The New Sudoku Players' Forum

[tarek]

I enjoyed the challenge of programming this 9*9*9 3D variant. This thread will introduce some concepts and reference material to help solvers of this variant in general and my posted puzzles in particular.

The CUBE

* The complete overlap of 27 Sudoku grids has made it possible to present this variant as a cube.
* There are 6 faces in each cube and 9 grids are positioned in succession spanning the distance between 2 opposite faces.
* This Extreme overlap has made it possible to fit 729 cells (9*9*9) into 27 grids (See picture)



The CELLS and GRIDS

* I will be adopting the following principles when presenting puzzles:

looking horizontally at one surface of the cube, the cells are numbered from 1-729 in a Left to Right, Top to bottom then front to back fashion (See picture)
Cell 1 will always be the leftmost, topmost and frontmost cell - The complete opposite of cell 729 -.
The 27 grids can be presented as 3 ways to slice the cube into 9 equal grids.
9 grids will run from the Front of the cube to the back. 9 will run from top to bottom and 9 grids will run from left to right (This allows an easy correlation between the pictured cube and the grids)
The 9 successive slices (grids) in any of the 3 dimensions will will be sufficient to place the clues in the remaining 18 grids because the grids would have covered all 729 cells.
Presenting the 27 Grids will be preferable for manual solvers.
Programmers and computer solvers would probably like the puzzle in line format (729 characters representing cells 1-729)

* Localizing a cell can be achieved using the cube cell number (1-729) or using the Grid, Row and Column method.

Grids 1-9 will run from the front to the back and can be referenced as g1-g9 or xy1-xy9
Grids 10-18 will run from top to bottom and can be referenced as g10-g18 or xz1-xz9
Grids 19-27 will run from left to right and can be referenced as g19-g27 or yz1-yz9
g1r1c1 is cell 1 g1r9c9 is cell 81
g10r1c1 is cell 649 g10r9c9 is cell 9
g19r1c1 is cell 649 g19r9c9 is cell 73
The pictured cube will help in visualizing this.

Sudoku cube puzzles on the net

* The Dion Cube is still available.
* Many are available on http://www.menneske.no/sudoku3d/eng/
* Puzzles that I've posted can be found here. The 1st two puzzles were titled "The Barren Surface" and "WYSIWYG".

I will also be posting some puzzles from time to time, so check this site regularly and search for Sudoku Cube or Sudoku3D. I will update this post regularly (I hope).


tarek

[dukuso]

each of the 27 rows,columns,piles,aligned 3*3*1 boxes contain each of the
9 digits exactly once

viewing it as a set of 729 5-tuples from {1,..,9}^4 (symbol,row,column,pile,box)

we can exchange the roles of row,columns,piles because of the 3d-symmetry
symbols and boxes are special ?!


a normal sudokugrid can be viewd as a 9*9*9 binary cube such that
exactly one cell per pile(symbols) , row,column,block is filled.
Imagine a cube from glass, some cells have a black ball in them
When you look from any side into the cube, you will see 81 projected balls.
Each of the 3*3*1 boxes has exactly one ball in it, but not each 1*3*3 or 3*1*3 box

a 3d-cube can be viewed a a 9*9*9*9 binary hypercube such that
eactly one cell per ....

[dukuso]

well, basically a normal sudoku is a 6-dimensional problem over {1,2,3}
and the 3d-cube is 8 dimensional over {1,2,3}


sudoku-is-a-6-dimensional-problem-t2151.html

[tarek]

This is very interesting dukuso,

One simple thing derived from looking at the Vanilla sudoku as a 9*9*9 problem would be the Full symmetry & Full Symbol symmetry which can be achived if a full 3D symmetry.

tarek

[tarek]

Presenting the puzzle as a series of 9 grids consumes plenty of space & will dissect the cube into slices which do not look as nice as the original 3D structure.

I tried to generate puzzles with clues only on the faces of the cube (complete opposite of Barren Surface puzzle) with success ... Then I tried to generate puzzles with clues only on the visible 3 surfaces & finally found one.

This will allow presenting the puzzle in one picture. The solver will then need 27 empty grids to solve (Still not perfect but can be an improvent if a series of cubes are put together).

Therefore, all my next puzzles will be of the 3 face clues only variety.

The 1st puzzle introduced like that will be puzzle 002 : WYSIWYG

tarek

[dukuso]

AFAIR all 9*9*9 sudokugrids are isomorphic

[tarek]

AFAIR all 9*9*9 sudokugrids are isomorphic

I can't comprehensively disprove this statement without canonicalization. I have however puzzles that can't be solved using singles and puzzles that require singles backdoors of sizes 1-4 and some that I had to stop the program as it couldn't prove or disprove the puzzle's unique solution even after an hour.

I'll be posting examples here in the next few days

Tarek

[tarek]

Here are 2 closely related puzzles which are not isomorphic. They are puzzle#002 & a related puzzle

WYSIWYG Cube solved with singles: Show

Code: Select all

............5.9.....4.3.6...9.7.3.6...1...8...7.2.5.3...9.7.2.....3.6............
...2.3.....................8.................1...................................
..2.9.7...........5.................7.................4..........................
.1.7.9.4.7.................3.................2.................6.................
..7...1...........1...................................3..........................
.4.5.1.7.5.................7.................8.................2.................
..4.3.6...........2.................4.................8..........................
...6.8.....................9.................7...................................
.................................................................................
............6.8.....4.3.6...4.5.1.7...7...1...1.7.9.4...2.9.7.....2.3............
...........................5.................7.............................5.9...
..................2.................1.................5...................4.3.6..
.........9.................7.................3.................8.........9.7.3.6.
..................4...................................7...................1...8..
.........7.................8.................2.................1.........7.2.5.3.
..................8.................3.................4...................9.7.2..
...........................2.................6.............................3.6...
.................................................................................
............5.7.....2.1.5...9.7.3.8...4...7...7.8.2.1...8.3.4.....2.6............
...4.1.............................9.................7...........................
..4.7.2...................4.................1.................9..................
.6.5.7.2.........5.................7.................2.................3.........
..3...9...................3...................................7..................
.8.1.9.3.........9.................3.................5.................6.........
..6.1.7...................6.................8.................2..................
...7.4.............................6.................3...........................
.................................................................................

