You have 20 rectangular pieces (2x1) with the letters A and B, as shown:

           +---+---+
           | A | B |
           +---+---+

Your task is to place all of them in the 8x8 board below, where the position of the pieces is already indicated. The numbers at right and below the "(A)" indicates how many A´s there are in each column and in each row, respectively. Similarly, the numbers at left and above the "(B)", indicates the same for the B´s. The only restriction in placing the pieces is that no two A´s nor two B´s touch each other.

    (A)   3   4   1   3   1   3   2   3
        +---+---+---+---+---+---+---+---+
     2  |       |   |       |       |   |  2
        +---+---+   +---+---+---+---+   +
     3  |       |   |   |   |   |   |   |  1
        +---+---+---+   +   +   +   +---+
     1  |       |   |   |   |   |   |   |  3
        +---+---+   +---+---+---+---+   +
     3  |   |   |   |   |       |   |   |  3
        +   +   +---+   +---+---+   +---+
     1  |   |   |   |   |   |   |   |   |  2
        +---+---+   +---+   +   +---+   +
     3  |   |   |   |   |   |   |   |   |  2
        +   +   +---+   +---+---+   +---+
     3  |   |   |   |   |       |   |   |  4
        +---+---+   +---+---+---+---+   +
     4  |       |   |       |       |   |  3
        +---+---+---+---+---+---+---+---+
          4   3   1   2   2   3   2   3   (B)

(In reply to a solution by goFish)

The only other solution is:

BA---BA-

AB-A-A--

--AB-B-B

BAB-BA-A

AB-----B

BA-A--BA

AB-BABAB

BA-ABABA

Posted by Eric on 2006-01-15 22:51:21