If the number of visited squares are equal
    // to the total number of squares
    if (visited == N * N) {
        isPossible = true;
 
        // Print the current state of ChessBoard
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                cout << ChessBoard[i][j] << " ";
            }
            cout << endl;
        }
        cout << endl;
 
        // Backtrack to the previous move
        ChessBoard[x][y] = 0;
        return;
    }
 
    // Iterate through all the eight possible moves
    // for a knight
    for (int i = 0; i < 8; i++) {
 
        // Stores the new position of the knight
        // after a move
        int newX = x + DirX[i];
        int newY = y + DirY[i];
 
        // If the new position is a valid position
        // recursively call for the next move
        if (isSafe(newX, newY, N, ChessBoard)
            && !ChessBoard[newX][newY]) {
            knightTour(ChessBoard, N, newX, newY,
                       visited + 1);
        }
    }
 
    // Backtrack to the previous move
    ChessBoard[x][y] = 0;
}
 
// Driver Code
int main()
{
    vector<vector<int> > ChessBoard(5, vector<int>(5, 0));
    int N = ChessBoard.size();
    int X = 1;
    int Y = 1;
 
    knightTour(ChessBoard, N, X - 1, Y - 1);
 
    // If no valid sequence of moves exist
    if (!isPossible) {
        cout << -1;
    }
 
    return 0;
}

Java

// Java program of the above approach
class GFG {
 
    // Stores the 8 possible combinations of
    // moves that the knight can follow
    static int[] DirX = { 2, 1, -1, -2, -2, -1, 1, 2 };
    static int[] DirY = { 1, 2, 2, 1, -1, -2, -2, -1 };
 
    // Function to find if (i, j) is a valid
    // cell for the knight to move and it
    // exists within the chessboard
    static boolean isSafe(int i, int j, int n, int[][] Board) {
        return (i >= 0 && j >= 0 && i < n && j < n && Board[i][j] == 0);
    }
 
    // Stores whether there exist any valid path
    static boolean isPossible = false;
 
    // Recursive function to iterate through all
    // the paths that the knight can follow
    static void knightTour(int[][] ChessBoard, int N, int x, int y, int visited)
    {
        // Mark the current square of the chessboard
        ChessBoard[x][y] = visited;
 
        // If the number of visited squares are equal
        // to the total number of squares
        if (visited == N * N) {
            isPossible = true;
 
            // Print the current state of ChessBoard
            for (int i = 0; i < N; i++) {
                for (int j = 0; j < N; j++) {
                    System.out.print(ChessBoard[i][j] + " ");
                }
                System.out.println();
            }
            System.out.println();
 
            // Backtrack to the previous move
            ChessBoard[x][y] = 0;
            return;
        }
 
        // Iterate through all the eight possible moves
        // for a knight
        for (int i = 0; i < 8; i++) {
 
            // Stores the new position of the knight
            // after a move
            int newX = x + DirX[i];
            int newY = y + DirY[i];
 
            // If the new position is a valid position
            // recursively call for the next move
            if (isSafe(newX, newY, N, ChessBoard)
                && ChessBoard[newX][newY] == 0) {
                knightTour(ChessBoard, N, newX, newY,
                           visited + 1);
            }
        }
 
        // Backtrack to the previous move
        ChessBoard[x][y] = 0;
    }
 
    // Driver Code
    public static void main(String args[]) {
        int[][] ChessBoard = new int[5][5];
 
        int N = ChessBoard.length;
        int X = 1;
        int Y = 1;
 
        knightTour(ChessBoard, N, X - 1, Y - 1, 1);
 
        // If no valid sequence of moves exist
        if (isPossible == false) {
            System.out.println(-1);
        }
    }
}
 
// This code is contributed by Saurabh Jaiswal

C#

// C# program of the above approach
using System;
class GFG {
 
    // Stores the 8 possible combinations of
    // moves that the knight can follow
    static int[] DirX = { 2, 1, -1, -2, -2, -1, 1, 2 };
    static int[] DirY = { 1, 2, 2, 1, -1, -2, -2, -1 };
 