WYSIWYG Cube close relative not solved with singles: Show

Code: Select all

............5.9.....4.3.6...9.7.3.6...1...8...7.2.4.3...7.9.2.....3.8............
...2.3.....................8.................1...................................
..2.9.7...........5.................7.................4..........................
.1.7.9.4.7.................3.................2.................6.................
..7...1...........1...................................3..........................
.4.5.1.7.5.................7.................8.................2.................
..4.3.6...........2.................4.................5..........................
...6.8.....................9.................7...................................
.................................................................................
............6.8.....4.3.6...4.5.1.7...7...1...1.7.9.4...2.9.7.....2.3............
...........................5.................7.............................5.9...
..................2.................1.................5...................4.3.6..
.........9.................7.................3.................8.........9.7.3.6.
..................4...................................7...................1...8..
.........7.................8.................2.................1.........7.2.4.3.
..................5.................3.................4...................7.9.2..
...........................2.................6.............................3.8...
.................................................................................
............5.7.....2.1.5...9.7.3.8...4...7...7.8.2.1...5.3.4.....2.6............
...4.1.............................9.................7...........................
..4.7.2...................4.................1.................7..................
.6.5.7.2.........5.................7.................2.................3.........
..3...9...................3...................................9..................
.8.1.9.3.........9.................3.................4.................8.........
..6.1.7...................6.................8.................2..................
...7.4.............................6.................3...........................
.................................................................................

tarek

[dukuso]

the grids (solved puzzles) are isomorphic (?)
not the puzzles

when you know that, you may build that into your solver ...

[K Pres]

Hello!

I have been developing 9x9x9 Sudoku puzzles since June 2011, and I'm at a point where I can't take it further. I used Visual Basic in Excel for developing puzzles. I've created several macros for my sudoku developer spreadsheet, including scripts that

1. rotate the puzzle along the x and y axes
2. imitate a pattern of numbers to fill the sheet
3. check to make sure the rules are being followed
4. export the numbers to a new workbook, etc.

These are tools to make sudoku puzzles based in excel workbooks. I haven't been able to take it further, such as by adding fancy flash graphics, because I don't have the tools and knowledge of such programming methods. If you can make the graphics, I can populate the cells. That would be the coolest thing ever.

Here is an example of one of my puzzles:

Sudoku001.xlsx

(16.43 KiB) Downloaded 492 times

The puzzle doesn't have any macros in it, such as the ones for rotating the cube. Unless you write one, you'll have to view it one sheet at a time.

The puzzles have a set of modified rules:

A "line" is a row, column, or rank of cells parallel to the x, y, or z axes. Each line must have the numbers 1 through 9.
A "box" is a 3x3 square of numbers any of the three planes (xy, yz, xz). Each box must have the numbers 1 through 9.
A "cube" is the 3D extension of a box; it must have the numbers 1 through 9 three times. A cube is simply an observation of what happens with boxes when extended to 3D. When you know two identical numbers in a cube, then you know exactly where the third number is, by process of elimination.
The puzzle can be rotated and sliced in different ways to be viewed as sudoku puzzles in three different planes: xy, yz, and xz. In this way, there should be 27 different views.
The puzzle is complete when all cells are filled.

In a way, these puzzles are easier to solve, because of the cube rule; however, it will often take 9 times longer to solve, because of the sheer volume of cells.

[K Pres]

Sudoku001 Solution.xlsx

(40.15 KiB) Downloaded 440 times

Here is the solution for the 3D puzzle above:

[tarek]

Here is an example of one of my puzzles

Hi & Welcome to the forum ....
You definitely have made it very difficult for people to copy your puzzle into another solver to verify. With the puzzle being in Excel, even sudoku monkey couldn't capture the candidates. I gave up shortly after. It would have been easy to provide 9 lines of 81 characters for that.
Good luck with your puzzle creations ...

Tarek

[Pat]

It would have been easy to provide 9 lines of 81 characters

i hope i got it right---

..61378...8.....1.3.......21...9...66..713..99...6...18.......7.1.....2...23719..
...........34896...6.....4..5.137.9..8.6.5.1..7.948.6..3.....5...57134...........
....................85623....4...1....3...6....2...9....61378....................
...........42561...1.....2..7.948.6..5.1.7.9..8.625.1..4.....7...78942...........
..85623...3.....5.6.......95...7...88..256..77...8...53.......2.5.....9...96257..
...........61378...8.....1..4.562.7..3.8.4.5..2.713.8..6.....4...42561...........
....................62541....9...7....1...5....4...8....57136....................
...........85423...3.....5..1.689.2..4.3.1.6..9.254.3..8.....1...19685...........
..94257...7.....4.2.......64...1...99..542..11...9...47.......5.4.....6...62541..

