The New Sudoku Players' Forum

[holdout]

In the following two puzzles, only "hints" are given.
For example, the first cell in each grid must be
either a 3, 4, 7 or 8.

Novelty Soduko #1 has 69 solutions.
Novelty Soduko #2 has only one solution
(one of the 69 solutions to Puzzle #1).

Can you solve Puzzle #2?
Did you find this harder or easier than the standard Soduko?
Be the first to post a correct solution.
Comments are appreciated.

*** Novelty Soduko #1 ***

Code: Select all

  3478  1457  1358  |  1569  1245  2469  |  6789  2369  2378
  3679  2567  2359  |  1379  1348  4789  |  1468  2456  1258
  4689  1246  1289  |  3567  2358  2678  |  1479  3459  1357

  1257  1248  4578  |  1489  3689  1346  |  2357  2679  3569
  1367  1389  6789  |  2459  2379  3457  |  1245  1268  4568
  2356  2349  4569  |  1258  2678  1567  |  1347  1789  3489

  2489  3789  2347  |  2468  1456  1258  |  3569  1357  1679
  1259  5679  1267  |  3478  4579  3589  |  2368  1348  1246
  1458  3568  1346  |  2367  1679  1239  |  2589  4578  2479

*** Novelty Soduko #2 ***

Code: Select all

  3478  1457  1358  |  1569  1245  246.  |  6789  2369  2378
  3679  2567  2359  |  1379  1348  4789  |  168.  2456  158.
  4689  1246  1289  |  3567  2358  2678  |  1479  3459  1357

  1257  1248  4578  |  1489  3689  1346  |  2357  2679  3569
  1367  1389  6789  |  2459  279.  3457  |  1245  1268  4568
  2356  2349  4569  |  1258  2678  1567  |  1347  1789  3489

  2489  389.  2347  |  2468  1456  1258  |  3569  1357  1679
  1259  5679  1267  |  3478  479.  389.  |  2368  1348  1246
  1458  3568  1346  |  2367  1679  239.  |  2589  4578  2479

[Hud]

I think that might be too much for one solver to figure out but maybe if everyone could get a clue or 2 it could be done. I'll start by noting that in box 8, 5s are only in row 7 thus eliminating the 5s in box 9 row 7. From there there are only 5s in box 9 row 9 so we can eliminate the 5s in box 7 row 9.
That's all I've found thus far and I'm getting a headache.

[bluemoose]

It may be easier to solve if 9 separate grids were made, 1 for each number.

[r.e.s.]

holdout,
Given that Puzzle #2 has a unique solution, it must be this one (you asked for it to be posted) ...

Code: Select all

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

... which follows from simple moves (singles and row/col/block intersections) after setting r8c6=3 and r9c6=2.
Don't ask why those two settings -- they came to me in a Susser dream.

[MCC]

I got as far as Hud with the locked 5's in boxes 7,8 and 9, and then nothing.

It may be easier to solve if 9 separate grids were made, 1 for each number.

It dosen't help.

What res has used is T&E.
If r8c6=3 and r9c6=2 solves the puzzle then we need the logic behind these placements.

[Ruud]

You'd have to modify DLX to work with candidates in stead of clues. Then DLX could at least confirm that only one solution exists.

My solver is not prepared for this type of input, so all the standard techniques are unavailable.

holdout, can this 0-clue sudoku be solved without guessing? I'm really interested in the solving path for this one.

Ruud.

[r.e.s.]

What res has used is T&E. If r8c6=3 and r9c6=2 solves the puzzle then we need the logic behind these placements.

Yes, I came to those settings by guessing. (There are other such pairs of cells as well.)
I pasted the grid into <Sudoku Susser>, which does seem to apply its full arsenal of strategies to it ...
T&E on r8c6 alone is enough to solve the rest using Tabling (so it might pay to concentrate on finding logical reductions leading first to that one setting), and T&E on both r8c6 and r9c6 is enough to solve the rest by simple moves.

[holdout]

To r.e.s.: Your posted solution is correct. Well done.

To Rudd : Sorry, I don't know if the puzzle can be solved without guessing. It was generated as a by-product of something else I've been working on. I suspect that some guessing is needed.

To All: I thought it was interesting -- since most solution programs need some clues to get started.

[Lardarse]

holdout: Yes, it's an interesting puzzle. It's just bloody hard...

[r.e.s.]

holdout: I too agree that these can give some interesting variety. For another idea along these lines, see <this> variation.
Yet another idea is to just take the usual candidate grid for any valid puzzle and add consistent candidates to all the solved cells, essentially making a "hidden candidate grid" that's known to have a unique solution. With care to ensure a unique solution, candidates can also be added to unsolved cells as well; here's one of this kind ...

