The New Sudoku Players' Forum

[keith]

I am sure this thread exists somewhere else:


What are the most difficult puzzles that do not require advanced solving techniques?

Advanced = X-wings, Uniqueness.

For example, what is the most difficult known puzzle that requires only naked singles?

Keith

[Ruud]

Some answers can be found in the Inferior collection.

The puzzles by Wapati are a good collection of hard puzzles which do not require coloring or chains.

[JPF]

I don't know the answer for naked singles only, but for singles and using as rating the number of steps defined in this thread, here is the "most difficult" puzzle, given by Gordon Royle :

Code: Select all

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



30 steps

JPF

[RW]

Once again, "most difficult" may be defined in many different ways. To me difficulty in an easy puzzle, indicates a narrow solving path. It's not only about what techniques are required and how many steps of those techniques, but should also take in consideration what alternative paths are available. Easy puzzles are meant to be solved by humans, therefore the rating should try to rate puzzles like humans would. Human solvers do not look for techniques in a specific order, but usually have a set of techniques that they apply whenever possible. If a singles 30 stepper breaks down to a 15 stepper by applying locked candidates once, then it really isn't that difficult for human solvers. I tried to start a thread on puzzles where the alternative paths would be as hard as possible a while ago, here. Here's the first example from the thread:

Code: Select all

 *-----------*
 |..2|..7|...|
 |..4|...|..5|
 |9.6|...|81.|
 |---+---+---|
 |...|...|34.|
 |2..|.1.|...|
 |.8.|..5|7..|
 |---+---+---|
 |.4.|8.1|.6.|
 |...|...|...|
 |3..|69.|...|
 *-----------*

If you cannot find the naked triplet, then you'll have a very hard time solving the puzzle.

RW

[Pat]

For example, what is the most difficult known puzzle that requires only -- ?

"singles" + box-line interactions --

[ 21 clues ]

Code: Select all

...6.9.....1...7...2.....9.8...5...77...4...64...2...8.3.....2...5...3.....4.8...

Code: Select all

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



[keith]

Thank you, all.

Greatly appreciated!

Keith