The New Sudoku Players' Forum

[tso]

Puzzle in question:

Code: Select all

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

Pappocom rated HARD
Tactics other than naked and hidden singles required:
Locked Candidates -- seven times
Naked Triples -- Twice

After all naked and hidden singles filled:

Code: Select all

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

{37}    {9}     {8}     {6}     {1}     {2}     {37}    {4}     {5}     
{5}     {6}     {2}     {3}     {48}    {478}   {179}   {178}   {789}   
{347}   {17}    {134}   {478}   {5}     {9}     {1237}  {13678} {2678} 
{2489}  {258}   {459}   {478}   {2348}  {34578} {6}     {378}   {1}     
{248}   {3}     {6}     {1478}  {248}   {1478}  {5}     {9}     {2478} 
{1}     {258}   {7}     {9}     {6}     {3458}  {23}    {38}    {248}   
{36789} {1578}  {1359}  {2}     {3489}  {1348}  {179}   {167}   {679}   
{2789}  {1278}  {19}    {18}    {89}    {6}     {4}     {5}     {3}     
{369}   {4}     {139}   {5}     {7}     {13}    {8}     {2}     {69}   

Number of empty cells when first candidate elimination is used: 48
Number of cells at this point with 4 or 5 candidates: a buttload.
Chances that a paper-only solver doesn't like putting more than 4 candidates in a cell: a whole lot.

Randomly generated Pappocom HARD for comparison:

Code: Select all

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

Tactics other than naked and hidden singles required: NONE
Pencil marks not required at all.

Randomly generated Pappocom VERY HARD:

Code: Select all

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

Tactics other than naked and hidden singles required:
Naked Pair -- Twice
Locked Candidates -- Once
X-wings -- Once
An expert *might* be able to solve this without pencil marks.

After all naked and hidden singles filled:

Code: Select all

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

{6}    {4}    {1}    {237}  {8}    {23}   {3579} {37}   {59}   
{3}    {7}    {9}    {1}    {6}    {5}    {4}    {2}    {8}   
{5}    {8}    {2}    {37}   {4}    {9}    {37}   {1}    {6}   
{8}    {6}    {4}    {235}  {1}    {7}    {35}   {9}    {25}   
{2}    {5}    {3}    {4}    {9}    {8}    {1}    {6}    {7}   
{1}    {9}    {7}    {6}    {35}   {23}   {8}    {34}   {245} 
{7}    {3}    {8}    {9}    {2}    {14}   {6}    {5}    {14}   
{9}    {1}    {56}   {8}    {57}   {46}   {2}    {47}   {3}   
{4}    {2}    {56}   {357}  {357}  {136}  {79}   {8}    {19} 

Number of empty cells when first candidate elimination is used: 26
Number of cells at this point with 4 or 5 candidates: ONE
Number of cells at this point with 3 candidates: A few.

[lunababy_moonchild]

I take it you were referring to me there Luna, I hoped I wasn't being too bad. Just another one of those straws, I guess.

No, actually, I was referring to the 'group' (think that's the collective word) as a whole - otherwise I'd have named you, in quotes, like I'm doing just now. I thought your particular post was very funny though (and not at all bad).

Someone is going to have to write a newbie gateway thingy.

I've been thinking of suggesting this myself, some kind of Rules of Conduct, but given the total lack of reading before posting that goes on is it worth it? Or are you meaning some kind of 'you can't get into the Forum until you've read the 'how not to be annoying' rules'?

Maybe we should have a competition for the best one?

Ah yes, indeed. An impossibly hard sudoku to the best one.

As for pencil marks - getting back on topic - how can it not occur to anybody to use them? Reading somewhat on on the subject I find that Mick Huckvale's top tip for solving any sudoku of any difficulty in 15 minutes or less is to write in all candidates for all cells. Also mentioned in the ten solving tips at the front of the Guardian's book, although I will say that they don't recommend it.

Or is it only me that reads on the subject?

Luna

[dukuso]

I don't understand why people aren' using photocopying machines
or cameras or blueprints to solve the hard puzzles.
How do they keep track of the bifurcations when walking
through the search tree ?

[lunababy_moonchild]

I don't understand why people aren' using photocopying machines
or cameras or blueprints to solve the hard puzzles.
How do they keep track of the bifurcations when walking
through the search tree ?

I don't know, which is why I don't use them, I find it too confusing.

Although I have been known to use the odd pencil mark here and there.