[tarek]

It would have been easy to provide 9 lines of 81 characters

i hope i got it right---

..61378...8.....1.3.......21...9...66..713..99...6...18.......7.1.....2...23719..
...........34896...6.....4..5.137.9..8.6.5.1..7.948.6..3.....5...57134...........
....................85623....4...1....3...6....2...9....61378....................
...........42561...1.....2..7.948.6..5.1.7.9..8.625.1..4.....7...78942...........
..85623...3.....5.6.......95...7...88..256..77...8...53.......2.5.....9...96257..
...........61378...8.....1..4.562.7..3.8.4.5..2.713.8..6.....4...42561...........
....................62541....9...7....1...5....4...8....57136....................
...........85423...3.....5..1.689.2..4.3.1.6..9.254.3..8.....1...19685...........
..94257...7.....4.2.......64...1...99..542..11...9...47.......5.4.....6...62541..

Thanks to Pat -again-

I can confirm the unique solution & solvability using singles only

here are the 27 puzzle grids & solutions in line & grid format, There is nice symmetry display

Hidden Text: Show

Code: Select all

..61378...8.....1.3.......21...9...66..713..99...6...18.......7.1.....2...23719..
...........34896...6.....4..5.137.9..8.6.5.1..7.948.6..3.....5...57134...........
....................85623....4...1....3...6....2...9....61378....................
...........42561...1.....2..7.948.6..5.1.7.9..8.625.1..4.....7...78942...........
..85623...3.....5.6.......95...7...88..256..77...8...53.......2.5.....9...96257..
...........61378...8.....1..4.562.7..3.8.4.5..2.713.8..6.....4...42561...........
....................62541....9...7....1...5....4...8....57136....................
...........85423...3.....5..1.689.2..4.3.1.6..9.254.3..8.....1...19685...........
..94257...7.....4.2.......64...1...99..542..11...9...47.......5.4.....6...62541..
..94257...............................85623...............................61378..
.7.....4...85423.............61378...3.....5...42561.............34896...8.....1.
2.......6.3.....5...62541...8.....1.6.......9.1.....2...85623...6.....4.3.......2
4...1...9.1.689.2...9...7...4.562.7.5...7...8.7.948.6...4...1...5.137.9.1...9...6
9..542..1.4.3.1.6...1...5...3.8.4.5.8..256..7.5.1.7.9...3...6...8.6.5.1.6..713..9
1...9...4.9.254.3...4...8...2.713.8.7...8...5.8.625.1...2...9...7.948.6.9...6...1
7.......5.8.....1...57136...6.....4.3.......2.4.....7...61378...3.....5.8.......7
.4.....6...19685.............42561...5.....9...78942.............57134...1.....2.
..62541...............................96257...............................23719..
..................2...6...34...5...19...8...61...7...97...3...8..................
.........7...3...8.3.8.1.6..1.4.7.5..4.3.5.8..9.2.8.7..8.6.4.3.4...5...1.........
9...8...6.8.6.4.3...6...8....9...4....1...3....4...2....5...6...1.4.7.5.6...9...2
4...5...1.5.1.2.4...2...5...6.5.9.1.53.821.67.2.7.6.9...7...1...9.2.8.7.2...6...3
2...6...3.4.3.5.8...5...6..18.674.394...5...195.182.46..1...3...6.5.9.1.5...2...7
5...2...7.2.7.6.9...4...2...9.2.8.7.21.467.53.4.3.5.8...3...7...8.6.4.3.4...5...1
7...3...8.3.8.1.6...1...3....7...1....5...6....8...9....6...8...5.1.2.4.1...7...9
.........4...5...1.5.1.2.4..2.7.6.9..6.5.9.1..3.8.1.6..1.4.7.5.6...9...2.........
..................6...9...29...8...61...7...94...5...15...2...7..................

256137894489625713371948562137894256625713489948562371894256137713489625562371948
894256137713489625562371948256137894489625713371948562137894256625713489948562371
137894256625713489948562371894256137713489625562371948256137894489625713371948562
562371948894256137713489625371948562256137894489625713948562371137894256625713489
948562371137894256625713489562371948894256137713489625371948562256137894489625713
371948562256137894489625713948562371137894256625713489562371948894256137713489625
713689425542371968896254137689425713371968542254137896425713689968542371137896254
425713689968542371137896254713689425542371968896254137689425713371968542254137896
689425713371968542254137896425713689968542371137896254713689425542371968896254137
689425713425713689713689425371948562948562371562371948137894256894256137256137894
371968542968542371542371968256137894137894256894256137625713489713489625489625713
254137896137896254896254137489625713625713489713489625948562371562371948371948562
425713689713689425689425713948562371562371948371948562894256137256137894137894256
968542371542371968371968542137894256894256137256137894713489625489625713625713489
137896254896254137254137896625713489713489625489625713562371948371948562948562371
713689425689425713425713689562371948371948562948562371256137894137894256894256137
542371968371968542968542371894256137256137894137894256489625713625713489713489625
896254137254137896137896254713489625489625713625713489371948562948562371562371948
647395182395218674218467953476953821953182746182674539764539218539821467821746395
821746395764539218539821467218467953647395182395218674182674539476953821953182746
953182746182674539476953821539821467821746395764539218395218674218467953647395182
476953821953182746182674539764539218539821467821746395647395182395218674218467953
218467953647395182395218674182674539476953821953182746821746395764539218539821467
539821467821746395764539218395218674218467953647395182953182746182674539476953821
764539218539821467821746395647395182395218674218467953476953821953182746182674539
182674539476953821953182746821746395764539218539821467218467953647395182395218674
395218674218467953647395182953182746182674539476953821539821467821746395764539218

 . . 6 | 1 3 7 | 8 . . 
 . 8 . | . . . | . 1 . 
 3 . . | . . . | . . 2 
-------+-------+------
 1 . . | . 9 . | . . 6 
 6 . . | 7 1 3 | . . 9 
 9 . . | . 6 . | . . 1 
-------+-------+------
 8 . . | . . . | . . 7 
 . 1 . | . . . | . 2 . 
 . . 2 | 3 7 1 | 9 . . 

