The New Sudoku Players' Forum

by **coloin** » Mon Aug 18, 2008 8:55 am

Solution grid...from this thread here

Code: Select all: +---+---+---+ |195|276|384| |842|953|761| |637|418|529| +---+---+---+ |384|195|276| |761|842|953| |529|637|418| +---+---+---+ |276|384|195| |953|761|842| |418|529|637| +---+---+---+

This is one of the automorphic grids......all 6 bands are equivalent.

But this isomorph has similar boxes
B1=B5=B9
B2=B6=B7
B3=B4=B8

We can make an easy puzzle with this constraint

Code: Select all: +---+---+---+ |1..|2..|3..| |8..|...|.61| |..7|..8|..9| +---+---+---+ |3..|1..|2..| |...|...|...| |...|..7|4.8| +---+---+---+ |...|3..|1..| |.5.|...|...| |4.8|..9|..7| +---+---+---+ [minmal under normal 9*9 rules]

How many more clues can be removed.......?

Code: Select all: +---+---+---+ |...|2..|...| |8..|...|.61| |..7|..8|..9| +---+---+---+ |...|...|...| |...|...|...| |...|...|4..| +---+---+---+ |...|3..|1..| |.5.|...|...| |...|...|...| +---+---+---+

C

by **tarek** » Mon Aug 18, 2008 10:04 am

I have a small idea to validate this ....

will return on this tomorrow....

tarek

by **tarek** » Mon Aug 18, 2008 4:57 pm

How about these minimal puzzles (moved clues to 1st 3 boxes):

Code: Select all: . . .|2 . .|3 . . 8 . .|. 5 .|. 6 1 . . 7|4 . 8|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . 9 clues 1 . .|. . .|3 . . 8 . .|. 5 .|. 6 1 . . 7|4 . .|. . 9 -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . 9 clues . . .|2 . .|. . . 8 . .|. 5 .|. 6 1 . . 7|4 . .|. . 9 -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . 8 clues . . .|2 . .|3 . . 8 . .|. . .|. 6 1 . . 7|4 . .|. . 9 -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . 8 clues . . .|2 . .|3 . . 8 . .|. 5 .|. 6 1 . . .|4 . .|. . 9 -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . 8 clues

tarek

by **tarek** » Mon Aug 18, 2008 7:07 pm

A difficult one ???

Code: Select all: . 2 .|7 . .|. 5 . 8 4 .|. . .|6 . . 1 . 5|. 9 .|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . .

tarek

by **Glyn** » Mon Aug 18, 2008 11:52 pm

tarek wrote:A difficult one ???
Code: Select all
. 2 .|7 . .|. 5 . 8 4 .|. . .|6 . . 1 . 5|. 9 .|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . .
tarek

It might be difficult ER 7.2 here's the PMs.

Code: Select all: .------------------.------------------.------------------. | 39 2 369 | 7 1368 13468| 349 5 13489| | 8 4 379 | 235 13 123 | 6 137 12379| | 1 367 5 | 234 9 23468| 234 378 23478| :------------------+------------------+------------------: | 349 5 13489| 39 2 369 | 7 1368 13468| | 6 137 12379| 8 4 379 | 235 13 123 | | 234 378 23478| 1 367 5 | 234 9 23468| :------------------+------------------+------------------: | 7 1368 13468| 349 5 13489| 39 2 369 | | 235 13 123 | 6 137 12379| 8 4 379 | | 234 9 23468| 234 378 23478| 1 367 5 | '------------------'------------------'------------------'

However we know that r1c3=6 or r3c2=6. Also symmetry gives r7c9=r1c3.
Therefore either r7c9=6 or r3c2=6 => r7c2<>6.
Hidden singles r3c2,r6c5,r9c8=6 using the symmetry.
Singles to finish irrespective of symmetry.

by **StrmCkr** » Tue Aug 19, 2008 2:13 am

nice one glen that is exactly what i was getting at

{i know diffrent thread but still}

the grids boxes are equal with or with out the clues beinging the same

thanks
colin

for starting this variation with respect to me and my idea/concepts.

by **tarek** » Tue Aug 19, 2008 6:35 am

Glyn wrote:It might be difficult ER 7.2 .....
.
.
.
However .....

