Desafio

import java.awt.Graphics;

public class Desafio {
    private short lin;
    private short col;
    private Desafio des;

    public Desafio (short c, Desafio q)
    {
      col = c;
      lin = 1;
      des = q;
    }

    public boolean achaSolucao()
    {
      while (des!=null && des.podeAtacar(lin, col))
        if (!avanca())
	      return false;
	return true;
    }

    public boolean avanca()
    {
      if ( lin<8 ) {
	    lin++;
	    return achaSolucao();
      }
      if (des!= null) {
        if (!des.avanca())
	      return false;
        if (!des.achaSolucao())
	      return false;
      }
      else 
        return false;
      lin = 1;
      return achaSolucao();
    }

    private boolean podeAtacar(int tlin, int tcol) {
      int colDif = tcol - col;
      if ( (lin == tlin) || (lin + colDif == tlin) ||//
	     (lin - colDif == tlin))
        return true;
      if (des!= null)
	return des.podeAtacar(tlin, tcol);
      return false;
    }

    public String toString()
    {
      return("("+col + ", "+lin+")");
    }

    public void imprime()
    {
      if(des!= null)
	des.imprime();
      System.out.println(this);
    }

    public void paint(Graphics g) {
	if (des!= null) 
          des.paint(g);
	int x = (lin-1)*50;
	int y = (col-1)*50;
        g.drawOval(x+20, y+20, 10,10);
    }

}

testar...

/*
 * soluciona o problema
 */

public class Principal{

  public static void main (String[] xyz) {
    Desafio desafio;
    desafio= null;
    for (short i=1; i<=8; i++)
    {
	  desafio= new Desafio(i, desafio);
	  desafio.achaSolucao();
    }
    desafio.imprime();
  }
}

public class AgentTable {
	public final static int size = 8;
	byte[][] table;
	
	public AgentTable(){
		table = new byte[size][size];
		for (int i=0 ; i < size; i++) {
			table[i] = new byte[size]; 
		}
		for (int i=0 ; i < size; i++) {
			for (int j=0 ; j < size; j++) {
				table[i][j] = 0;
			}
		}
	}
	
	public void putQueen(int row, int col) {		
		for (int i =0; i < size; i++) {
			table[row][i]++;
		}
		for (int i =0; i < size; i++) {
			table[i][col]++;
		}
		
		for (int i = row, j = col; i >= 0 && j >= 0; i--,j--) {			
			table[i][j]++;
		}
		for (int i = row, j = col; i >= 0 && j < 8; i--,j++) {			
			table[i][j]++;
		}		
		for (int i = row, j = col; i < 8 && j < 8 ; i++,j++) {			
			table[i][j]++;
		}
		
		for (int i = row, j = col; i < 8 && j >= 0; i++,j--) {			
			table[i][j]++;
		}
		table[row][col] = 88;
	}
	
	public void removeQueen(int row, int col) {
		for (int i =0; i < size; i++) {
			table[row][i]--;
		}
		for (int i =0; i < size; i++) {
			table[i][col]--;
		}
		
		for (int i = row, j = col; i >= 0 && j >= 0; i--,j--) {			
			table[i][j]--;
		}
		for (int i = row, j = col; i >= 0 && j < 8 ; i--,j++) {			
			table[i][j]--;
		}
		for (int i = row, j = col; i < 8 && j < 8 ; i++,j++) {			
			table[i][j]--;
		}		
		
		for (int i = row, j = col; i < 8 && j >= 0; i++,j--) {			
			table[i][j]--;
		}
		table[row][col] = 0;
		
		
	}
	NumberFormat decimalFormat = new DecimalFormat("00");
	@Override
	public String toString() {
		StringBuffer buffer = new StringBuffer(); 		
		for (int i=0 ; i < size; i++) {
		buffer.append('-');
			for (int j=0 ; j < size; j++) {
				buffer.append(decimalFormat.format(table[i][j]));
				buffer.append('-');
			}
			buffer.append('\n');
		}
		return buffer.toString();		
	}
	
	public String getSequence(){
		StringBuffer buffer = new StringBuffer();
		for (int i=0 ; i < size; i++) {
			buffer.append('-');
				for (int j=0 ; j < size; j++) {
					if (table[i][j] > 80) {
						buffer.append(i*8 +j);
						buffer.append('-');						
					}
				}
			}
		return buffer.toString();
	}

}

public class Agent {
	
	public static void main(String[] args) {
		Agent agent = new Agent();
		agent.execute();
	}

	private AgentTable agentTable;

	private void execute() {
		agentTable = new AgentTable();
		colocaPecas(8, 0);
		System.out.println(agentTable);
		System.out.println(agentTable.getSequence());
		
	}
	int count = 0; 
	private boolean colocaPecas(int i, int j) {		 
		boolean move = false;
		 
		while (!move) {
			j = posicaoPossivel(j);
			if (j == -1) return false;
			agentTable.putQueen(j/8, j%8);
			if (count < 8) {
				count++;
			}
			if (i > 1){
				move = colocaPecas(i - 1, j + 1);	
			} else {
				move = true;
			}
			if (!move) agentTable.removeQueen(j/8, j%8);
			j++;
		}
		return move;
		
		
	}

	private int posicaoPossivel(int j) {
		for(int i  = j ; i < 64 ; i++)
			if (agentTable.table[i/8][i%8] ==0 ) return i; 
		return -1;
	}

}