The New Sudoku Players' Forum

by **evert** » Sun Aug 24, 2008 7:16 pm

The cells forming a V-shape are a constraint - i.e. must contain all digits 1-9.

Code: Select all: X . . | . . . | . . X . . . | . . . | . . . . X . | . . . | . X . ------+-------+------- . . . | . . . | . . . . . X | . . . | X . . . . . | . . . | . . . ------+-------+------- . . . | X . X | . . . . . . | . . . | . . . . . . | . X . | . . .

The consecutive cells are separated by a knight's move.

Also, the rotated/mirrored V-shapes are constraints:

Code: Select all: . . . | . X . | . . . . . . | . . . | . . . . . . | X . X | . . . ------+-------+------- . . . | . . . | . . . . . X | . . . | X . . . . . | . . . | . . . ------+-------+------- . X . | . . . | . X . . . . | . . . | . . . X . . | . . . | . . X X . . | . . . | . . . . . X | . . . | . . . . . . | . X . | . . . ------+-------+------- . . . | . . . | X . . . . . | . . . | . . X . . . | . . . | X . . ------+-------+------- . . . | . X . | . . . . . X | . . . | . . . X . . | . . . | . . . . . . | . . . | . . X . . . | . . . | X . . . . . | . X . | . . . ------+-------+------- . . X | . . . | . . . X . . | . . . | . . . . . X | . . . | . . . ------+-------+------- . . . | . X . | . . . . . . | . . . | X . . . . . | . . . | . . X

Here's a puzzle with this constraint:

Code: Select all: 000000020 000002750 070830100 000003200 040000070 500000000 000000040 000006082 005000000

by **Smythe Dakota** » Sun Aug 24, 2008 8:39 pm

I assume all four of the V-constraints apply simultaneously.

Bill Smythe

by **Glyn** » Sun Aug 24, 2008 9:33 pm

Bill I found a solution using three constraints v,^,>. The first two were not sufficient to solve the puzzle.
To solve with singles all four constraints were required.

by **evert** » Mon Aug 25, 2008 2:45 am

Interesting thought that in certain cases not all constraints are actually used.

Here's one combined with X:

Code: Select all: 000405000 000900083 000030000 002000000 040000000 000000040 300050000 070890001 000000000

(so < > ^ V and two main diagonals)

by **evert** » Wed Sep 03, 2008 5:21 pm

This 10-clue one should be a little bit more fun:

Code: Select all: 500000006 300000000 000106000 000000000 090200000 018000000 000007000 000000000 000000000

It's all V-constraints and also both main diagonals - let's say Sudoku V-X.

I also found some situations with very few clues and no solutions.
For example:

Code: Select all: 100000000 007000000 000050000 000000600 000000002 000000300 050090000 004000000 800000000

has no solutions (with or without X).

Either windoku-V has no solutions AT ALL.

by **HATMAN** » Wed Sep 03, 2008 6:09 pm

Evert

Nice one - Matt and I have been collecting interacting constaints that either have no solutions or more importantly minimal solutions.

Can I clarify: with windoku how many Vs cause failure?

by **udosuk** » Fri Sep 05, 2008 1:18 pm

Nice puzzles. Enjoyed all 3 of them!

evert wrote:I also found some situations with very few clues and no solutions.
For example:
Code: Select all
100000000 007000000 000050000 000000600 000000002 000000300 050090000 004000000 800000000

has no solutions (with or without X).

This shouldn't come as any surprise, because you have r3c5=5, which rules out 5 from r1c9 (<), r3c28 (r3), & r9c5 (c5). As a result, 5 @ V is locked @ r5c37+r7c46, which has a pointing elimination @ r7c2 (Λ & r7). So you can't have r7c2=5. :idea:

evert wrote:Either windoku-V has no solutions AT ALL.

Again this is easy to prove:

Code: Select all: V . . | . Λ . | . . V . . . | . . . | . . . . . . | . . . | . . . ---------+---------+--------- . . . | . . . | . . . R . * | . R . | . . R . . . | . . . | . . . ---------+---------+--------- . . . | . . . | . . . . . . | . . . | . . . Λ . . | . V . | . . Λ

Consider r5c3. It eliminates all identical candidates @ r159c159 (through V, Λ or r5). But in windoku this is a hidden group of 9 different values, so a clear contradiction there. Therefore no windoku is possible as long as there are 2 opposite V's existing. :idea:

by **evert** » Fri Sep 05, 2008 5:37 pm

Tx udosuk!

With only two and non-opposite V-groups, Windoku-V is possible.
Following puzzle has constraints (>,V) and windoku:

Code: Select all: 000000000 000000200 004070000 000000000 003000010 000000050 000000300 000000820 090050600

Having both main diagonals (X) and windoku (NRC) and two non-opposite V-groups - there are zero solutions.

by **udosuk** » Sat Sep 06, 2008 2:49 am

evert wrote:Having both main diagonals (X) and windoku (NRC) and two non-opposite V-groups - there are zero solutions.

