The New Sudoku Players' Forum

by **dobrichev** » Sun Feb 09, 2014 12:31 pm

How many easy puzzles there are?
Are there symmetric ones?
What is the lower/higher clue limit?

Below is an example of a minimal unique puzzle with 31 givens having 1.2/1.0/1.0 SE rating coming from the 8 givens in the first column.

Code: Select all: 1...2.9.. 8.7..52.1 92.38.57. 29387.1.. 58.2..... 6........ 3....7..9 ......... 7..91..3.

Code: Select all: 1...2.9..8.7..52.192.38.57.29387.1..58.2.....6........3....7..9.........7..91..3. ED=1.2/1.0/1.0

Enjoy,
MD

by **tarek** » Sat Feb 15, 2014 10:47 am

A few years back forum members were active in collating lists of puzzles with special qualities.

One of these was the Low stepper puzzle: A puzzles that was so easy that can be solved in few singles steps
The other interesting one was the High stepper puzzle: A puzzle solved only with singles but requiring many steps to solve

by **dobrichev** » Sun Feb 16, 2014 9:10 am

Thank you tarek.

Although "locate singles (naked or hidden) - but don't place any numbers" rule sounds a bit strange, the job on easiest area seems to be done years ago.

by **Pat** » Sun Feb 16, 2014 9:26 am

dobrichev wrote:---the job on easiest area seems to be done years ago.

but you gave us a new definition of "easiest"

/1.0

by **dobrichev** » Sun Feb 16, 2014 11:53 am

Pat wrote:but you gave us a new definition of "easiest"

/1.0 (last cell in house) in minimal puzzle

Isn't it the Nicolas Juillerat's definition?

I found x/1.0/1.0 minimal puzzles are not so rare. I have few hundreds of them generated as a side effect in the testing of my puzzle minimization tool (guess what I minimized). From memory few of them were 8.x/1.0/1.0 and the most frequent were 7.x/1.0/1.0.
This was the only 1.2/1.0/1.0.

by **tarek** » Sun Feb 16, 2014 8:20 pm

There are several ways of grading singles:

Naked v Hidden

Then you also have:

Last Placement the 9th same-digit in the Grid
Last Placement of the 9th different-digit in a Sector
A single that is both a Naked & Hidden Single.
A single that is a Hidden single for more than 1 Sector

Tarek

by **daj95376** » Tue Feb 18, 2014 1:04 am

_

Assuming easiest implies "solvable with singles only", then I use a rating based on my solver's steps to solve a puzzle.

My n_singles() routine examines a grid and finds all Naked Singles present. It then lists them and performs the associated eliminations as one step. My h_singles() routine performs likewise for Hidden Singles. Let's consider your puzzle.

Hidden Text: Show

At runtime, my process() routine can be directed to emulate:

Code: Select all: while (1) { if ( n_singles() ) continue; if ( h_singles() ) continue; break; }

This results in 21 steps to solve the puzzle.

Hidden Text: Show

Code: Select all: Naked Single = 4 r8c1 Finished Step: 1 Hidden Single = 1 r3c6,r6c4 Hidden Single = 3 r1c9,r2c2 Hidden Single = 7 r1c4,r6c2 Hidden Single = 9 r2c5,r8c3 Finished Step: 2 Naked Single = 4 r6c3 Finished Step: 3 Naked Single = 1 r5c3 Naked Single = 6 r3c3 Finished Step: 4 Naked Single = 4 r3c9 Naked Single = 5 r1c3 Finished Step: 5 Naked Single = 4 r1c2 Naked Single = 6 r2c8 Finished Step: 6 Naked Single = 4 r2c4 Naked Single = 6 r1c6 Naked Single = 8 r1c8 Finished Step: 7 Naked Single = 4 r4c6 Finished Step: 8 Naked Single = 5 r4c8 Finished Step: 9 Naked Single = 6 r4c9 Finished Step: 10 Naked Single = 7 r5c9 Finished Step: 11 Hidden Single = 4 r7c5,r9c7 Hidden Single = 5 r6c5 Hidden Single = 6 r5c5 Hidden Single = 7 r8c7 Finished Step: 12 Naked Single = 3 r5c7,r8c5 Finished Step: 13 Naked Single = 8 r6c7 Naked Single = 9 r5c6 Finished Step: 14 Naked Single = 2 r6c9 Naked Single = 3 r6c6 Naked Single = 4 r5c8 Naked Single = 6 r7c7 Finished Step: 15 Naked Single = 5 r7c4 Naked Single = 9 r6c8 Finished Step: 16 Naked Single = 1 r7c2 Naked Single = 6 r8c4 Finished Step: 17 Naked Single = 2 r7c8 Naked Single = 5 r8c2 Finished Step: 18 Naked Single = 1 r8c8 Naked Single = 6 r9c2 Naked Single = 8 r7c3,r8c9 Finished Step: 19 Naked Single = 2 r8c6,r9c3 Naked Single = 5 r9c9 Finished Step: 20 Naked Single = 8 r9c6 Finished Step: 21