I'm glad that this one provides a good example of how this variant is helpful....

I must say this casts a shadow of doubt on the minimality issue that my solver does.

hopefully someone else can validate their minimality.

tarek

by **coloin** » Tue Aug 19, 2008 9:17 am

Well done on getting the 8 clues....it seems we got there very easily [no lower please.]

More difficult to program the minimality issue - i think most puzzles will reduce significantly.

The number of essentially different grids which comply with

Code: Select all: B1=B5=B9 B2=B6=B7 B3=B4=B8

wont be very large.

EDIT

Certainly it will be devided into ones which have 3 repeating minirows [MC] and those which have a 2:1 split.

Code: Select all: 123|***|*** 456|312|*** 789|***|231 or 123|***|*** 456|3*2|**1 789|*1*|23*

There are only 3 different grids with the 3* property !

Here are 3 puzzles which define the 3 grids !

One with all of the 6 bands of repeating 3-tuple minirows - MC grid

Code: Select all: +---+---+---+ |123|...|.4.| |456|231|.7.| |789|...|.1.| +---+---+---+ |.4.|123|...| |.7.|456|231| |.1.|789|...| +---+---+---+ |...|.4.|123| |231|.7.|456| |...|.1.|789| +---+---+---+ MC grid

One with all 6 bands of repeating 2+1 -tuple minirows -

Code: Select all: +---+---+---+ |123|...|.4.| |456|238|.7.| |789|...|.6.| +---+---+---+ |.4.|123|...| |.7.|456|238| |.6.|789|...| +---+---+---+ |...|.4.|123| |238|.7.|456| |...|.6.|789| +---+---+---+

One with all 3 bands of 3-tuple minirows and 3 bands of 2+1 tupel-minirows

Code: Select all: +---+---+---+ |123|...|.4.| |456|231|.9.| |789|...|312| +---+---+---+ |.4.|123|...| |.9.|456|231| |312|789|...| +---+---+---+ |...|.4.|123| |231|.9.|456| |...|312|789| +---+---+---+

C

by **coloin** » Tue Aug 19, 2008 12:47 pm

Thinking about it.

A better, more interesting puzzle would be.

Solution grid with identical B1B5B9. [B2B3B4B6B7B8 variable]

Given clues only in B2B3B4B6B7B8.

C

by **tarek** » Tue Aug 19, 2008 7:29 pm

coloin wrote:A better, more interesting puzzle would be.
Solution grid with identical B1B5B9. [B2B3B4B6B7B8 variable]
Given clues only in B2B3B4B6B7B8.

Singles example:

Code: Select all: ...42.1........6.................9.85.........92....5...7...........4............ . . .|4 2 .|1 . . . . .|. . .|6 . . . . .|. . .|. . . -----+-----+----- . . .|. . .|9 . 8 5 . .|. . .|. . . . 9 2|. . .|. 5 . -----+-----+----- . . 7|. . .|. . . . . .|. . 4|. . . . . .|. . .|. . .

tarek

by **tarek** » Wed Aug 20, 2008 6:39 pm

with 3 identical blocks, this could go as "Trisonomous Sudoku" or Sudoku159

BTW, if anyone wants the 1st walkthrough for the 1st published "Trisonomous sudoku" (or Sudoku159) Then here you go:

