## Color Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Color Sudoku

I haven't posted any puzzle designs here in awhile, but I figured this would be a good mixed sudoku variant for this forum.

Color Sudoku:
Solve the following set of 3 puzzles using the given clues in the upper-left grid. The puzzles themselves are red, yellow, and blue, and the clues you receive may be in these primary colors, in the secondary colors (orange, purple, green), or in the color black. A number in a secondary color represents the sum of the two digits in the corresponding primary color puzzles that form that color (green 4 could mean yellow 1 + blue 3) while a number in black represents the sum over all three puzzles (black 7 could mean red 1 + yellow 2 + blue 4). In this example, there are only primary and secondary colored clues.

The standard sudoku rules of 1 to 6 in each row/column/box apply, but NO NUMBER IS REPEATED in the same place in two puzzles. A green 4 cannot mean yellow 2 + blue 2 as this would have two 2's in the same cell.

I've posted one easy example here, and I have two others that are harder on my blog.

Thomas Snyder
motris.livejournal.com
motris

Posts: 71
Joined: 13 March 2006

Aaargh! What are those of us without color printers supposed to do?

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

Motris

A fine puzzle, the first 3D puzzle I've seen that works. Good difficulty level for a first attempt at a new type - probably doable without pencil marks if one is used to them.

Red Solution:

413625
526143
164352
235416
342561
651234

Bill just do it in Excel as I did
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

Motris

I've posted a killer variant on DJApe's forum at:

http://www.djape.net/sudoku/forum/viewtopic.php?p=8842#p8842
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

Colour Pyramid 1

To celebrate Motris's victory, here is a variant on his colour sudoku - Pyramid Sudoku.

There are four pyramids: the bottom layer is black, the windoku layer is blue, the 2*2 squares layer is green and the peaks are red. The colour of the given tells you the level it is in.

The solution at each layer forms part of a valid (but maybe not unique) sudoku. At each level the numbers in a cage are a continuous sequence.

Vertically numbers must not repeat and must increase: except that 1 can be above 9 (and only 9) and 9 can be below 1 (and only 1).

The green layer is the hard bit.

Last edited by HATMAN on Tue Apr 29, 2008 9:26 am, edited 1 time in total.
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

HATMAN wrote:Vertically numbers must not repeat and must increase: except that 1 can be above 9 (and only 9) and 9 can be below 1 (and only 1).
Some confusions here: does that mean [7914] is a possible vertical sequence? Or only [9136] or [4791] etc are possible, i.e. 1 can act as "10" and 9 can act as "0", like Ace can act as both "1" & "14" in a poker deck?

Also, are r37c37 the only 4 cells with 4 vertical levels, and r3467c3467 the only 16 cells with 3 or more vertical levels, r234678c234678 are the only 36 cells with 2 or more vertical levels?
udosuk

Posts: 2698
Joined: 17 July 2005

Okay, even if I further restrict that [91] can only appear as a 2-level vertical sequence (i.e. [9135] & [5791] are both not allowed), I found no fewer than FIVE solutions for the Black Level.

Triple click to see the solutions I wrote:Red Level
.........
.........
..4...6..
.........
.........
.........
..5...4..
.........
.........

Green Level
.........
.........
..36.75..
..54.86..
.........
..67.54..
..45.63..
.........
.........

Blue Level
.........
.697.182.
.125.643.
.843.759.
.........
.756.438.
.934.521.
.218.976.
.........

Black Level (5 solutions!)
245831769
738629514
691475328
173296485
826547931
954183276
582364197
319758642
467912853

347812569
258639714
691475328
173296485
825147936
964583271
582364197
419728653
736951842

437812569
258639714
691475328
173296485
825147936
964583271
582364197
319758642
746921853

437821569
258639714
691475328
173296485
825147936
964583271
582364197
319758642
746912853

735812964
248639715
691475328
173256489
826947531
954183276
582364197
419728653
367591842

This is the pencilmark state for the Black Level before one has to guess away for one of the five solutions:

+-------------+-------------+-----------+
| 2347  34 57 |  8   123 12 | 579  6 49 |
|  27  345  8 |  6   23   9 |  57  1 45 |
|   6   9   1 |  4    7   5 |  3   2  8 |
+-------------+-------------+-----------+
|   1   7   3 |  2   59   6 |  4   8 59 |
|   8   2  56 | 159   4   7 |  59  3 16 |
|   9   56  4 |  15   8   3 |  2   7 16 |
+-------------+-------------+-----------+
|   5   8   2 |  3    6   4 |  1   9  7 |
|  34   1   9 |  7   25   8 |  6  45 23 |
|  347 346 67 |  59 1259 12 |  8  45 23 |
+-------------+-------------+-----------+

However, you can make it unique (sort of) by imposing one or both of the following 2 constraints:

1. The Black Level must be a Windoku (like the Blue Level)

2. Vertical numbers not only must form increasing sequences, but must form continuous increasing sequences e.g. [1234], [567].

In that case the unique solution grid for the Black Level is the 2nd one above.

As a matter of fact, from that Black Level solution one can complete the 3 levels above canonically by repeatingly adding one to each cell and converting the 10s to 1s:

Triple click to see the canonical solutions I wrote:Black Level
347812569
258639714
691475328
173296485
825147936
964583271
582364197
419728653
736951842

Blue Level
458923671
369741825
712586439
284317596
936258147
175694382
693475218
521839764
847162953

Green Level
569134782
471852936
823697541
395428617
147369258
286715493
714586329
632941875
958273164

Red Level
671245893
582963147
934718652
416539728
258471369
397826514
825697431
743152986
169384275

udosuk

Posts: 2698
Joined: 17 July 2005

Matt

In Nigeria now and this is the first chance I've had to respond.
On the nine issue the wording is not perfectly clear. You can have
1
9

but not
2
1
9
or
1
9
8

Hence the 1s on the blue level cannot be below the green squares - hence the green squares cannot contain 1 or 2.

I thought that the black level was forced to be windoku, by the blue level -however thinking about it - perhaps not. I'll go over it again later.

Maurice
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

Maurice, wow you're travelling around the world now. Bon Voyage!

(Next year I might go to Turkey to explore the real Noah's Ark. We might get to meet after missing the chances in Sydney & Singapore. )

HATMAN wrote:I thought that the black level was forced to be windoku, by the blue level -however thinking about it - perhaps not. I'll go over it again later.

The black level could be forced to be windoku if you restrict that vertical levels must increase by 1. But if you don't restrict the gaps between vertical levels then all bets are off. Just check my 5 solutions for the black levels to see the counter-examples.
udosuk

Posts: 2698
Joined: 17 July 2005