At runtime, my process() routine can also be directed to emulate:

Code: Select all: while (1) { if ( h_singles() ) continue; if ( n_singles() ) continue; break; }

This results in 14 steps to solve the puzzle.

Hidden Text: Show

Code: Select all: Hidden Single = 1 r3c6,r6c4 Hidden Single = 3 r1c9,r2c2 Hidden Single = 7 r1c4,r6c2 Hidden Single = 9 r2c5,r8c3 Finished Step: 1 Hidden Single = 1 r5c3 Hidden Single = 5 r6c5 Hidden Single = 8 r1c8 Finished Step: 2 Naked Single = 4 r6c3,r8c1 Finished Step: 3 Hidden Single = 4 r1c2,r3c9 Finished Step: 4 Hidden Single = 4 r2c4 Hidden Single = 5 r1c3 Finished Step: 5 Naked Single = 6 r1c6,r2c8,r3c3 Finished Step: 6 Hidden Single = 6 r4c9,r5c5 Finished Step: 7 Hidden Single = 5 r4c8 Finished Step: 8 Naked Single = 3 r8c5 Naked Single = 4 r4c6,r7c5 Naked Single = 7 r5c9 Finished Step: 9 Hidden Single = 4 r5c8,r9c7 Hidden Single = 7 r8c7 Finished Step: 10 Hidden Single = 6 r7c7,r9c2 Hidden Single = 9 r5c6,r6c8 Finished Step: 11 Hidden Single = 2 r6c9 Hidden Single = 5 r9c9 Hidden Single = 6 r8c4 Hidden Single = 8 r6c7,r7c3 Finished Step: 12 Hidden Single = 2 r7c8 Hidden Single = 5 r8c2 Hidden Single = 8 r9c6 Finished Step: 13 Naked Single = 1 r7c2,r8c8 Naked Single = 2 r8c6,r9c3 Naked Single = 3 r5c7,r6c6 Naked Single = 5 r7c4 Naked Single = 8 r8c9 Finished Step: 14

Leading to a combined rating of (21+14) = 35 step_singles for your puzzle.

by **Pat** » Tue Feb 18, 2014 12:10 pm

dobrichev wrote:

1...2.9..8.7..52.192.38.57.29387.1..58.2.....6........3....7..9.........7..91..3.
minimal puzzle
31 givens
SE rating 1.2/1.0/1.0
Code: Select all
1 . . | . 2 . | 9 . . 8 . 7 | . . 5 | 2 . 1 9 2 . | 3 8 . | 5 7 . -------+-------+------ 2 9 3 | 8 7 . | 1 . . 5 8 . | 2 . . | . . . 6 . . | . . . | . . . -------+-------+------ 3 . . | . . 7 | . . 9 . . . | . . . | . . . 7 . . | 9 1 . | . 3 .

5 ways to rate "singles"

"hidden singles" only
==> 13 steps
(where "hidden singles" insufficient, i use "99" to indicate infinity)
"naked singles" only
==> 99 steps
for the "inferior" rating,
we used a compromise:
"hidden singles" + "naked singles" treated as equal dificulty,
done in same step
==> 9 steps
"hidden singles" considered easier and done first
==> 13 steps of "hidden singles"
(and never needed to go to "naked singles")
"naked singles" considered easier and done first
==> 21 steps total,
including 2 steps of "hidden singles"

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