Horse problem solved with my niece.

gistfile1.txt

import java.util.Arrays;

/**
 * Horse problem solved with my niece.
 */
public class Caballo {
    private static byte[][] tablero = new byte[][]
            {{0, 0, 0, 0, 0, 0, 0, 0},
            {0, 0, 0, 0, 0, 0, 0, 0},
            {0, 0, 0, 0, 0, 0, 0, 0},
            {0, 0, 0, 0, 0, 0, 0, 0},
            {0, 0, 0, 0, 0, 0, 0, 0},
            {0, 0, 0, 0, 0, 0, 0, 0},
            {0, 0, 0, 0, 0, 0, 0, 0},
            {0, 0, 0, 0, 0, 0, 0, 0}};

    public static void main(String[] args) {
        explorarDesde(0,0, (byte) 0);
    }

    private static void explorarDesde(int i, int j, byte pasosDados) {
        if (noPuedePisar(i, j)) {
            return;
        }
        // analizamos los 8 passos.
        byte nuevoPaso = (byte) (pasosDados + 1);
        tablero[i][j] = nuevoPaso;
        if (nuevoPaso == 64) {
            print();
            System.exit(0);
        }

        for(int i1 = -2 ; i1 <= 2 ; i1++) {
            for(int j1 = -2 ; j1 <= 2 ; j1++) {
                if (pasoValido(i1, j1)) {
                    explorarDesde( i + i1, j + j1, nuevoPaso);
                }
            }
        }
        tablero[i][j] = 0;
    }

    private static void print() {
        System.out.println(Arrays.toString(tablero[0]));
        System.out.println(Arrays.toString(tablero[1]));
        System.out.println(Arrays.toString(tablero[2]));
        System.out.println(Arrays.toString(tablero[3]));
        System.out.println(Arrays.toString(tablero[4]));
        System.out.println(Arrays.toString(tablero[5]));
        System.out.println(Arrays.toString(tablero[6]));
        System.out.println(Arrays.toString(tablero[7]));
    }

    private static boolean pasoValido(int i1, int j1) {
        return (i1 != 0 && j1 != 0)
                && Math.abs(i1) != Math.abs(j1);
    }

    /**
     * Niega puedePisar.
     *
     * @see #puedePisar(int, int)
     */
    private static boolean noPuedePisar(int i, int j) {
        return ! puedePisar(i, j);
    }

    /**
     * Puede pisar si no paso por ahi, y queda dentro del tablero.
     * @param i
     * @param j
     * @return
     */
    private static boolean puedePisar(int i, int j) {
        return (i >= 0 && i <= 7)
                && (j >= 0 && j <= 7)
                && tablero[i][j] == 0;
    }
}

[1, 12, 9, 6, 3, 14, 17, 20]
[10, 7, 2, 13, 18, 21, 4, 15]
[31, 28, 11, 8, 5, 16, 19, 22]
[64, 25, 32, 29, 36, 23, 48, 45]
[33, 30, 27, 24, 49, 46, 37, 58]
[26, 63, 52, 35, 40, 57, 44, 47]
[53, 34, 61, 50, 55, 42, 59, 38]
[62, 51, 54, 41, 60, 39, 56, 43]

Process finished with exit code 0