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 Did anyone notice... by Dustin)

When you point that out, you remind me of another puzzle...
<anecdote>
I don't know if anyone remembers the 2005 Google puzzle championship, but the very last puzzle was called a "toroidal sudoku"  It was basically a sudoku puzzle on a grid that was topologically equivalent to a donut.  Instead of 3x3 boxes, there were a bunch of identical, but oddly shaped... polygons.  Anyway, the limiting factor on the Google puzzle championship is always time, and this puzzle took a lot of time.  It was only towards the end that I noticed a pattern.  The first row of each polygon always consisted of the same three digits, in some order, and the same with the second row and third.  This made the last few parts of the puzzle considerably easier.

But you know, I had no way of proving that this pattern was always true.  Basically, I just made a bunch of lucky guesses.  Well, it worked out, so no problems.
</anecdote>

I'm sure you could create a 3d sudoku puzzle that doesn't have such a pattern, Dustin...

123  845  697
456  971  238
789  362  514

Hmmm... but I can't figure out which numbers you would remove.

Posted by Tristan on 2006-03-08 00:54:31