## Difficulty levels

Everything about Sudoku that doesn't fit in one of the other sections

### Difficulty levels

Hey, I've been browsing around this forum but I can't seem to find a straight answer. What are the characteristics that make a sudoku puzzle easy, medium or hard?
newhere

Posts: 4
Joined: 06 February 2006

Usually puzzles are rated two ways.

For Humans:
if its a easy-medium its based upon how many singles there are at any step in the puzzle.

If its medium-feinish its rated upon what techiques are needed.

For Computers:
Ratings are based almost exclusively upon what techniqes and how many times they are used.
eclark

Posts: 14
Joined: 26 January 2006

hey
i have to work on some sudoku puzzles for my discrete math class. Apparently we got an easy one this week and we're getting a medium one next week and a hard one the following week. We need to explain what makes each one easy, hard or difficult. Of course, since it's my first time doing one of these puzzles it's hard for me to know what are the techniques needed for each level and stuff like that. I did think that this first one was easy but I don't really know how a medium or hard one looks like.
newhere

Posts: 4
Joined: 06 February 2006

I like to assess difficulty by considering the number of solutions paths, i.e. the number of different "paths" (series of steps) that leads to the solution of a puzzle. Calculating this could be a bit tricky, though.

Another way (and this is what my solver program does) is to solve as many naked singles as possible as one step, and the puzzle's overall difficulty is simply the number of steps taken from start to finish. Very easy puzzles are often cracked in 4-5 steps (meaning there are lots of naked singles at every point), while the harder ones can reach 20-25 steps (meaning that there are few).

Additionally, more advanced techniques should probably add a few points in the difficulty rating. I've seen a puzzle that was nothing but singles, then a Jellyfish, then nothing but singles to the end. Not what I would rate as easy, despite the large amount of singles.

Vidar
vidarino

Posts: 295
Joined: 02 January 2006

eclark's answer is on the nose. Further, difficulty is very subjective and dependant on the solving methods used and how they are implemented.
tso

Posts: 798
Joined: 22 June 2005

### Puzzle creation

On a related note, for my sins, I have been tasked to create some puzzles for our company newsletter. (As I am the 'computer guy', I am supposed to be an expert on everything and anything remotely mathematical).

Somebody here has a book of puzzles that are rated easy, medium, hard and fiendish and I have to create on these lines.

I am not, in any shape or form, a Sudoku expert. Can anybody help me by defining some rules that would allow me to create puzzles along the lines I have mentioned above.

Any and all help will receive my eternal gratitude.

Sincerely,
Kevin Bell
Thruster

Posts: 1
Joined: 08 February 2006

### Re: Puzzle creation

Thruster wrote:On a related note, for my sins, I have been tasked to create some puzzles for our company newsletter. (As I am the 'computer guy', I am supposed to be an expert on everything and anything remotely mathematical).

Somebody here has a book of puzzles that are rated easy, medium, hard and fiendish and I have to create on these lines.

I am not, in any shape or form, a Sudoku expert. Can anybody help me by defining some rules that would allow me to create puzzles along the lines I have mentioned above.

Any and all help will receive my eternal gratitude.

Sincerely,
Kevin Bell

http://www.websudoku.com/

Pick one on the right, and have at it.

In case anyone asks, and they prolly will, if you really doubt your skills, you could use an online solver to help provide an answer.

http://markbyers.com/sudoku/solve9x9

This one works reasonably well.

Enjoy, and keep away from sins....
Darth Tater

Posts: 6
Joined: 02 December 2005

### Re: Difficulty levels

newhere wrote:"..What are the characteristics that make a sudoku puzzle easy, medium or hard?"

Whilst there may be exceptions, I usually find the number of "clues" (given numbers) in a puzzle indicates the degree of difficulty. This seems to be supported by the minimum number of clues - I think it's 17 - which are considered necessary to solve a puzzle. Unless I'm missing something I would expect a puzzle is more difficult when identical clues are repeated within the boxes like this:
Code: Select all
` *-----------* |123|...|...| |...|123|...| |...|...|123| |---+---+---| |...|.12|3..| |...|...|.12| |---+---+---| |..1|2..|...| |...|..1|2..| |...|...|..1| *-----------*`

Cec
Cec

Posts: 1039
Joined: 16 June 2005

Thanks so much!
I'll see how I do in the 'medium difficulty' sudoku next week. Hopefully I'l l notice the things that you guys have mentioned.
newhere

Posts: 4
Joined: 06 February 2006

### Re: Difficulty levels

cecbevwr wrote:
newhere wrote:"..What are the characteristics that make a sudoku puzzle easy, medium or hard?"