    // Function to find if (i, j) is a valid
    // cell for the knight to move and it
    // exists within the chessboard
    static bool isSafe(int i, int j, int n, int[, ] Board)
    {
        return (i >= 0 && j >= 0 && i < n && j < n
                && Board[i, j] == 0);
    }
 
    // Stores whether there exist any valid path
    static bool isPossible = false;
 
    // Recursive function to iterate through all
    // the paths that the knight can follow
    static void knightTour(int[, ] ChessBoard, int N, int x,
                           int y, int visited = 1)
    {
        // Mark the current square of the chessboard
        ChessBoard[x, y] = visited;
 
        // If the number of visited squares are equal
        // to the total number of squares
        if (visited == N * N) {
            isPossible = true;
 
            // Print the current state of ChessBoard
            for (int i = 0; i < N; i++) {
                for (int j = 0; j < N; j++) {
                    Console.Write(ChessBoard[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
 
            // Backtrack to the previous move
            ChessBoard[x, y] = 0;
            return;
        }
 
        // Iterate through all the eight possible moves
        // for a knight
        for (int i = 0; i < 8; i++) {
 
            // Stores the new position of the knight
            // after a move
            int newX = x + DirX[i];
            int newY = y + DirY[i];
 
            // If the new position is a valid position
            // recursively call for the next move
            if (isSafe(newX, newY, N, ChessBoard)
                && ChessBoard[newX, newY] == 0) {
                knightTour(ChessBoard, N, newX, newY,
                           visited + 1);
            }
        }
 
        // Backtrack to the previous move
        ChessBoard[x, y] = 0;
    }
 
    // Driver Code
    public static void Main()
    {
        int[, ] ChessBoard = new int[5, 5];
 
        int N = ChessBoard.GetLength(0);
        int X = 1;
        int Y = 1;
 
        knightTour(ChessBoard, N, X - 1, Y - 1);
 
        // If no valid sequence of moves exist
        if (isPossible == false) {
            Console.WriteLine(-1);
        }
    }
}
 
// This code is contributed by ukasp.

Javascript

<script>
// Javascript program of the above approach
 
// Stores the 8 possible combinations of
// moves that the knight can follow
let DirX = [2, 1, -1, -2, -2, -1, 1, 2];
let DirY = [1, 2, 2, 1, -1, -2, -2, -1];
 
// Function to find if (i, j) is a valid
// cell for the knight to move and it
// exists within the chessboard
function isSafe(i, j, n, Board) {
  return i >= 0 && j >= 0 && i < n && j < n && Board[i][j] == 0;
}
 
// Stores whether there exist any valid path
let isPossible = false;
 
// Recursive function to iterate through all
// the paths that the knight can follow
function knightTour(ChessBoard, N, x, y, visited = 1) {
  // Mark the current square of the chessboard
  ChessBoard[x][y] = visited;
 
  // If the number of visited squares are equal
  // to the total number of squares
  if (visited == N * N) {
    isPossible = true;
 
    // Print the current state of ChessBoard
    for (let i = 0; i < N; i++) {
      for (let j = 0; j < N; j++) {
        document.write(ChessBoard[i][j] + " ");
      }
      document.write("<br>");
    }
    document.write("<br>");
 
    // Backtrack to the previous move
    ChessBoard[x][y] = 0;
    return;
  }
 
  // Iterate through all the eight possible moves
  // for a knight
  for (let i = 0; i < 8; i++) {
    // Stores the new position of the knight
    // after a move
    let newX = x + DirX[i];
    let newY = y + DirY[i];
 
    // If the new position is a valid position
    // recursively call for the next move
    if (isSafe(newX, newY, N, ChessBoard) && !ChessBoard[newX][newY]) {
      knightTour(ChessBoard, N, newX, newY, visited + 1);
    }
  }
 
