perplexus.info :: Numbers : 3D Sudoku

3D Sudoku - Part I (Posted on 2006-03-06)

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)

Submitted by Dustin

Rating: 3.0000 (3 votes)

Solution: (Hide)

The third 6 can only go in the NW corner of the bottom layer. The 1 in the middle layer can only go on the W side in the center, and the third 1 can only go on the S side in the center, of the bottom layer. The 2 in the top layer can only go in the center square, and the third 2 must be in the NE corner of the bottom layer.
+ - + - + - + | | 5 | 1 | + - + - + - + | | 2 | 6 | + - + - + - + | 3 | | | + - + - + - + + - + - + - + | | | | + - + - + - + | 1 | 8 | | + - + - + - + | 2 | 6 | | + - + - + - + + - + - + - + | 6 | 7 | 2 | + - + - + - + | 9 | 4 | | + - + - + - + | | 1 | | + - + - + - +
The 8 in the bottom layer must be in the S row, so the 8 in the top layer must be in the N row, and therefore in the NW corner. The 3 in the bottom layer cannot be on the W side anywhere, so it is on the E side in the center. The third 3 must be on the N side in the center, of the middle layer. The final number in the bottom layer must be a 5, and the third 5 goes on the E side in the center, of the middle row.
+ - + - + - + | 8 | 5 | 1 | + - + - + - + | | 2 | 6 | + - + - + - + | 3 | | | + - + - + - + + - + - + - + | | 3 | | + - + - + - + | 1 | 8 | 5 | + - + - + - + | 2 | 6 | | + - + - + - + + - + - + - + | 6 | 7 | 2 | + - + - + - + | 9 | 4 | 3 | + - + - + - + | 5 | 1 | 8 | + - + - + - +
The 4 in the top layer must go in a corner, namely, the SE corner. The third 4 must go in the NW corner of the middle layer. The 7 in the middle layer cannot be on the N side anywhere, so it must be in the SE corner. The third 7 must be on the W side in the center, of the top layer. The remaining two blank squares must each contain a 9.
+ - + - + - + | 8 | 5 | 1 | + - + - + - + | 7 | 2 | 6 | + - + - + - + | 3 | 9 | 4 | + - + - + - + + - + - + - + | 4 | 3 | 9 | + - + - + - + | 1 | 8 | 5 | + - + - + - + | 2 | 6 | 7 | + - + - + - + + - + - + - + | 6 | 7 | 2 | + - + - + - + | 9 | 4 | 3 | + - + - + - + | 5 | 1 | 8 | + - + - + - +

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
easy peasy	alex	2006-03-14 19:54:02
re(3): Did anyone notice...	Gamer	2006-03-13 12:34:57
re(2): Did anyone notice...	John Reid	2006-03-08 20:24:29
re(2): Did anyone notice...	Dustin	2006-03-08 10:26:10
re: Did anyone notice...	Tristan	2006-03-08 00:54:31
re: Did anyone notice...	tomarken	2006-03-07 17:41:30
Did anyone notice...	Dustin	2006-03-07 16:58:44
re(2): Solution (fixed)	tomarken	2006-03-06 13:07:04
re: Solution (fixed)	Bob Smith	2006-03-06 12:44:00
Solution	tomarken	2006-03-06 09:58:10

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