## Cubic Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Cubic Sudoku

Anybody ever see these before?

This comes from the world sudoku championship.

Grace

Posts: 12
Joined: 13 November 2007

What are the rules? Digits 1-8 in all the visible 2x4 boxes? Fill in only the cells on the 3 visible sides of the cube? Are there any row or column restrictions?

Bill Smythe
Smythe Dakota

Posts: 536
Joined: 11 February 2006

Those puzzles are a mainstay in many Japanese nanpure magazines and indeed, they have appeared at the WSC.

Place the digits 1 to 8 in each row, column, and 2x4 box so that the numbers appear just once. The "rows" and "columns" wrap around the faces of this cube as indicated by the arrows outside the grid.
motris

Posts: 71
Joined: 13 March 2006

Do the "cells" consist of little cubes, or little square surfaces? In the former case, there are only 7 cells in each "row" and "column" (and "shaft", I assume) because the corner "cell" is duplicated. In the latter case, do you put a digit only (for example) on the top surface of each cube, or only on the bottom, or both? And do you put digits only on the visible (outside) surfaces, or on the surfaces of the interior cubes as well?

How many cells are there altogether in this puzzle? (Maybe an answer to this one question would clear things up.)

Bill Smythe
Smythe Dakota

Posts: 536
Joined: 11 February 2006

Only the 3 visible sides of the cube are taken into consideration. Despite its appearance, it is a 2D puzzle, with 18 alldifferent constraints (6 2x4 boxes, 3 x 4 linear constraints in the directions of the arrows.
Ruud

Posts: 664
Joined: 28 October 2005

OK, now I see it. Thanks. When I first saw the puzzle, I was thinking of a 4x4x4 cube with 64 cells and the digits 1-4, but then the "boxes" would have to be 2x2x1 or something.

Thanks again.

Bill Smythe
Smythe Dakota

Posts: 536
Joined: 11 February 2006

There exist different variants of the cubic theme. One of them is the variant Smythe Dakota suggested. I'v example of some of these variants on my page.

(Krychle is the czech word for cube. I call the variant which was played at the last Czech Sudoku Championship so for difference.)

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

where can I play this variant?
mizuki

Posts: 15
Joined: 03 December 2007

oh, haven't seen the link from Pyrrhon.

thx!
mizuki

Posts: 15
Joined: 03 December 2007

Nice puzzle! Inspired by this thread I wrote some software to do these puzzles:
http://uk.geocities.com/aidan_001

These puzzles come in right and left handed forms. For example the line dividing the boxes on the uppermost face can go from bottom left to top right or from top left to bottom right. Now if you take a valid puzzle, for instance the one above, and rub out these dividing lines (one on each face) and draw them going the other way, the puzzle is still valid. I'm not sure if this is always true, or why it should be, but it might help in solving them.
ab

Posts: 451
Joined: 06 September 2005