  // Backtrack to the previous move
  ChessBoard[x][y] = 0;
}
 
// Driver Code
 
let ChessBoard = new Array(5).fill(0).map(() => new Array(5).fill(0));
let N = ChessBoard.length;
let X = 1;
let Y = 1;
 
knightTour(ChessBoard, N, X - 1, Y - 1);
 
// If no valid sequence of moves exist
if (!isPossible) {
  document.write("-1");
}
 
</script>

Producción

1 6 15 10 21 
14 9 20 5 16 
19 2 7 22 11 
8 13 24 17 4 
25 18 3 12 23 

1 6 11 18 21 
12 17 20 5 10 
7 2 15 22 19 
16 13 24 9 4 
25 8 3 14 23 

1 6 11 16 21 
12 15 20 5 10 
7 2 13 22 17 
14 19 24 9 4 
25 8 3 18 23 

1 6 17 12 21 
16 11 20 5 18 
7 2 9 22 13 
10 15 24 19 4 
25 8 3 14 23 

1 12 17 6 21 
18 5 20 11 16 
13 2 9 22 7 
4 19 24 15 10 
25 14 3 8 23 

1 16 11 6 21 
10 5 20 15 12 
17 2 13 22 7 
4 9 24 19 14 
25 18 3 8 23 

1 18 11 6 21 
10 5 20 17 12 
19 2 15 22 7 
4 9 24 13 16 
25 14 3 8 23 

1 10 15 6 21 
16 5 20 9 14 
11 2 7 22 19 
4 17 24 13 8 
25 12 3 18 23 

1 16 5 10 21 
6 11 20 15 4 
19 2 17 22 9 
12 7 24 3 14 
25 18 13 8 23 

1 12 5 18 21 
6 17 20 13 4 
11 2 9 22 19 
16 7 24 3 14 
25 10 15 8 23 

1 10 5 16 21 
6 15 20 11 4 
9 2 7 22 17 
14 19 24 3 12 
25 8 13 18 23 

1 18 7 12 21 
8 13 20 17 6 
19 2 5 22 11 
14 9 24 3 16 
25 4 15 10 23 

1 6 17 12 21 
18 11 20 7 16 
5 2 15 22 13 
10 19 24 3 8 
25 4 9 14 23 

1 6 15 12 21 
16 11 20 7 14 
5 2 13 22 19 
10 17 24 3 8 
25 4 9 18 23 

1 12 17 8 21 
18 7 20 3 16 
13 2 11 22 9 
6 19 24 15 4 
25 14 5 10 23 

1 16 13 8 21 
12 7 20 3 14 
17 2 15 22 9 
6 11 24 19 4 
25 18 5 10 23 

1 18 13 8 21 
12 7 20 3 14 
19 2 17 22 9 
6 11 24 15 4 
25 16 5 10 23 

1 10 15 8 21 
16 7 20 3 14 
11 2 9 22 19 
6 17 24 13 4 
25 12 5 18 23 

1 4 15 10 21 
14 9 20 3 16 
19 2 5 22 11 
8 13 24 17 6 
25 18 7 12 23 

1 4 9 18 21 
10 17 20 3 8 
5 2 13 22 19 
16 11 24 7 14 
25 6 15 12 23 

1 4 9 16 21 
10 15 20 3 8 
5 2 11 22 17 
14 19 24 7 12 
25 6 13 18 23 

1 4 17 12 21 
16 11 20 3 18 
5 2 7 22 13 
10 15 24 19 8 
25 6 9 14 23 

1 16 3 10 21 
6 11 20 15 4 
17 2 5 22 9 
12 7 24 19 14 
25 18 13 8 23 

1 18 3 12 21 
8 13 20 17 4 
19 2 7 22 11 
14 9 24 5 16 
25 6 15 10 23 

1 8 3 14 21 
18 13 20 9 4 
7 2 17 22 15 
12 19 24 5 10 
25 6 11 16 23 

1 8 3 14 21 
