Remember 3D Sudoku - Part I? Now, it has become a 4x4x4 cube made of 64 little cubies. Each of these cubies has a number 1 through 16 in it. No two cubies in a plane have the same number. A plane is a horizontal, vertical(left-right), or vertical(up-down) cross-section of 16 cubies.

You know the numbers in some of the cubies. What are the others?

Grid Diagram

+ - + - + - + - +               3D Diagram
|   | 13| 4 | 2 |
+ - + - + - + - +                + - + - + - + - +
|   |   |   |   |               /   / 13/ 4 / 2 /|
+ - + - + - + - +              + - + - + - + - +2+
|   | 15|   |   |             /   /   /   /   /|/|
+ - + - + - + - +            + - + - + - + - + + +
| 16| 10| 9 |   |           /   / 15/   /   /|/|/|
+ - + - + - + - +          + - + - + - + - + + +8+
                          / 16/ 10/ 9 /   /|/|/|/|
+ - + - + - + - +        + - + - + - + - + + + +5+
|   |   | 15|   |        | 16| 10| 9 |   |/|/|/|/
+ - + - + - + - +        + - + - + - + - +4+1+7+
| 12| 8 | 11|   |        | 13|   |   | 4 |/|/|/
+ - + - + - + - +        + - + - + - + - + +6+
| 5 |   | 14|   |        |   | 11|   |   |/|/
+ - + - + - + - +        + - + - + - + - + +
| 13|   |   | 4 |        | 14|   |   |   |/
+ - + - + - + - +        + - + - + - + - +

+ - + - + - + - +
| 10|   |   | 8 |
+ - + - + - + - +
|   |   | 6 |   |
+ - + - + - + - +
|   | 4 |   | 1 |
+ - + - + - + - +
|   | 11|   |   |
+ - + - + - + - +

+ - + - + - + - +
|   | 16| 3 | 5 |
+ - + - + - + - +
|   |   |   | 7 |
+ - + - + - + - +
| 9 |   |   | 6 |
+ - + - + - + - +
| 14|   |   |   |
+ - + - + - + - +

Note: The 2, 4, 9, 10, 13, 15, and 16 are in the same horizontal plane. (top)
The 1, 2, 4, 5, 6, 7, and 8 are in the same vertical(up-down) plane. (right-most)
The 4, 9, 10, 11, 13, 14, and 16 are in the same vertical(left-right) plane. (front)

(In reply to re(2): Solution by TeWuicah)

But it is not necessarily true that each vertical group of four be filled with one of four sets of numbers.  It's possible for example, that one vertical group of four be {1,2,3,4} while another one is {1,2,5,6}, as long as these two groups are not in the same row or column.

Posted by Tristan on 2006-03-18 17:50:29