Look at the 3x3 grid below :

             (3) (1) (6)
            +---+---+---+
        (2) | 6 | 6 | 9 |
            +---+---+---+
        (5) | 9 | 6 | 9 |
            +---+---+---+
        (4) | 9 | 6 | 6 |
            +---+---+---+

To fill it, we used only the digits 6 and 9, achieving 6 different three-digit numbers, three horizontally and three vertically. The (1) outside the second column indicates that 666 is the first number, when the six numbers are arranged in ascending order. The (4) outside of the third row indicates that 966 is the fourth number in the sequence, etc... Thus, reading the six numbers in the grid, following the sequence showed by the outside numbers, we have : 666 / 669 / 699 / 966 / 969 / 996.

Using the same rule above, fill the three 4x4 grids below (note, you can use only the digits 6 and 9 to fill each grid, and you have no restrictions on how many 6īs or how many 9īs you may use).

       (3) (7) (6) (4)          (3) (2) (8) (5)          (2) (4) (5) (6)  
      +---+---+---+---+        +---+---+---+---+        +---+---+---+---+
  (5) |   |   |   |   |    (1) |   |   |   |   |    (1) |   |   |   |   |
      +---+---+---+---+        +---+---+---+---+        +---+---+---+---+          
  (2) |   |   |   |   |    (7) |   |   |   |   |    (7) |   |   |   |   |
      +---+---+---+---+        +---+---+---+---+        +---+---+---+---+
  (8) |   |   |   |   |    (6) |   |   |   |   |    (3) |   |   |   |   |
      +---+---+---+---+        +---+---+---+---+        +---+---+---+---+
  (1) |   |   |   |   |    (4) |   |   |   |   |    (8) |   |   |   |   |
      +---+---+---+---+        +---+---+---+---+        +---+---+---+---+

Is each of the grids a separate problem?  If so I have an answer, otherwise I do not think there is one.

Posted by goFish on 2005-11-14 09:24:27