16 13 20 9 4 
7 2 15 22 19 
12 17 24 5 10 
25 6 11 18 23 

1 14 3 8 21 
4 9 20 13 16 
19 2 15 22 7 
10 5 24 17 12 
25 18 11 6 23 

1 14 3 8 21 
4 9 20 13 18 
15 2 17 22 7 
10 5 24 19 12 
25 16 11 6 23 

1 12 3 18 21 
4 17 20 13 8 
11 2 7 22 19 
16 5 24 9 14 
25 10 15 6 23 

1 10 3 16 21 
4 15 20 11 6 
9 2 5 22 17 
14 19 24 7 12 
25 8 13 18 23 

1 22 11 16 7 
12 17 8 21 10 
25 2 23 6 15 
18 13 4 9 20 
3 24 19 14 5 

1 22 11 16 7 
12 17 8 21 10 
23 2 25 6 15 
18 13 4 9 20 
3 24 19 14 5 

1 24 11 16 7 
12 17 8 25 10 
23 2 21 6 15 
18 13 4 9 20 
3 22 19 14 5 

1 22 11 16 7 
12 17 8 23 10 
21 2 19 6 15 
18 13 4 9 24 
3 20 25 14 5 

1 20 11 16 7 
12 25 8 21 10 
19 2 17 6 15 
24 13 4 9 22 
3 18 23 14 5 

1 18 11 24 7 
12 23 8 19 10 
17 2 15 6 25 
22 13 4 9 20 
3 16 21 14 5 

1 16 11 22 7 
12 21 8 17 10 
15 2 13 6 23 
20 25 4 9 18 
3 14 19 24 5 

1 14 25 20 7 
24 19 8 15 10 
13 2 11 6 21 
18 23 4 9 16 
3 12 17 22 5 

1 24 13 18 7 
14 19 8 23 12 
25 2 11 6 17 
20 15 4 9 22 
3 10 21 16 5 

1 12 15 20 7 
16 21 8 25 14 
11 2 13 6 19 
22 17 4 9 24 
3 10 23 18 5 

1 12 17 22 7 
18 23 8 13 16 
11 2 15 6 21 
24 19 4 9 14 
3 10 25 20 5 

1 12 19 24 7 
20 25 8 13 18 
11 2 17 6 23 
16 21 4 9 14 
3 10 15 22 5 

1 12 23 18 7 
24 17 8 13 22 
11 2 21 6 19 
16 25 4 9 14 
3 10 15 20 5 

1 12 25 18 7 
22 17 8 13 24 
11 2 23 6 19 
16 21 4 9 14 
3 10 15 20 5 

1 12 23 18 7 
22 17 8 13 24 
11 2 25 6 19 
16 21 4 9 14 
3 10 15 20 5 

1 12 21 18 7 
22 17 8 13 20 
11 2 19 6 25 
16 23 4 9 14 
3 10 15 24 5 

1 16 21 10 7 
20 11 8 15 22 
25 2 17 6 9 
12 19 4 23 14 
3 24 13 18 5 

1 16 21 10 7 
22 11 8 15 20 
17 2 25 6 9 
12 23 4 19 14 
3 18 13 24 5 

1 16 21 10 7 
22 11 8 15 20 
17 2 23 6 9 
12 25 4 19 14 
3 18 13 24 5 

1 16 25 10 7 
24 11 8 15 20 
17 2 21 6 9 
12 23 4 19 14 
3 18 13 22 5 

1 16 23 10 7 
22 11 8 15 24 
17 2 19 6 9 
12 21 4 25 14 
3 18 13 20 5 

1 24 19 10 7 
18 11 8 25 20 
23 2 15 6 9 
12 17 4 21 14 
3 22 13 16 5 

1 22 17 10 7 
16 11 8 23 18 
21 2 13 6 9 
12 15 4 19 24 
3 20 25 14 5 

1 20 15 10 7 
14 25 8 21 16 
19 2 11 6 9 
24 13 4 17 22 
3 18 23 12 5 

1 18 23 12 7 
24 13 8 17 22 
19 2 11 6 9 
14 25 4 21 16 
3 20 15 10 5 

1 20 25 14 7 
