Imagine a 3x3x3 cube made of 27 little cubies. Imagine each of these cubies has a number 1 through 9 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 9 cubies.

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

Grid diagram

+ - + - + - +            3D diagram
|   | 5 | 1 |
+ - + - + - +              + - + - + - +
|   |   | 6 |             /   / 5 / 1 /|
+ - + - + - +            + - + - + - +1+
| 3 |   |   |           /   /   / 6 /|/|
+ - + - + - +          + - + - + - +6+ +
                      / 3 /   /   /|/|/|
+ - + - + - +        + - + - + - + + + +
|   |   |   |        | 3 |   |   |/|/|/
+ - + - + - +        + - + - + - + + +
|   | 8 |   |        | 2 | 6 |   |/|/
+ - + - + - +        + - + - + - + +
| 2 | 6 |   |        |   |   |   |/
+ - + - + - +        + - + - + - +

+ - + - + - +
|   | 7 |   |
+ - + - + - +
| 9 | 4 |   |
+ - + - + - +
|   |   |   |
+ - + - + - +

Note: The 1, 3, 5, and 6 are in the same horizontal plane. (top)
The 1 and 6 are in the same vertical(up-down) plane. (right-most)
The 2, 3, and 6 are in the same vertical(left-right) plane. (front)

...that the solution tomarken and Bob Smith found (which is the only solution) contains the same combinations of numbers in rows?  Let me clarify; the 3, 4, and 9, for example, are in the same row in each layer.  I was going to change it so the numbers appeared more random, but I figured by the time a solver noticed the pattern, he or she would almost be finished anyway.

Posted by Dustin on 2006-03-07 16:58:44