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)

(In reply to re: Did anyone notice... by Tristan)

Now that you mention it Tristan, I do remember that puzzle from the Google championship!  I also remember giving up on it during the test as it seemed too hard, and then finding that it was one of those that came out easily when I was solving the puzzles at leisure after the competition was over (I hate that!  It was worth a lot of points too!).  I also remember that I never noticed the patterns in the digits until I read something somebody had posted in a blog somewhere about it.  (I also didn't notice the same symmetry in this puzzle of Dustin's until it was brought to my attention).

Thanks for the reminder of that toroidal sudoku puzzle, and thanks to Dustin for this nice variant.  Isn't it just amazing how these sudokus have taken off these days?  I was in Borders one day at least 6 months ago and they had a whole display case of them, with what must have been a dozen different books by different authors.  Amazing!  I remember they used to be published in Games magazine and were just called 'Number Place'.  You never know what's going to happen next in this crazy world.

See you all.  Happy puzzling!

-John

Posted by John Reid on 2006-03-08 20:24:29