12 15 8 19 24 
21 2 13 6 9 
16 11 4 23 18 
3 22 17 10 5 

1 22 13 16 7 
12 17 8 21 14 
23 2 15 6 9 
18 11 4 25 20 
3 24 19 10 5 

1 24 13 18 7 
12 19 8 23 14 
25 2 17 6 9 
20 11 4 15 22 
3 16 21 10 5 

1 18 13 20 7 
12 21 8 25 14 
17 2 19 6 9 
22 11 4 15 24 
3 16 23 10 5 

1 18 13 22 7 
12 23 8 19 14 
17 2 21 6 9 
24 11 4 15 20 
3 16 25 10 5 

1 18 13 24 7 
12 25 8 19 14 
17 2 23 6 9 
22 11 4 15 20 
3 16 21 10 5 

1 18 13 24 7 
12 23 8 19 14 
17 2 25 6 9 
22 11 4 15 20 
3 16 21 10 5 

1 24 13 18 7 
14 19 8 23 12 
9 2 25 6 17 
20 15 4 11 22 
3 10 21 16 5 

1 24 13 18 7 
14 19 8 25 12 
9 2 23 6 17 
20 15 4 11 22 
3 10 21 16 5 

1 22 13 18 7 
14 19 8 23 12 
9 2 21 6 17 
20 15 4 11 24 
3 10 25 16 5 

1 20 13 18 7 
14 25 8 21 12 
9 2 19 6 17 
24 15 4 11 22 
3 10 23 16 5 

1 18 13 24 7 
14 23 8 19 12 
9 2 17 6 25 
22 15 4 11 20 
3 10 21 16 5 

1 16 13 22 7 
14 21 8 17 12 
9 2 15 6 23 
20 25 4 11 18 
3 10 19 24 5 

1 14 25 20 7 
24 19 8 15 12 
9 2 13 6 21 
18 23 4 11 16 
3 10 17 22 5 

1 12 23 18 7 
22 17 8 13 24 
9 2 11 6 19 
16 21 4 25 14 
3 10 15 20 5 

1 10 15 20 7 
16 21 8 25 14 
9 2 11 6 19 
22 17 4 13 24 
3 12 23 18 5 

1 10 17 22 7 
18 23 8 11 16 
9 2 13 6 21 
24 19 4 15 12 
3 14 25 20 5 

1 10 19 24 7 
20 25 8 11 18 
9 2 15 6 23 
14 21 4 17 12 
3 16 13 22 5 

1 10 23 16 7 
24 15 8 11 22 
9 2 19 6 17 
14 25 4 21 12 
3 20 13 18 5 

1 10 25 16 7 
20 15 8 11 24 
9 2 21 6 17 
14 19 4 23 12 
3 22 13 18 5 

1 10 21 16 7 
20 15 8 11 22 
9 2 23 6 17 
14 19 4 25 12 
3 24 13 18 5 

1 10 21 16 7 
20 15 8 11 22 
9 2 25 6 17 
14 19 4 23 12 
3 24 13 18 5 

1 10 21 16 7 
22 15 8 11 20 
9 2 17 6 25 
14 23 4 19 12 
3 18 13 24 5 

1 18 21 12 7 
20 13 8 17 22 
25 2 19 6 11 
14 9 4 23 16 
3 24 15 10 5 

1 18 23 12 7 
24 13 8 17 22 
19 2 25 6 11 
14 9 4 21 16 
3 20 15 10 5 

1 18 25 12 7 
24 13 8 17 22 
19 2 23 6 11 
14 9 4 21 16 
3 20 15 10 5 

1 18 23 12 7 
22 13 8 17 24 
19 2 21 6 11 
14 9 4 25 16 
3 20 15 10 5 

1 24 19 12 7 
18 13 8 25 20 
23 2 17 6 11 
14 9 4 21 16 
3 22 15 10 5 

1 22 17 12 7 
16 13 8 23 18 
21 2 15 6 11 
14 9 4 19 24 
3 20 25 10 5 

1 20 15 12 7 
14 25 8 21 16 
19 2 13 6 11 
24 9 4 17 22 
3 18 23 10 5 

1 18 13 24 7 