 . . . | . . . | . . . 
 . . 3 | 4 8 9 | 6 . . 
 . 6 . | . . . | . 4 . 
-------+-------+------
 . 5 . | 1 3 7 | . 9 . 
 . 8 . | 6 . 5 | . 1 . 
 . 7 . | 9 4 8 | . 6 . 
-------+-------+------
 . 3 . | . . . | . 5 . 
 . . 5 | 7 1 3 | 4 . . 
 . . . | . . . | . . . 

 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . 8 | 5 6 2 | 3 . . 
-------+-------+------
 . . 4 | . . . | 1 . . 
 . . 3 | . . . | 6 . . 
 . . 2 | . . . | 9 . . 
-------+-------+------
 . . 6 | 1 3 7 | 8 . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 

 . . . | . . . | . . . 
 . . 4 | 2 5 6 | 1 . . 
 . 1 . | . . . | . 2 . 
-------+-------+------
 . 7 . | 9 4 8 | . 6 . 
 . 5 . | 1 . 7 | . 9 . 
 . 8 . | 6 2 5 | . 1 . 
-------+-------+------
 . 4 . | . . . | . 7 . 
 . . 7 | 8 9 4 | 2 . . 
 . . . | . . . | . . . 

 . . 8 | 5 6 2 | 3 . . 
 . 3 . | . . . | . 5 . 
 6 . . | . . . | . . 9 
-------+-------+------
 5 . . | . 7 . | . . 8 
 8 . . | 2 5 6 | . . 7 
 7 . . | . 8 . | . . 5 
-------+-------+------
 3 . . | . . . | . . 2 
 . 5 . | . . . | . 9 . 
 . . 9 | 6 2 5 | 7 . . 

 . . . | . . . | . . . 
 . . 6 | 1 3 7 | 8 . . 
 . 8 . | . . . | . 1 . 
-------+-------+------
 . 4 . | 5 6 2 | . 7 . 
 . 3 . | 8 . 4 | . 5 . 
 . 2 . | 7 1 3 | . 8 . 
-------+-------+------
 . 6 . | . . . | . 4 . 
 . . 4 | 2 5 6 | 1 . . 
 . . . | . . . | . . . 

 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . 6 | 2 5 4 | 1 . . 
-------+-------+------
 . . 9 | . . . | 7 . . 
 . . 1 | . . . | 5 . . 
 . . 4 | . . . | 8 . . 
-------+-------+------
 . . 5 | 7 1 3 | 6 . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 

 . . . | . . . | . . . 
 . . 8 | 5 4 2 | 3 . . 
 . 3 . | . . . | . 5 . 
-------+-------+------
 . 1 . | 6 8 9 | . 2 . 
 . 4 . | 3 . 1 | . 6 . 
 . 9 . | 2 5 4 | . 3 . 
-------+-------+------
 . 8 . | . . . | . 1 . 
 . . 1 | 9 6 8 | 5 . . 
 . . . | . . . | . . . 

 . . 9 | 4 2 5 | 7 . . 
 . 7 . | . . . | . 4 . 
 2 . . | . . . | . . 6 
-------+-------+------
 4 . . | . 1 . | . . 9 
 9 . . | 5 4 2 | . . 1 
 1 . . | . 9 . | . . 4 
-------+-------+------
 7 . . | . . . | . . 5 
 . 4 . | . . . | . 6 . 
 . . 6 | 2 5 4 | 1 . . 

 . . 9 | 4 2 5 | 7 . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . . 8 | 5 6 2 | 3 . . 
 . . . | . . . | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . 6 | 1 3 7 | 8 . . 

 . 7 . | . . . | . 4 . 
 . . 8 | 5 4 2 | 3 . . 
 . . . | . . . | . . . 
-------+-------+------
 . . 6 | 1 3 7 | 8 . . 
 . 3 . | . . . | . 5 . 
 . . 4 | 2 5 6 | 1 . . 
-------+-------+------
 . . . | . . . | . . . 
 . . 3 | 4 8 9 | 6 . . 
 . 8 . | . . . | . 1 . 

 2 . . | . . . | . . 6 
 . 3 . | . . . | . 5 . 
 . . 6 | 2 5 4 | 1 . . 
-------+-------+------
 . 8 . | . . . | . 1 . 
 6 . . | . . . | . . 9 
 . 1 . | . . . | . 2 . 
-------+-------+------
 . . 8 | 5 6 2 | 3 . . 
 . 6 . | . . . | . 4 . 
 3 . . | . . . | . . 2 

 4 . . | . 1 . | . . 9 
 . 1 . | 6 8 9 | . 2 . 
 . . 9 | . . . | 7 . . 
-------+-------+------
 . 4 . | 5 6 2 | . 7 . 
 5 . . | . 7 . | . . 8 
 . 7 . | 9 4 8 | . 6 . 
-------+-------+------
 . . 4 | . . . | 1 . . 
 . 5 . | 1 3 7 | . 9 . 
 1 . . | . 9 . | . . 6 

