Some examples of backtracking algorithms implemented in Python

Fill a 10x10 board with 1 to 100 integers.

1. Start by writing 1 where you want on the board.

2. To write the next number, you must skip 2 cells in a straight line or one cell diagonally (any direction).

    * they are separated by 2 empty cells on a straight line :
        `10 . . 11`
    * or one cell diagonally :
        ```
        10 .  .
        .  .  .
        .  .  11
        ```
   

3. Repeat last step untill you are strucked or have reached 100.

A solution found:

  1 43 70 16 42 65 11 41 64 10
 56100 34 55 99 31 52 98 30 51
 71 17 95 82 24 88 79 23 89 78
  2 44 69 15 35 66 12 40 63  9
 57 83 33 54 96 32 53 97 29 50
 72 18 94 81 25 87 80 22 90 77
  3 45 68 14 36 67 13 39 62  8
 58 84 26 47 85 27 48 86 28 49
 73 19 93 74 20 92 75 21 91 76
  4 46 59  5 37 60  6 38 61  7

Dispose N queens on a NxN chess board without any pair attacking each other.

A solution for 10 queens on a 10x10 board:

       a b c d e f g h i j
    10 ♛ . . . . . . . . .
     9 . . ♛ . . . . . . .
     8 . . . . . ♛ . . . .
     7 . . . . . . . ♛ . .
     6 . . . . . . . . . ♛
     5 . . . . ♛ . . . . .
     4 . . . . . . . . ♛ .
     3 . ♛ . . . . . . . .
     2 . . . ♛ . . . . . .
     1 . . . . . . ♛ . . .