Code: Select all: ...42.1........6.................9.85.........92....5...7...........4............ . . .|4 2 .|1 . . . . .|. . .|6 . . . . .|. . .|. . . -----+-----+----- . . .|. . .|9 . 8 5 . .|. . .|. . . . 9 2|. . .|. 5 . -----+-----+----- . . 7|. . .|. . . . . .|. . 4|. . . . . .|. . .|. . . (Remeber that Blocks 1,5 & 9 are identical) 4 is a given clue in r1c4 [r1c123689][r23c1456][r789c4]<>4 2 is a given clue in r1c5 [r1c123689][r23c2456][r789c5]<>2 1 is a given clue in r1c7 [r1c123689][r2c189][r3c1789][r56c7]<>1 6 is a given clue in r2c7 [r1c189][r2c12345689][r3c1789][r56c7]<>6 9 is a given clue in r4c7 [r1c123][r234c1][r356c7][r4c238][r5c89][r6c9]<>9 8 is a given clue in r4c9 [r1c1239][r23c39][r4c1238][r5c789][r6c79]<>8 5 is a given clue in r5c1 [r12346789c1][r24c23][r5c23789]<>5 9 is a given clue in r6c2 [r235789c2][r35c3][r6c1]<>9 2 is a given clue in r6c3 [r234589c3][r346c1][r45c2][r6c79]<>2 5 is a given clue in r6c8 [r1c28][r234c8][r3c23][r6c79]<>5 7 is a given clue in r7c3 [r1c123][r234589c3][r7c12456][r89c12]<>7 4 is a given clue in r8c6 [r2c23][r38c3][r79c56][r8c125]<>4 5 in r4c6 is a hidden single in more than one sector [r123c69][r7c2456][r89c3][r9c6]<>5 2 in r2c1 is a hidden single in more than one sector [r25c89][r35c7][r79c14][r8c124]<>2 9 in r5c6 is a hidden single in more than one sector [r13c69][r2c45689][r79c6][r8c1345][r9c3]<>9 4 in r6c5 is a hidden single in more than one sector [r2345c8][r3c79][r4579c2][r6c179][r9c13]<>4 4 in r2c9 is a hidden single in more than one sector [r5c9]<>4 5 in r3c7 is a hidden single in more than one sector [r3c45]<>5 2 in r4c8 is a hidden single in more than one sector [r3c8]<>2 2 in r3c9 is a hidden single in more than one sector 4 in r5c7 is a hidden single in more than one sector [r5c3]<>4 4 in r7c1 is a hidden single in more than one sector [r4c1]<>4 r4c3 has the last 4 uncovered 9 in r9c1 is a hidden single in more than one sector [r9c45]<>9 9 in r1c8 is a hidden single for r1 [r3c8]<>9 8 in r1c6 is a hidden single for r1 [r23c456][r79c6]<>8 6 in r1c2 is a hidden single for r1 [r3c35][r4c12][r5c28][r7c2456][r89c25]<>6 7 in r1c9 is a hidden single for r1 [r23c8][r56c9]<>7 3 in r1c1 is the last digit to fill the sector [r2c24][r3c134][r4c12][r6c17][r7c2456][r8c14][r9c4]<>3 3 in r6c9 is a hidden single for r6 [r5c89]<>3 6 in r5c9 is a hidden single in more than one sector [r5c3]<>6 1 in r9c9 is the last digit to fill the sector [r2c26][r3c456][r589c3][r6c1][r79c6][r9c245]<>1 1 in r5c8 is a hidden single in more than one sector [r5c2]<>1 7 in r6c7 is the last digit to fill the sector [r36c1]<>7 8 in r9c7 is the last digit to fill the sector [r29c2][r3c8][r68c1][r789c4][r9c35]<>8 7 in r8c8 is the last digit to fill the sector [r2c456][r389c5][r45c2][r8c4]<>7 6 in r6c1 is the last digit to fill the sector [r8c1]<>6 8 in r2c8 is a hidden single in more than one sector 3 in r3c8 is the last digit to fill the sector [r3c56]<>3 7 in r4c1 is a hidden single in more than one sector 1 in r4c2 is the last digit to fill the sector [r78c2]<>1 1 in r8c1 is the last digit to fill the sector [r8c45]<>1 3 in r2c6 is a Naked single [r2c5][r9c6]<>3 9 in r3c5 is a Naked single [r3c4][r7c5]<>9 r7c4 has the last 9 uncovered 1 in r7c5 is a hidden single in more than one sector [r2c5]<>1 r2c4 has the last 1 uncovered 5 in r2c5 is the last digit to fill the sector [r89c5]<>5 8 in r8c5 is a hidden single in more than one sector [r8c23]<>8 3 in r9c5 is the last digit to fill the sector [r9c23]<>3 8 in r7c2 is a hidden single in more than one sector [r5c2]<>8 2 in r7c6 is the last digit to fill the sector [r9c6]<>2 r5c3 has the last 8 uncovered 3 in r5c2 is the last digit to fill the sector [r8c2]<>3 r8c3 has the last 3 uncovered 6 in r9c3 is the last digit to fill the sector [r9c46]<>6 r9c2 has the last 2 uncovered 5 in r8c2 is the last digit to fill the sector [r8c4]<>5 6 in r8c4 is the last digit to fill the sector [r3c4]<>6 r3c6 has the last 6 uncovered 7 in r3c4 is the last digit to fill the sector [r9c4]<>7 5 in r9c4 is the last digit to fill the sector 7 in r9c6 is the last digit to fill the sector Puzzle Solved Solution: 365428197279153684841796532714365928538279416692841753487912365153684279926537841 3 6 5|4 2 8|1 9 7 2 7 9|1 5 3|6 8 4 8 4 1|7 9 6|5 3 2 -----+-----+----- 7 1 4|3 6 5|9 2 8 5 3 8|2 7 9|4 1 6 6 9 2|8 4 1|7 5 3 -----+-----+----- 4 8 7|9 1 2|3 6 5 1 5 3|6 8 4|2 7 9 9 2 6|5 3 7|8 4 1