 9 . . | 5 4 2 | . . 1 
 . 4 . | 3 . 1 | . 6 . 
 . . 1 | . . . | 5 . . 
-------+-------+------
 . 3 . | 8 . 4 | . 5 . 
 8 . . | 2 5 6 | . . 7 
 . 5 . | 1 . 7 | . 9 . 
-------+-------+------
 . . 3 | . . . | 6 . . 
 . 8 . | 6 . 5 | . 1 . 
 6 . . | 7 1 3 | . . 9 

 1 . . | . 9 . | . . 4 
 . 9 . | 2 5 4 | . 3 . 
 . . 4 | . . . | 8 . . 
-------+-------+------
 . 2 . | 7 1 3 | . 8 . 
 7 . . | . 8 . | . . 5 
 . 8 . | 6 2 5 | . 1 . 
-------+-------+------
 . . 2 | . . . | 9 . . 
 . 7 . | 9 4 8 | . 6 . 
 9 . . | . 6 . | . . 1 

 7 . . | . . . | . . 5 
 . 8 . | . . . | . 1 . 
 . . 5 | 7 1 3 | 6 . . 
-------+-------+------
 . 6 . | . . . | . 4 . 
 3 . . | . . . | . . 2 
 . 4 . | . . . | . 7 . 
-------+-------+------
 . . 6 | 1 3 7 | 8 . . 
 . 3 . | . . . | . 5 . 
 8 . . | . . . | . . 7 

 . 4 . | . . . | . 6 . 
 . . 1 | 9 6 8 | 5 . . 
 . . . | . . . | . . . 
-------+-------+------
 . . 4 | 2 5 6 | 1 . . 
 . 5 . | . . . | . 9 . 
 . . 7 | 8 9 4 | 2 . . 
-------+-------+------
 . . . | . . . | . . . 
 . . 5 | 7 1 3 | 4 . . 
 . 1 . | . . . | . 2 . 

 . . 6 | 2 5 4 | 1 . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . . 9 | 6 2 5 | 7 . . 
 . . . | . . . | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . 2 | 3 7 1 | 9 . . 

 . . . | . . . | . . . 
 . . . | . . . | . . . 
 2 . . | . 6 . | . . 3 
-------+-------+------
 4 . . | . 5 . | . . 1 
 9 . . | . 8 . | . . 6 
 1 . . | . 7 . | . . 9 
-------+-------+------
 7 . . | . 3 . | . . 8 
 . . . | . . . | . . . 
 . . . | . . . | . . . 

 . . . | . . . | . . . 
 7 . . | . 3 . | . . 8 
 . 3 . | 8 . 1 | . 6 . 
-------+-------+------
 . 1 . | 4 . 7 | . 5 . 
 . 4 . | 3 . 5 | . 8 . 
 . 9 . | 2 . 8 | . 7 . 
-------+-------+------
 . 8 . | 6 . 4 | . 3 . 
 4 . . | . 5 . | . . 1 
 . . . | . . . | . . . 

 9 . . | . 8 . | . . 6 
 . 8 . | 6 . 4 | . 3 . 
 . . 6 | . . . | 8 . . 
-------+-------+------
 . . 9 | . . . | 4 . . 
 . . 1 | . . . | 3 . . 
 . . 4 | . . . | 2 . . 
-------+-------+------
 . . 5 | . . . | 6 . . 
 . 1 . | 4 . 7 | . 5 . 
 6 . . | . 9 . | . . 2 

 4 . . | . 5 . | . . 1 
 . 5 . | 1 . 2 | . 4 . 
 . . 2 | . . . | 5 . . 
-------+-------+------
 . 6 . | 5 . 9 | . 1 . 
 5 3 . | 8 2 1 | . 6 7 
 . 2 . | 7 . 6 | . 9 . 
-------+-------+------
 . . 7 | . . . | 1 . . 
 . 9 . | 2 . 8 | . 7 . 
 2 . . | . 6 . | . . 3 

 2 . . | . 6 . | . . 3 
 . 4 . | 3 . 5 | . 8 . 
 . . 5 | . . . | 6 . . 
-------+-------+------
 1 8 . | 6 7 4 | . 3 9 
 4 . . | . 5 . | . . 1 
 9 5 . | 1 8 2 | . 4 6 
-------+-------+------
 . . 1 | . . . | 3 . . 
 . 6 . | 5 . 9 | . 1 . 
 5 . . | . 2 . | . . 7 

 5 . . | . 2 . | . . 7 
 . 2 . | 7 . 6 | . 9 . 
 . . 4 | . . . | 2 . . 
-------+-------+------
 . 9 . | 2 . 8 | . 7 . 
 2 1 . | 4 6 7 | . 5 3 
 . 4 . | 3 . 5 | . 8 . 
-------+-------+------
 . . 3 | . . . | 7 . . 
 . 8 . | 6 . 4 | . 3 . 
 4 . . | . 5 . | . . 1 

 7 . . | . 3 . | . . 8 
 . 3 . | 8 . 1 | . 6 . 
 . . 1 | . . . | 3 . . 
-------+-------+------
 . . 7 | . . . | 1 . . 
 . . 5 | . . . | 6 . . 
 . . 8 | . . . | 9 . . 
-------+-------+------
 . . 6 | . . . | 8 . . 
 . 5 . | 1 . 2 | . 4 . 
 1 . . | . 7 . | . . 9 

 . . . | . . . | . . . 
 4 . . | . 5 . | . . 1 
 . 5 . | 1 . 2 | . 4 . 
-------+-------+------
 . 2 . | 7 . 6 | . 9 . 
 . 6 . | 5 . 9 | . 1 . 
 . 3 . | 8 . 1 | . 6 . 
-------+-------+------
 . 1 . | 4 . 7 | . 5 . 
 6 . . | . 9 . | . . 2 
 . . . | . . . | . . . 