Yep that's true, but it's very difficult to prove explicitly. I'm running out for free time this weekend so it has to be put into the waiting list (for me)...

At the mean time, here is a side product - I found that with X, V, >, 2 upper windows (r234c234+r234c678) and the "outside dots" (r159c159) you get a puzzle with an essentially unique solution (barring digit mapping). In other words, if you fill in 8 cells of any established constraint group (the 9th cell can be forced as a naked single) you get a valid puzzle. Note there are a total of 36 constraint groups here: 9 rows, 9 columns, 9 boxes, 2 diagonals, 2 V's, 2 upper windows, 1 outside dots, 2 hidden windows (r234c159, r678c159).

Or, if you ditch the outside dots, you can have a valid 8-clue puzzle like this:

Code: Select all: Sudoku X-V->-UW (Upper Windows: r234c234, r234c678) 1 . . | . 2 . | . . 3 . . . | . . . | . . . . . . | . . . | . . . -------+-------+------- . . . | . . . | . . . 4 . . | . 5 . | . . 6 . . . | . . . | . . . -------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . 8 . | . . 9

Note because I didn't specify the r159c159 group so r9c1 could be 2 or 7 at the start. It's not easy to eliminate the 2 to confirm r9c1=7, and even then it's still diabolical to solve.

But I like the elegancy of the extra constraints here: 2 diagonals, 2 non-opposite V's and 2 non-opposite windows.

There are also 2 alternative (slightly easier) 8-clue versions of this:

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

by **evert** » Mon Sep 15, 2008 3:32 pm

I've tried to add some more interactions between the V-groups and the other groups:

Here's three Sudoku V:

Code: Select all: 006000090 000010000 010080000 000300002 930000000 000070900 000040000 000000000 065000000 040003000 090002000 000670000 006009000 000000000 080700000 020106000 000000000 000800091 003000000 000800074 000000000 000080607 100060908 000200000 000005000 050000000 092000000

Here's three Sudoku VX:

Code: Select all: 000040006 000000000 000000003 000000060 900000000 020560090 008000010 000080002 000100000 000000000 000500000 000009001 002000009 100000000 000006082 000000000 000000000 400030000 050030000 010000020 000010000 000000000 000070002 080040600 000000000 004050000 000000000

by **evert** » Mon Nov 17, 2008 1:47 pm

What am I missing in the following puzzle? It's Sudoku VX: V^<>/ \

Code: Select all: ...|..1|..3 .49|...|... 8..|...|... ---+---+--- ...|...|372 ..8|...|... 7..|...|... ---+---+--- ..2|...|... ...|...|5.. ...|...|...

I completed it until:

Code: Select all: 2 | 7 | 56 | 45689 | 4569 | 1 | 4689 | 45689 | 3 1356 | 4 | 9 | 368 | 7 | 3568 | 2 | 568 | 168 8 | 156 | 35 | 234569| 46 | 23469 | 7 | 1569 | 1469 -------+-------+-------+-------+-------+-------+-------+-------+------- 456 | 56 | 146 | 1689 | 1469 | 4689 | 3 | 7 | 2 9 | 23 | 8 | 237 | 16 | 237 | 46 | 146 | 5 7 | 23 | 146 | 456 | 23 | 56 | 16 | 89 | 89 -------+-------+-------+-------+-------+-------+-------+-------+------- 3456 | 1569 | 2 | 145679| 8 | 45679 | 169 | 1369 | 1469 1346 | 1689 | 7 | 123469| 23 | 2346 | 5 | 3689 | 14689 146 | 15689 | 3456 | 134569| 1569 | 34569 | 4689 | 2 | 7

I expect some pointing pair...

by **udosuk** » Sat Nov 22, 2008 3:24 am

evert you're indeed missing some pointing eliminations.

There is an easy pair of pointing cells of 8 @ r24c6 (pointing @ r2c8) but it isn't critical to solve the puzzle.

Here is one possible short path to solve it from that position:

4 @ ">" locked @ r3c5+r9c1 (pointing @ r1c5+r3c46)
4 @ "^" locked @ r5c7+r9c1 (pointing @ r9c7)
4 @ b9 locked @ r78c9 (not elsewhere @ c9)
Hidden single @ r3: r3c5=4 (not elsewhere @ "<",">")
Hidden single @ "^": r5c7=4 (not elsewhere @ "V")
Hidden single @ r6: r6c4=4
Hidden single @ r6: r6c6=5 (not elsewhere @ d\)
Naked single: r3c3=3 (not elsewhere @ d\)
Naked pair: r5c58={16} (pointing @ r28c8)
Naked pair: r68c8={89} (not elsewhere @ c8)

All singles from here.

Another random observation: from your position it only takes X^ or V^ to give a unique solution, but you probably need wings/fishes to crack it. :idea:

The New Sudoku Players' Forum

Sudoku-V (or did this already exist?)

Sudoku-V (or did this already exist?)