Luna

[simes]

I don't understand why people aren' using photocopying machines or cameras or blueprints to solve the hard puzzles.
How do they keep track of the bifurcations when walking through the search tree ?

Or perhaps it's because the puzzles don't require any bifurcation?

S

[Karyobin]

Yaay! He's back - only a PM this time, seems quite annoyed as well, can't be angry with him/her about that though. Now can anybody out there explain what this is about?...

I waited a few days before answering your post so that you had time to get your foot out of your mouth.

In reference to your statement, "... 'True' logic? What on earth are you talking about? Are you saying that every computing and mathematics student/graduate who frequents this site (not to mention all the highly experienced experts who have been solving puzzles for years) has not used logic when solving their sudoku?

I have been doing these puzzles for almot seven years and back when I started the were called "NUMBERS" in Europe and had a great following.
For two years I even created puzzles for two English papers.

Which papers?

Then you wrote "... You clearly have no idea what a Naked Triple is, or what it implies in the context of a puzzle. This particular Naked Triple tells you exactly where the values 1, 8 and 9 can be in that particular row, no more, no less. This knowledge can then be used to remove candidates from other cells in that row.

When I refered to the Naked Triple I assumed that even a dummy such as you would understand that just about all of us know exactly how they are used. Some puzzles have more than one set that reflect on each of the others and it is here that the guessing game is used.

Guessing game?

Just for informational puposes only I have two degrees in Mathematics and I taught Mathematics for seven years from the Basic through the Caculus.

Now if you would just stop and think a while why don't you show me how to arrive at the next step of the puzzle I posted. The last step was #49. and it woul seem that step 48 is either where the 2 and 7 go in row H.
As you must have noticed there are several answers on just where the 4 goes in Row B as there are 3 distinct possibilities but as yet nobody has shown how to place it, and where, but only state that the 4 HAS TO GO in a specific spot without giving the reason.

Y'see, I'm not sure what #48/#49 actually are! tso asked for the puzzle to be posted at the stuck point, and to me this is with about 33 cells complete. Apparently there are then three places for a '4' in 'Row B' - not in my book there ain't. It' early, I'm hungover and SOMEONE IS MESSING WITH MY HEAD!

[emm]

All that space you're using up! - apologies to Coldplay - why do we have such big quotes from the last person? We've already read that once.

[Karyobin]

That's what he sent me. In each of the quotes there's my earlier missive, preceded/followed by Smart3's brutal and cutting retort.

The mystery of Smart3 continues, though I think the 'guessing game' comment sheds a deal of light on the situation.

[Edit, for the second time: In response to a well-made point, I posted the entire PM above, not just bits that I could attack or that made it in any way appear biased, and Nick70 - I hope that your explanation meets with more open ears than my earlier attempt did! As a friend of mine frequently says "There's those that know, there's those that don't know, and there's those that don't know they don't know."]

[emm]

Ah- I see! The anonymity of the net can be conducive to rudeness. Nuke him.

[PaulIQ164]

You know, when I've finished my maths degree, I now think it'd be a good idea to go and do another maths degree. Maybe then I too will be able to teach mathematics, from the Basic to the Calculus.

[lunababy_moonchild]

I'm still waiting for an explanation of 'true logic'.

*Sigh* Maybe somebody with a maths degree .......................................


Luna

[Nick70]

I have studied the puzzle carefully, and I think the following is the easiest way to solve it.

Code: Select all

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

After the initial easy placements:

Code: Select all

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

Now:
- 1 must be in either r3c2 or r3c3.
- because of this, in col 7, 1 and 9 can only go in r2c7 and r7c7, so they must occupy both cells.
- this means that 7 can only be in r1c7 or r3c7.
- in either case, in row 2 the only place where 7 can be is r2c6. Put it there.

It's easy after this.

[udosuk]

Nick70's line of reasoning is perfectly right, and reduces the whole solving process to 1 difficult step... but unfortunately I think Mr. smart3 still will not consider it as "logic". My guess is his interpretation of the word "logic" means only "1-step logic" or "logic without pencilmarks" i.e. naked/hidden singles... which you don't need to mentally "look ahead".

Nick70's step could be broken up in 4 mini-steps, so is 4-step logic:
1. Locked candidate (1) in row 3/box 1.
2. Hidden pair (1,9) in column 7.
3. Locked candidate (7) in box 3/column 7.
4. Hidden single (7) in row 2.