tarek

by **StrmCkr** » Thu Aug 21, 2008 1:54 am

more fun would be mdksudoku or 187

blocks 1 - 8 -7 are identical.

there is only a 2 combinations of this function as well.

like

this set:

box 3-5-7
boxes 2,4,9
boxs 1,6,8

or: others to explore.

sets of three equal boxes. (few combinations of arangment of = boxs)

4 groups of 2 and odd man out. (many combinations)

The number of essentially different grids which comply with
Code:
B1=B5=B9
B2=B6=B7
B3=B4=B8

wont be very large.

all the automorphs are this i belive....

checking that list you refered me to and so far the ones i have checked are the above. after row/column swaps on the grids (check my thread for a puzzle listed so far) not sure if its the same puzzle or not...
but it has the exact same properties.

by **tarek** » Thu Aug 21, 2008 4:40 am

As I have said before.....

These Vanilla puzzles that are generated from Constrained Grids should ideally be sudoku variants & the puzzle should be generated as such.

I fthe qualities of the solution grid are not known at the time of generation. Then the resultant vanilla puzzle will have extra solving techniques hidden in the bag .... That is of course when you discover that quality.

tarek

by **StrmCkr** » Sun Dec 21, 2008 9:32 pm

We three kings: {Rating 8.2}

Code: Select all: *-----------* |5..|4..|8..| |..7|..5|..6| |...|.3.|...| |---+---+---| |7..|9..|4..| |...|..7|.9.| |..9|.2.|..8| |---+---+---| |64.|8..|.5.| |.25|..6|1..| |...|.1.|.24| *-----------*

if you can figure this one out have fund happy holidays

hints:

Box:
3 = 8 ,
5 = 9,
2 = 6,

boxs 5 & 9 = box 1 with the notation that there is a diagonal swap.
boxs 3 & 8 = box 4 with the notation that there is a diagonal swap.

box 2 & 6 = Box 7 with the notation that there is a row/column swap
=> which directly correlates to the above diagonal swaps.

by **udosuk** » Tue Dec 23, 2008 3:23 am

StrmCkr wrote:
Code: Select all
+---+---+---+ |5..|4..|8..| |..7|..5|..6| |...|.3.|...| +---+---+---+ |7..|9..|4..| |...|..7|.9.| |..9|.2.|..8| +---+---+---+ |64.|8..|.5.| |.25|..6|1..| |...|.1.|.24| +---+---+---+

If you swap c1 & c2, it becomes very obvious which sets of 3 blocks are identical to each other.

It is just way too easy with the given property that the grid consists of 3 sets of 3 idential blocks. Easier than an all-singles puzzle. I don't see any point of doing it.

On the other hand, without the given property the puzzle is still valid and solvable with some chains. But from the layout of the given clues you can't deduce anything about the "stormdoku" property, so you can't use it with any sound logical base.

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