 . . . | . . . | . . . 
 . . . | . . . | . . . 
 6 . . | . 9 . | . . 2 
-------+-------+------
 9 . . | . 8 . | . . 6 
 1 . . | . 7 . | . . 9 
 4 . . | . 5 . | . . 1 
-------+-------+------
 5 . . | . 2 . | . . 7 
 . . . | . . . | . . . 
 . . . | . . . | . . . 

 2 5 6 | 1 3 7 | 8 9 4 
 4 8 9 | 6 2 5 | 7 1 3 
 3 7 1 | 9 4 8 | 5 6 2 
-------+-------+------
 1 3 7 | 8 9 4 | 2 5 6 
 6 2 5 | 7 1 3 | 4 8 9 
 9 4 8 | 5 6 2 | 3 7 1 
-------+-------+------
 8 9 4 | 2 5 6 | 1 3 7 
 7 1 3 | 4 8 9 | 6 2 5 
 5 6 2 | 3 7 1 | 9 4 8 

 8 9 4 | 2 5 6 | 1 3 7 
 7 1 3 | 4 8 9 | 6 2 5 
 5 6 2 | 3 7 1 | 9 4 8 
-------+-------+------
 2 5 6 | 1 3 7 | 8 9 4 
 4 8 9 | 6 2 5 | 7 1 3 
 3 7 1 | 9 4 8 | 5 6 2 
-------+-------+------
 1 3 7 | 8 9 4 | 2 5 6 
 6 2 5 | 7 1 3 | 4 8 9 
 9 4 8 | 5 6 2 | 3 7 1 

 1 3 7 | 8 9 4 | 2 5 6 
 6 2 5 | 7 1 3 | 4 8 9 
 9 4 8 | 5 6 2 | 3 7 1 
-------+-------+------
 8 9 4 | 2 5 6 | 1 3 7 
 7 1 3 | 4 8 9 | 6 2 5 
 5 6 2 | 3 7 1 | 9 4 8 
-------+-------+------
 2 5 6 | 1 3 7 | 8 9 4 
 4 8 9 | 6 2 5 | 7 1 3 
 3 7 1 | 9 4 8 | 5 6 2 

 5 6 2 | 3 7 1 | 9 4 8 
 8 9 4 | 2 5 6 | 1 3 7 
 7 1 3 | 4 8 9 | 6 2 5 
-------+-------+------
 3 7 1 | 9 4 8 | 5 6 2 
 2 5 6 | 1 3 7 | 8 9 4 
 4 8 9 | 6 2 5 | 7 1 3 
-------+-------+------
 9 4 8 | 5 6 2 | 3 7 1 
 1 3 7 | 8 9 4 | 2 5 6 
 6 2 5 | 7 1 3 | 4 8 9 

 9 4 8 | 5 6 2 | 3 7 1 
 1 3 7 | 8 9 4 | 2 5 6 
 6 2 5 | 7 1 3 | 4 8 9 
-------+-------+------
 5 6 2 | 3 7 1 | 9 4 8 
 8 9 4 | 2 5 6 | 1 3 7 
 7 1 3 | 4 8 9 | 6 2 5 
-------+-------+------
 3 7 1 | 9 4 8 | 5 6 2 
 2 5 6 | 1 3 7 | 8 9 4 
 4 8 9 | 6 2 5 | 7 1 3 

 3 7 1 | 9 4 8 | 5 6 2 
 2 5 6 | 1 3 7 | 8 9 4 
 4 8 9 | 6 2 5 | 7 1 3 
-------+-------+------
 9 4 8 | 5 6 2 | 3 7 1 
 1 3 7 | 8 9 4 | 2 5 6 
 6 2 5 | 7 1 3 | 4 8 9 
-------+-------+------
 5 6 2 | 3 7 1 | 9 4 8 
 8 9 4 | 2 5 6 | 1 3 7 
 7 1 3 | 4 8 9 | 6 2 5 

 7 1 3 | 6 8 9 | 4 2 5 
 5 4 2 | 3 7 1 | 9 6 8 
 8 9 6 | 2 5 4 | 1 3 7 
-------+-------+------
 6 8 9 | 4 2 5 | 7 1 3 
 3 7 1 | 9 6 8 | 5 4 2 
 2 5 4 | 1 3 7 | 8 9 6 
-------+-------+------
 4 2 5 | 7 1 3 | 6 8 9 
 9 6 8 | 5 4 2 | 3 7 1 
 1 3 7 | 8 9 6 | 2 5 4 

 4 2 5 | 7 1 3 | 6 8 9 
 9 6 8 | 5 4 2 | 3 7 1 
 1 3 7 | 8 9 6 | 2 5 4 
-------+-------+------
 7 1 3 | 6 8 9 | 4 2 5 
 5 4 2 | 3 7 1 | 9 6 8 
 8 9 6 | 2 5 4 | 1 3 7 
-------+-------+------
 6 8 9 | 4 2 5 | 7 1 3 
 3 7 1 | 9 6 8 | 5 4 2 
 2 5 4 | 1 3 7 | 8 9 6 

