## Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9*9)

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9*9)

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
Last edited by tarek on Thu Dec 19, 2019 7:15 pm, edited 6 times in total.

tarek

Posts: 3759
Joined: 05 January 2006

### Re: Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9

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

Posts: 479
Joined: 25 June 2005

### Re: Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9

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
Last edited by dukuso on Sun Jun 27, 2010 5:00 pm, edited 1 time in total.
dukuso

Posts: 479
Joined: 25 June 2005

### Re: Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9

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

Posts: 3759
Joined: 05 January 2006

### 3 faces only 9*9*9

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

tarek

Posts: 3759
Joined: 05 January 2006

### Re: Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9

AFAIR all 9*9*9 sudokugrids are isomorphic
dukuso

Posts: 479
Joined: 25 June 2005

### Re: Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9

dukuso wrote: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

Posts: 3759
Joined: 05 January 2006

### Re: Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9

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

tarek

Posts: 3759
Joined: 05 January 2006

### Re: Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9

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

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

Posts: 479
Joined: 25 June 2005

### Re: Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9

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 352 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

Posts: 2
Joined: 17 December 2011

### Re: Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9

Sudoku001 Solution.xlsx
(40.15 KiB) Downloaded 300 times

Here is the solution for the 3D puzzle above:
K Pres

Posts: 2
Joined: 17 December 2011

### Re: Re-introducing The Sudoku Cube (3D sudoku, Sudoku3D, 9*9

K Pres wrote: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

tarek

Posts: 3759
Joined: 05 January 2006

tarek wrote: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..

Pat

Posts: 3968
Joined: 18 July 2005

### Re:

Pat wrote:
tarek wrote: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.......24...1...9.1.689.2...9...7...4.562.7.5...7...8.7.948.6...4...1...5.137.9.1...9...69..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..91...9...4.9.254.3...4...8...2.713.8.7...8...5.8.625.1...2...9...7.948.6.9...6...17.......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...24...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...32...6...3.4.3.5.8...5...6..18.674.394...5...195.182.46..1...3...6.5.9.1.5...2...75...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...17...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..................256137894489625713371948562137894256625713489948562371894256137713489625562371948894256137713489625562371948256137894489625713371948562137894256625713489948562371137894256625713489948562371894256137713489625562371948256137894489625713371948562562371948894256137713489625371948562256137894489625713948562371137894256625713489948562371137894256625713489562371948894256137713489625371948562256137894489625713371948562256137894489625713948562371137894256625713489562371948894256137713489625713689425542371968896254137689425713371968542254137896425713689968542371137896254425713689968542371137896254713689425542371968896254137689425713371968542254137896689425713371968542254137896425713689968542371137896254713689425542371968896254137689425713425713689713689425371948562948562371562371948137894256894256137256137894371968542968542371542371968256137894137894256894256137625713489713489625489625713254137896137896254896254137489625713625713489713489625948562371562371948371948562425713689713689425689425713948562371562371948371948562894256137256137894137894256968542371542371968371968542137894256894256137256137894713489625489625713625713489137896254896254137254137896625713489713489625489625713562371948371948562948562371713689425689425713425713689562371948371948562948562371256137894137894256894256137542371968371968542968542371894256137256137894137894256489625713625713489713489625896254137254137896137896254713489625489625713625713489371948562948562371562371948647395182395218674218467953476953821953182746182674539764539218539821467821746395821746395764539218539821467218467953647395182395218674182674539476953821953182746953182746182674539476953821539821467821746395764539218395218674218467953647395182476953821953182746182674539764539218539821467821746395647395182395218674218467953218467953647395182395218674182674539476953821953182746821746395764539218539821467539821467821746395764539218395218674218467953647395182953182746182674539476953821764539218539821467821746395647395182395218674218467953476953821953182746182674539182674539476953821953182746821746395764539218539821467218467953647395182395218674395218674218467953647395182953182746182674539476953821539821467821746395764539218 . . 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 `

tarek

Posts: 3759
Joined: 05 January 2006

### Re: 3 faces only 9*9*9

tarek wrote: .... 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
Smythe Dakota

Posts: 564
Joined: 11 February 2006

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