The New Sudoku Players' Forum

[olimpia]

I was wondering if anyone has seen or made a sudoku which gets HARDER as it is solved. Ideally such a puzzle would start really easy for a couple of cells, then each new value becomes progressively more difficult to solve, until finally the puzzle seizes-up (that is it becomes so difficult that it is near-impossible for a human to solve).

Best would be a sudoku with this property AND has symmetry.

Maybe such a sudoku would be a "backwards" sudoku (because more clues makes it harder), or maybe it is a "nightmare" because one might think they just need to get over the next hurdle, but really the hurdles get higher and higher (maximum frustration)!!

[Smythe Dakota]

Even newspaper puzzles sometimes have the property you seek, especially near the end of the week when the difficulty rating increases. I have seen several where all but the last 15 or so cells can be filled in using only (naked and hidden) singles, doubles, and triples, and perhaps box-line interactions, but then you suddenly hit a "wall" of sorts.

Bill Smythe

[m_b_metcalf]

I was wondering if anyone has seen or made a sudoku which gets HARDER as it is solved.

Is this the sort of thing you mean? It gets harder after 64 cells are solved, not incredibly so but hard enough. These are not difficult to produce.

Code: Select all

 . . . . . 2 9 . 8
 . . . . . 5 . 3 .
 . . . 8 . . . . 2
 1 . . . . 7 . 5 4
 7 . . . . . . . 3
 8 9 . 6 . . . . 7
 3 . . . . 1 . . .
 . 6 . 3 . . . . .
 9 . 2 4 6 . . . .

It's not quite symmetric, nor minimal, but just to get the idea.

[Edits]And two more, symmetric but not minimal:

Code: Select all

 . . . . 1 . . . .
 2 . . 3 4 5 . . 6
 . 4 . . . . . 3 .
 1 2 . . . . . 7 5
 3 . . 5 6 2 . . 8
 5 8 . . . . . 6 3
 . 1 . . . . . 2 .
 6 . . 7 2 8 . . 1
 . . . . 5 . . . .

Code: Select all

 . . . . . . . . .
 . 1 . 2 . 3 . 4 .
 . 3 5 . . . 6 7 .
 . . 2 . 5 . 8 . .
 1 4 . 9 . 2 . 3 5
 . . 3 . 4 . 2 . .
 . 2 8 . . . 9 1 .
 . 5 . 8 . 6 . 2 .
 . . . . . . . . .

Regards,

Mike Metcalf

[olimpia]

I tried the last one: I get stuck when there is 20 cells left to go. R1C3 has two options: 4 or 9. I tried a 4 and the puzzle continued to solve fairly easily. Not bad - a sticking point with just 20 clues left to go.

[zol]

Here's one from my website http://www.SudokuByZol.com. The Very Hard puzzles are almost all like the ones you are looking for and all the puzzles are symmetrical.

For example:

Code: Select all

. . 9 . . . . . .
. . 6 1 7 9 . . .
8 . . . 4 3 . . .
. . 8 3 . . 9 . .
6 . . 9 2 4 . . 3
. . 1 . . 6 5 . .
. . . 4 3 . . . 6
. . . 2 1 8 4 . .
. . . . . . 8 . .



Have fun,
Zol

[Pat]

puzzles with a tough ending --
see: Maximum number of clues for a given SE rating

[olimpia]

puzzles with a tough ending --
see: Maximum number of clues for a given SE rating

Those puzzles don't have a tough ending. They have a tough start.

The 37 clue sudoku is a good example of a sudoku which I describe as seized-up (but it starts that way). What I'm looking for would have 20 givens (for example), then there are 10 cells which solve easily, next 7 get tougher, and finally its seized-up (like how that 37 clue puzzle starts).

Oh yeah: should also have symmetry.

Or maybe its impossible for a 20 clue sudoku to "grow-up" into a 37 clue monster???

[tarek]

Or maybe its impossible for a 20 clue sudoku to "grow-up" into a 37 clue monster???

You will be surprised of how easy these might come up if you look in the right place ...

Code: Select all

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

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

tarek

[olimpia]

Those are really cool, exactly what I like. The first is a tease for about 25 cells, then plays hard. I didn't try the other one yet.

Heres another I found (19 givens, plays easy for about 20 cells). But in the end not as tough as the diagonals I think.

Code: Select all

. . . . . . . . .
. . 9 . 3 . 1 . .
. 4 . . 8 . . 2 .
. . . 1 . 7 . . .
. 8 . . 4 . . 6 .
. . . . 2 . . . .
. 2 . . 6 . . 8 .
. . 1 9 . 5 3 . .
. . . . . . . . .

[Pat]

puzzles with a tough ending --
see: Maximum number of clues for a given SE rating

Those puzzles don't have a tough ending. They have a tough start.

yes, for the purpose of that Topic they are posted with a high number of clues

but many clues can be dropped --
then you'd usually get puzzles which start easy and have a tough ending

[Mauricio]

Have fun with this:

Code: Select all

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

[udosuk]

Have fun with this:

Code: Select all

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

Did you mean to post this windmill here or should it be in another thread instead?

I'm ready to see the surprise of olimpia & co when they realise how easy this puzzle can be solved with a certain "shortcut".

[eleven]

Hm, i see a 90° symmetry (after inserting the singles), but no easy solution.

r4c8<>6 does not help much. What am i missing ?

[udosuk]

When I said "easy", I didn't mean "straight forward easy". But it's still much much more easier than the hellish forcing chains/nets without considering the symmetry.

The key to solving with this symmetry is to focus on the "windmills" (groups of 4 cells forming a cycle).

For example, look at the windmill r2c7+r7c8+r8c3+r3c2. Then look at the cell r2c3. What eliminations can you make on this windmill?

Also look at the windmill r1c7+r7c9+r9c3+r3c1. Then look at where the 1s are locked @ b1. Can you make some eliminations on this windmill?

These, together with your elimination on r4c8 (and 3 other cells), will lead you to the critical move which is just a touch more tricky. I'll leave you to spot it yourself.

[olimpia]

yes, for the purpose of that Topic they are posted with a high number of clues but many clues can be dropped --
then you'd usually get puzzles which start easy and have a tough ending

Thats interesting, but useless for me. I don't have the means to sweep through a sudoku and identify the redundant clues before solving it (and its not a skill I'm trying to develop). But, do any of those have a hidden symmetrical starting position with just a few givens?

The 27 clue by Maurico is neat (and unsolvable by me). I can work to a point where MANY cells have 3 possibilites. Yet not in any cell does a single guess lead to any more progress! Its nearly ideal according to my original request - BUT doesn't start with symmetry! (Sorry - I'm a purist).