Code: Select all

23689  2358   23689  | 1568   3479   1247   | 1245   1256   1269
1579   1568   2469   | 3457   1267   1678   | 2368   1268   12469
2468   1247   2468   | 1569   2568   3568   | 2345   3479   3578
---------------------+----------------------+--------------------
1348   1679   3468   | 1458   1358   2579   | 2469   1457   1238
23489  23478  1569   | 2458   3458   5689   | 1689   2457   2368
2389   1238   4579   | 1247   1368   1689   | 1237   2456   1238 
---------------------+----------------------+--------------------
1379   3459   2468   | 2568   2567   1378   | 2457   3468   2456
2368   2378   1579   | 1468   1468   2346   | 1236   3589   4579
34568  3468   3468   | 2369   2489   1568   | 1347   1678   1346

(This one is not so hard -- no guessing required, though it takes some work to discover the "logical reductions" needed to get started -- and of course the Susser will solve it.)

[holdout]

To r.e.s.: Your method of constructing an "all hints" puzzle is certainly viable; start with a solution and then add "hints" to all cells to hide the truth (so long as only one solution exists).

My puzzle was produced quite accidentally. See my posting Soduko Cubes: for Sub-humans and Programmers in the Solver Programs Forum.

To construct the cube, I started with the Front View (Slice #1) as given. This start inferred some limitations on what clues could be selected for the Front View (Slice #2), and the rest of the cube -- for that matter.

The restrictions placed on Front View (Slice #2), were posted as "Novelty Soduko #1"; it has exactly four hints per cell and has a lot of uniformity. For example, each digit appears exactly 36 times over the course of the whole grid. To produce "Novelty Soduko #2", I merely removed hints until the number of solutions was reduced to one.

I never actually solved #2, but knew that there was only one solution. In retrospect, it is not surprising that guessing was needed to solve #2. After all, the set of hints was produced by a method designed to fill the entire cube with 27 slices of valid Soduko grids.

In a very real sense, Novelty Soduko #1 and #2 are mathematical "projections" of the original puzzle selected for the front face of the cube.

[Condor]

In the following two puzzles, only "hints" are given.

...

Can you solve Puzzle #2?
Did you find this harder or easier than the standard Soduko?
Be the first to post a correct solution.
Comments are appreciated.

Interesting alternative to a normal sudoku.
The puzzle was harder than a normal hard sudoku.

I think that might be too much for one solver to figure out but maybe if everyone could get a clue or 2 it could be done. I'll start by noting that in box 8, 5s are only in row 7 thus eliminating the 5s in box 9 row 7. From there there are only 5s in box 9 row 9 so we can eliminate the 5s in box 7 row 9.
That's all I've found thus far and I'm getting a headache.

Like Hud I could only eliminate the 5s in rows 7 to 9. I used a computer to verify that there was 69 solutions to puzzle #1 and only 1 solution to puzzle #2.

Like a normal sudoku, there should be 1 solution (like puzzle 2) and solvable by logic alone.

You could vary the number of occurances of each digit in the rows, columns, and boxes. Puzzle 1 has 4 occurances of each digit in every row, column, and box. You could make it 3 to 5 occurances per row, column, or box (or even 2-6).

The hints could be a bit more mixed up. I noticed that within each box the 4 occurances of any digit were in two of the rows and two of the columns. You could have a digit occur in all 3 rows or columns in some boxes and in only 1 row or column in other boxes.

[MCC]

code]23689 2358 23689 | 1568 3479 1247 | 1245 1256 1269
1579 1568 2469 | 3457 1267 1678 | 2368 1268 12469
2468 1247 2468 | 1569 2568 3568 | 2345 3479 3578
---------------------+----------------------+--------------------
1348 1679 3468 | 1458 1358 2579 | 2469 1457 1238
23489 23478 1569 | 2458 3458 5689 | 1689 2457 2368
2389 1238 4579 | 1247 1368 1689 | 1237 2456 1238
---------------------+----------------------+--------------------
1379 3459 2468 | 2568 2567 1378 | 2457 3468 2456
2368 2378 1579 | 1468 1468 2346 | 1236 3589 4579
34568 3468 3468 | 2369 2489 1568 | 1347 1678 1346 [/code]
(This one is not so hard -- no guessing required, though it takes some work to discover the "logical reductions" needed to get started -- and of course the Susser will solve it.)

I don't know about 'no guessing required', but having use, in no particular order:
Many locked candidates
Naked singles
Hidden singles
Hidden triples
Naked pair
Hidden pair
3 x-wings

I reached this stage.

Code: Select all

368    38    9   |168   4     7   |5    2    16 
7      5     4   |3     2     16  |8    16   9   
68     1     2   |9     68    5   |4    3    7   
------------------------------------------------
348    6     38  |148   5     2   |9    7    138
23489  7     1   |48    38    89  |6    5    238
2389   238   5   |7     1368  689 |13   4    238
------------------------------------------------
1      9     68  |5     7     3   |2    68   4   
238    238   7   |68    168   4   |13   9    5     
5      4     368 |2     9     168 |7    168  36

Unable to proceed I used T&E on the 68 in r3c5.

Placing the 8 here quickly leads to a dead end where further guessing is required.
Placing the 6 leads to a solution.


I'm just wondering whether I could have used the uniqueness principle in placing the 8 in r1c4

MCC

[r.e.s.]

Unable to proceed I used T&E

In your grid, look at the 6's in row8, etc. ... then a couple of xy-wings.

[MCC]

DOH!
You would think,having waded through all those locked candidates, I would have seen this, thanks r.e.s.

MCC