12 23 8 19 14 
17 2 11 6 25 
22 9 4 15 20 
3 16 21 10 5 

1 20 25 14 7 
10 15 8 19 24 
21 2 11 6 13 
16 9 4 23 18 
3 22 17 12 5 

1 22 11 16 7 
10 17 8 21 12 
23 2 13 6 15 
18 9 4 25 20 
3 24 19 14 5 

1 24 11 18 7 
10 19 8 23 12 
25 2 15 6 17 
20 9 4 13 22 
3 14 21 16 5 

1 16 11 20 7 
10 21 8 25 12 
15 2 17 6 19 
22 9 4 13 24 
3 14 23 18 5 

1 16 11 22 7 
10 23 8 17 12 
15 2 19 6 21 
24 9 4 13 18 
3 14 25 20 5 

1 16 11 24 7 
10 25 8 17 12 
15 2 21 6 23 
20 9 4 13 18 
3 14 19 22 5 

1 16 11 22 7 
10 21 8 17 12 
15 2 25 6 23 
20 9 4 13 18 
3 14 19 24 5 

1 16 11 22 7 
10 21 8 17 12 
15 2 23 6 25 
20 9 4 13 18 
3 14 19 24 5 

1 20 7 14 25 
10 15 24 19 8 
21 2 9 6 13 
16 11 4 23 18 
3 22 17 12 5 

1 22 7 16 25 
12 17 24 21 8 
23 2 11 6 15 
18 13 4 9 20 
3 10 19 14 5 

1 12 7 18 25 
22 17 24 13 8 
11 2 21 6 19 
16 23 4 9 14 
3 10 15 20 5 

1 12 7 18 25 
20 17 24 13 8 
11 2 19 6 23 
16 21 4 9 14 
3 10 15 22 5 

1 18 7 12 25 
8 13 24 17 20 
23 2 19 6 11 
14 9 4 21 16 
3 22 15 10 5 

1 18 7 12 25 
8 13 24 17 22 
19 2 21 6 11 
14 9 4 23 16 
3 20 15 10 5 

1 16 7 22 25 
8 21 24 17 12 
15 2 11 6 23 
20 9 4 13 18 
3 14 19 10 5 

1 14 7 20 25 
8 19 24 15 10 
13 2 9 6 21 
18 23 4 11 16 
3 12 17 22 5 

1 16 21 8 25 
22 7 24 15 20 
17 2 11 6 9 
12 23 4 19 14 
3 18 13 10 5 

1 20 13 8 25 
12 7 24 19 14 
21 2 15 6 9 
16 11 4 23 18 
3 22 17 10 5 

1 22 13 8 25 
12 7 24 21 14 
23 2 17 6 9 
18 11 4 15 20 
3 16 19 10 5 

1 14 19 8 25 
20 7 24 13 18 
15 2 9 6 23 
10 21 4 17 12 
3 16 11 22 5 

1 12 19 14 25 
18 7 24 11 20 
23 2 13 6 15 
8 17 4 21 10 
3 22 9 16 5 

1 12 17 22 25 
18 7 24 11 16 
13 2 21 6 23 
8 19 4 15 10 
3 14 9 20 5 

1 12 17 20 25 
18 7 24 11 16 
13 2 19 6 21 
8 23 4 15 10 
3 14 9 22 5 

1 12 21 16 25 
20 7 24 11 22 
13 2 15 6 17 
8 19 4 23 10 
3 14 9 18 5 

1 16 19 10 25 
18 11 24 15 20 
23 2 17 6 9 
12 7 4 21 14 
3 22 13 8 5 

1 16 21 10 25 
20 11 24 15 22 
17 2 19 6 9 
12 7 4 23 14 
3 18 13 8 5 

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Publicación traducida automáticamente

Artículo escrito por dragonuncaged y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA

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