 6 8 9 | 4 2 5 | 7 1 3 
 3 7 1 | 9 6 8 | 5 4 2 
 2 5 4 | 1 3 7 | 8 9 6 
-------+-------+------
 4 2 5 | 7 1 3 | 6 8 9 
 9 6 8 | 5 4 2 | 3 7 1 
 1 3 7 | 8 9 6 | 2 5 4 
-------+-------+------
 7 1 3 | 6 8 9 | 4 2 5 
 5 4 2 | 3 7 1 | 9 6 8 
 8 9 6 | 2 5 4 | 1 3 7 

 6 8 9 | 4 2 5 | 7 1 3 
 4 2 5 | 7 1 3 | 6 8 9 
 7 1 3 | 6 8 9 | 4 2 5 
-------+-------+------
 3 7 1 | 9 4 8 | 5 6 2 
 9 4 8 | 5 6 2 | 3 7 1 
 5 6 2 | 3 7 1 | 9 4 8 
-------+-------+------
 1 3 7 | 8 9 4 | 2 5 6 
 8 9 4 | 2 5 6 | 1 3 7 
 2 5 6 | 1 3 7 | 8 9 4 

 3 7 1 | 9 6 8 | 5 4 2 
 9 6 8 | 5 4 2 | 3 7 1 
 5 4 2 | 3 7 1 | 9 6 8 
-------+-------+------
 2 5 6 | 1 3 7 | 8 9 4 
 1 3 7 | 8 9 4 | 2 5 6 
 8 9 4 | 2 5 6 | 1 3 7 
-------+-------+------
 6 2 5 | 7 1 3 | 4 8 9 
 7 1 3 | 4 8 9 | 6 2 5 
 4 8 9 | 6 2 5 | 7 1 3 

 2 5 4 | 1 3 7 | 8 9 6 
 1 3 7 | 8 9 6 | 2 5 4 
 8 9 6 | 2 5 4 | 1 3 7 
-------+-------+------
 4 8 9 | 6 2 5 | 7 1 3 
 6 2 5 | 7 1 3 | 4 8 9 
 7 1 3 | 4 8 9 | 6 2 5 
-------+-------+------
 9 4 8 | 5 6 2 | 3 7 1 
 5 6 2 | 3 7 1 | 9 4 8 
 3 7 1 | 9 4 8 | 5 6 2 

 4 2 5 | 7 1 3 | 6 8 9 
 7 1 3 | 6 8 9 | 4 2 5 
 6 8 9 | 4 2 5 | 7 1 3 
-------+-------+------
 9 4 8 | 5 6 2 | 3 7 1 
 5 6 2 | 3 7 1 | 9 4 8 
 3 7 1 | 9 4 8 | 5 6 2 
-------+-------+------
 8 9 4 | 2 5 6 | 1 3 7 
 2 5 6 | 1 3 7 | 8 9 4 
 1 3 7 | 8 9 4 | 2 5 6 

 9 6 8 | 5 4 2 | 3 7 1 
 5 4 2 | 3 7 1 | 9 6 8 
 3 7 1 | 9 6 8 | 5 4 2 
-------+-------+------
 1 3 7 | 8 9 4 | 2 5 6 
 8 9 4 | 2 5 6 | 1 3 7 
 2 5 6 | 1 3 7 | 8 9 4 
-------+-------+------
 7 1 3 | 4 8 9 | 6 2 5 
 4 8 9 | 6 2 5 | 7 1 3 
 6 2 5 | 7 1 3 | 4 8 9 

 1 3 7 | 8 9 6 | 2 5 4 
 8 9 6 | 2 5 4 | 1 3 7 
 2 5 4 | 1 3 7 | 8 9 6 
-------+-------+------
 6 2 5 | 7 1 3 | 4 8 9 
 7 1 3 | 4 8 9 | 6 2 5 
 4 8 9 | 6 2 5 | 7 1 3 
-------+-------+------
 5 6 2 | 3 7 1 | 9 4 8 
 3 7 1 | 9 4 8 | 5 6 2 
 9 4 8 | 5 6 2 | 3 7 1 

 7 1 3 | 6 8 9 | 4 2 5 
 6 8 9 | 4 2 5 | 7 1 3 
 4 2 5 | 7 1 3 | 6 8 9 
-------+-------+------
 5 6 2 | 3 7 1 | 9 4 8 
 3 7 1 | 9 4 8 | 5 6 2 
 9 4 8 | 5 6 2 | 3 7 1 
-------+-------+------
 2 5 6 | 1 3 7 | 8 9 4 
 1 3 7 | 8 9 4 | 2 5 6 
 8 9 4 | 2 5 6 | 1 3 7 

 5 4 2 | 3 7 1 | 9 6 8 
 3 7 1 | 9 6 8 | 5 4 2 
 9 6 8 | 5 4 2 | 3 7 1 
-------+-------+------
 8 9 4 | 2 5 6 | 1 3 7 
 2 5 6 | 1 3 7 | 8 9 4 
 1 3 7 | 8 9 4 | 2 5 6 
-------+-------+------
 4 8 9 | 6 2 5 | 7 1 3 
 6 2 5 | 7 1 3 | 4 8 9 
 7 1 3 | 4 8 9 | 6 2 5 

 8 9 6 | 2 5 4 | 1 3 7 
 2 5 4 | 1 3 7 | 8 9 6 
 1 3 7 | 8 9 6 | 2 5 4 
-------+-------+------
 7 1 3 | 4 8 9 | 6 2 5 
 4 8 9 | 6 2 5 | 7 1 3 
 6 2 5 | 7 1 3 | 4 8 9 
-------+-------+------
 3 7 1 | 9 4 8 | 5 6 2 
 9 4 8 | 5 6 2 | 3 7 1 
 5 6 2 | 3 7 1 | 9 4 8 