Whilst there may be exceptions, I usually find the number of "clues" (given numbers) in a puzzle indicates the degree of difficulty. This seems to be supported by the minimum number of clues - I think it's 17 - which are considered necessary to solve a puzzle. Unless I'm missing something I would expect a puzzle is more difficult when identical clues are repeated within the boxes like this:
Code: Select all
` *-----------* |123|...|...| |...|123|...| |...|...|123| |---+---+---| |...|.12|3..| |...|...|.12| |---+---+---| |..1|2..|...| |...|..1|2..| |...|...|..1| *-----------*`

Cec

The number of clues has *no* correlation with the difficulty of the puzzle. There 17's that are trivial and 17s that are very difficult. A 17 chosen at random from the 36 thousand here is more likely to be easy than hard.

For example, this one requires nothing but singles. Pappocom rates it as Medium, but I'm sure I could find one it would rate as Easy.

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

Conversely, one might find the hardest part of a particular puzzle when it is 2/3's filled in. You could then consider this position as the starting point of a very difficult puzzle that has 54 givens.

As to your second point -- I doubt it.
tso

Posts: 798
Joined: 22 June 2005

See, I would have thought that it was all based on how many givens there are. Last week we had to "build our own sudoku". So I basically just filled one out (the professor already gave us few filled cells) and then I just started erasing some cells, making sure that there will only be one possible number that could go there. I was able to get it down to like 37 givens which is till pretty high. I figured that since I was giving so many givens, it must be an easy sudoku.
newhere

Posts: 4
Joined: 06 February 2006

If you want to reduce the number of clues you will have to consider other techniques apart from:
Naked Singles - where only 1 number can go in a cell in a certain block/row/column
&
Hidden Singles - where in a Block/row/column a certain number only appears once so has to go in that cell.

For more basic/intermediate level techniques check out here and here

For your average Fiendish Puzzle (~24-28 clues), the techniques that are required are:
Locked Candidates, Hidden/Naked Singles/Pairs/Triples.
Crazy Girl

Posts: 189
Joined: 08 November 2005

I have made a puzzle with 21 clues which only requires hidden and naked singles. Also some of these puzzles can be quite tricky, if at any given time there are only a few possibilities.
ab

Posts: 451
Joined: 06 September 2005

from what i hear it is based of what the author of the puzzle belives it to be. it is more subjective, at least that is what it is form the person who makes the sudokus in the paper i use.
Chessmaster

Posts: 191
Joined: 21 December 2005

### Re: Difficulty levels

cecbevwr wrote:
newhere wrote:"..What are the characteristics that make a sudoku puzzle easy, medium or hard?"

Whilst there may be exceptions, I usually find the number of "clues" (given numbers) in a puzzle indicates the degree of difficulty. This seems to be supported by the minimum number of clues - I think it's 17 - which are considered necessary to solve a puzzle. Unless I'm missing something I would expect a puzzle is more difficult when identical clues are repeated within the boxes like this:
Code: Select all
` *-----------* |123|...|...| |...|123|...| |...|...|123| |---+---+---| |.12|3..|...| |...|.12|3..| |...|...|.12| |---+---+---| |..1|2..|...| |...|..1|2..| |...|...|..1| *-----------*`

Cec

tso wrote:The number of clues has *no* correlation with the difficulty of the puzzle. There 17's that are trivial and 17s that are very difficult. A 17 chosen at random from the 36 thousand here is more likely to be easy than hard.

For example, this one requires nothing but singles. Pappocom rates it as Medium, but I'm sure I could find one it would rate as Easy.

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

Conversely, one might find the hardest part of a particular puzzle when it is 2/3's filled in. You could then consider this position as the starting point of a very difficult puzzle that has 54 givens.
As to your second point -- I doubt it.
tso

Having read your above comments, as I respectively always find are informative and interesting, I'm left in two minds whether to throw my theories "out the window" that fewer givens (clues) increases the difficulty level of solving sudokus. My uncertainty relates to the following and please feel free to further respond.

In my above puzzle grid (showing only digits 1, 2 & 3) and suggesting that such repeated identical clues increases the difficulty of a puzzle, Simple Sudoku seems to agree in only being able to place one "big number" ( a hidden single [2] in r9c1) and then no further hint available.

In your above example that requires nothing but singles to solve I note the givens include all the digits 1 to 9 and are presumably so placed, not intentionally, but nevertheless do achieve a simple solution on account of their convenient placement.

One point that continues to baffle me is that because 17 'givens' is regarded as the minimum to solve a puzzle as shown in previous threads such as this thread then it would seem logical (to me anyway) that puzzles having more givens should be easier to solve - with some exceptions as I previously mentioned.

Whilst I acknowledge that my sudoku knowledge is limited in comparison to more "talented" members, my own experience has generally revealed that the Pappocom puzzles designated "Easy" usually provide about double the number of givens for a puzzle designated "Difficult". I'm simply stating what I believe to be the "norm" but others can have a different view.

I would of course be interested to know what characteristics you believe make a sudoku puzzle easy, medium or hard.?

Cec
Last edited by Cec on Fri Feb 10, 2006 11:48 am, edited 1 time in total.
Cec

Posts: 1039
Joined: 16 June 2005

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