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: Solution by Tristan)

That's a direct result of how the 3D sudoku is filled. If you think about it 3-diomensionally, the top rows of all the 4 grid tables form the up-down back plane of the cube, so they all must have different numbers. Same goes for all the other horizontal rows of the grid tables. As for the vertical rows of the grid tables, they form left-right vertical planes in the cube, so they all must also contain all numbers from 1 to 16.

Posted by TeWuicah on 2006-03-18 05:23:24