 6 4 7 | 3 9 5 | 1 8 2 
 3 9 5 | 2 1 8 | 6 7 4 
 2 1 8 | 4 6 7 | 9 5 3 
-------+-------+------
 4 7 6 | 9 5 3 | 8 2 1 
 9 5 3 | 1 8 2 | 7 4 6 
 1 8 2 | 6 7 4 | 5 3 9 
-------+-------+------
 7 6 4 | 5 3 9 | 2 1 8 
 5 3 9 | 8 2 1 | 4 6 7 
 8 2 1 | 7 4 6 | 3 9 5 

 8 2 1 | 7 4 6 | 3 9 5 
 7 6 4 | 5 3 9 | 2 1 8 
 5 3 9 | 8 2 1 | 4 6 7 
-------+-------+------
 2 1 8 | 4 6 7 | 9 5 3 
 6 4 7 | 3 9 5 | 1 8 2 
 3 9 5 | 2 1 8 | 6 7 4 
-------+-------+------
 1 8 2 | 6 7 4 | 5 3 9 
 4 7 6 | 9 5 3 | 8 2 1 
 9 5 3 | 1 8 2 | 7 4 6 

 9 5 3 | 1 8 2 | 7 4 6 
 1 8 2 | 6 7 4 | 5 3 9 
 4 7 6 | 9 5 3 | 8 2 1 
-------+-------+------
 5 3 9 | 8 2 1 | 4 6 7 
 8 2 1 | 7 4 6 | 3 9 5 
 7 6 4 | 5 3 9 | 2 1 8 
-------+-------+------
 3 9 5 | 2 1 8 | 6 7 4 
 2 1 8 | 4 6 7 | 9 5 3 
 6 4 7 | 3 9 5 | 1 8 2 

 4 7 6 | 9 5 3 | 8 2 1 
 9 5 3 | 1 8 2 | 7 4 6 
 1 8 2 | 6 7 4 | 5 3 9 
-------+-------+------
 7 6 4 | 5 3 9 | 2 1 8 
 5 3 9 | 8 2 1 | 4 6 7 
 8 2 1 | 7 4 6 | 3 9 5 
-------+-------+------
 6 4 7 | 3 9 5 | 1 8 2 
 3 9 5 | 2 1 8 | 6 7 4 
 2 1 8 | 4 6 7 | 9 5 3 

 2 1 8 | 4 6 7 | 9 5 3 
 6 4 7 | 3 9 5 | 1 8 2 
 3 9 5 | 2 1 8 | 6 7 4 
-------+-------+------
 1 8 2 | 6 7 4 | 5 3 9 
 4 7 6 | 9 5 3 | 8 2 1 
 9 5 3 | 1 8 2 | 7 4 6 
-------+-------+------
 8 2 1 | 7 4 6 | 3 9 5 
 7 6 4 | 5 3 9 | 2 1 8 
 5 3 9 | 8 2 1 | 4 6 7 

 5 3 9 | 8 2 1 | 4 6 7 
 8 2 1 | 7 4 6 | 3 9 5 
 7 6 4 | 5 3 9 | 2 1 8 
-------+-------+------
 3 9 5 | 2 1 8 | 6 7 4 
 2 1 8 | 4 6 7 | 9 5 3 
 6 4 7 | 3 9 5 | 1 8 2 
-------+-------+------
 9 5 3 | 1 8 2 | 7 4 6 
 1 8 2 | 6 7 4 | 5 3 9 
 4 7 6 | 9 5 3 | 8 2 1 

 7 6 4 | 5 3 9 | 2 1 8 
 5 3 9 | 8 2 1 | 4 6 7 
 8 2 1 | 7 4 6 | 3 9 5 
-------+-------+------
 6 4 7 | 3 9 5 | 1 8 2 
 3 9 5 | 2 1 8 | 6 7 4 
 2 1 8 | 4 6 7 | 9 5 3 
-------+-------+------
 4 7 6 | 9 5 3 | 8 2 1 
 9 5 3 | 1 8 2 | 7 4 6 
 1 8 2 | 6 7 4 | 5 3 9 

 1 8 2 | 6 7 4 | 5 3 9 
 4 7 6 | 9 5 3 | 8 2 1 
 9 5 3 | 1 8 2 | 7 4 6 
-------+-------+------
 8 2 1 | 7 4 6 | 3 9 5 
 7 6 4 | 5 3 9 | 2 1 8 
 5 3 9 | 8 2 1 | 4 6 7 
-------+-------+------
 2 1 8 | 4 6 7 | 9 5 3 
 6 4 7 | 3 9 5 | 1 8 2 
 3 9 5 | 2 1 8 | 6 7 4 

 3 9 5 | 2 1 8 | 6 7 4 
 2 1 8 | 4 6 7 | 9 5 3 
 6 4 7 | 3 9 5 | 1 8 2 
-------+-------+------
 9 5 3 | 1 8 2 | 7 4 6 
 1 8 2 | 6 7 4 | 5 3 9 
 4 7 6 | 9 5 3 | 8 2 1 
-------+-------+------
 5 3 9 | 8 2 1 | 4 6 7 
 8 2 1 | 7 4 6 | 3 9 5 
 7 6 4 | 5 3 9 | 2 1 8

[Smythe Dakota]

.... I tried to generate puzzles with clues only on the faces of the cube (complete opposite of Barren Surface puzzle) with success ....

That reminds me of Marilyn's Numbrix puzzles in the Sunday Parade newspaper supplement. For the past two years or so, all of hers have clues in, and only in, the odd-numbered squares around the perimeter.

Bill Smythe