To all who couldn't understand why some people only want 1-step logic, try to do a sudoku puzzle on paper without using pencil mark at all, or use angusj's simple sudoku software and toggle Ctrl-w to disable the showing of candidates. Then try solving it without pressing F7 or F11 i.e. "next hints" at all. So input only, never eliminate.

Although I could understand the aforementioned group's view of point, personally I still prefer puzzles which require more advanced techniques, even nishios/forcing chains or even backtracking, because if all puzzles are 1-step logic then sudoku will become a very boring kids' game and lose it's popularity soon (IMHO).

I'm totally into Killer's sudoku now and after solving a lot of them I must say candidate elimination/pencilmark logic/multi-step mentally lookahead is the only way to do those, so Mr. smart3 surely will not want them. In some of them you must even go to T&E/backtracking several times. For example try the infamous Sept 27 daily killer sudoku from djape's site: http://www.djape.net (click on "puzzle archive" under the link section).

Yeah, I know. But I tend to look for Naked stuff before Hidden stuff. Probably a personality thing.

I think a lot depends on whether you are a candidate eliminator having put in all possibilities or a candidate inputter.

Thassit!! Zigackly! (Ooops, Stella-pixie in the building) I'm by nature an inputter, not an eliminator. I just dubbed the original into Simple Sudoku, then played with what angusj gave me. Must admit I didn't see the {2,7} pair until I'd spotted the triple, but I like to think I'd have seen it if I'd done all the leg work myself.

From what I read here I think Karyobin is in fact more a candidate eliminator by nature rather than an inputter... not that I think any particular one is better than the other. Because in most cases an inputter is bound to find the "Hidden stuff" more easily than the "Naked stuff".

[Karyobin]

Yes, well spotted. Didn't see my earlier contradiction there. To explain further:

1. Your description is lovely and I will quote it at will from now on.

2. I meant inputter/eliminator in a much lesser sense, i.e. in newspaper puzzles I prefer to input the candidates (only when absolutely stuck) as forward-thinkingly (?!) as possible, then eliminate, and I do the same on computer to puzzles of comparable difficulty. The reason being that hidden stuff very often isn't when you go through the process of careful analysis yourself, rather than asking for candidates to be shown automatically. Hence my rather shallow use of the word inputter. I only become an eliminator when solving puzzles of the difficulty thrown up by Simple Sudoku, in which case I invariably ask for candidates to be shown - I mean, it's not like they're not already hard enough, is it?

I'm totally into Killer's sudoku now and after solving a lot of them I must say candidate elimination/pencilmark logic/multi-step mentally lookahead is the only way to do those

Oddly, I disagree. On the one hand I too am gripped by the 'Killer' bug and because of the non-arbritrary relationship of the correct cell entries, I find it much easier to hold possible combinations in mind when tackling 'Killer' than when tackling normal sudoku. I hardly ever use pencil marks, and certainly not on the ones in the paper (apart from those five back at the beginning!)

[Nick70]

"logic without pencilmarks"

I'd like to point out that I attempted to give a solution that didn't need use of pencilmarks. Surely the logic steps can be followed without need for them-however whether they could be noticed without putting any pencilmark on the grid is open for debate.

There is a line of reasoning that can lead on the right track.

Code: Select all

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

Box 2 is almost full, row 2 in box 1 is full, so that's the obvious candidate for attack.
Looking in boxes 5 and 8, the only digit not present in box 2 is the 7 in box 8. This leaves r3c4 and r2c6 as possibilities. To place the 7 taking advantage of box 1, one would want to show that in box 3 the 7 cannot be in row 2.
To take advantage of the 7 in row 6, one would need to look at column 7, showing that 7 cannot be in r2c7 and r7c7.
That can be done with a hidden pair. Looking at box 9, the 4 unused digits are 1 6 7 9, but 7 is the one we want to rule out, and 6 is already in col 7, so 1 and 9 are the only ones we can use.
The hidden pair is already almost working, but it's missing a 1 in row 3 outside of r3c7-which luckily we get thanks to the 1 in r6c1.

Because in most cases an inputter is bound to find the "Hidden stuff" more easily than the "Naked stuff".

This is something I was thinking about earlier today. When working without pencilmarks, hidden stuff is easier to see than naked stuff.
When looking for singles, I look for hidden singles in a box, then in a row/col-only as a last resort I look for naked singles. To find a hidden single you only need to focus on a digit and crisscross what's on the grid. To find a naked single you need to look for all other 8 digits, so it takes longer.

The same thing happens with hidden and naked pairs. When solving without pencilmarks, hidden pairs are just easier to see.