Difficult Games

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

Difficult Games

Hi everyone... I want to know many dufficult Sudoku Puzzles but to make things intresting i thought to do with the following way, so here are the rules:
-I will post a puzzle first and the person who will solve it first (and post the answer) will post the next puzzle that found difficult. That way i will have a good list
-The use of computers and programs to give solution are forbidden because it ruins the fun to other players. (If u are going to cheat dont play cause others try seriously)
-You CAN use programs to generate puzzles though (If so plz write dufficulty level/complexity/possiblesolutions if available)
-Difficult Puzzles are those who have many solutions (and need chains in order to be solved)
-The games will only be 9x9, [and if possible say the approximate time it took you to solve it if you want(I dont ask it for making players bragging but to know when to search 4 the next reply and when an average person will solve it)]
-Plz post the problem in an easy to read way
Thats all here it comes (It is the most difficult i have solved it took me more than an hour)

2XX|XXX|XXX
XX7|XX8|5XX
X5X|XXX|9X6
----------------
4XX|3X2|X65
3XX|X1X|4XX
XX6|XXX|XXX
----------------
X35|1XX|XX2
X1X|4X7|6XX
XXX|XXX|XX8

It has a total of 25 numbers and 972 possibible solutions (thats what computer says at least). You CANT solve it without chains of course.
Good luck and have fun.
Claw_gr

Posts: 9
Joined: 13 December 2005

Wrong

Well 942 wasnt posible solutions but compexity... I dont know the possible solutions But anyway if anyone solves it he can post the next
Claw_gr

Posts: 9
Joined: 13 December 2005

Claw_gr wrote:-Difficult Puzzles are those who have many solutions (and need chains in order to be solved)

Do you mean solutions or solving steps, Claw? Hopefully you mean steps otherwise no-one will be very interested.

This puzzle can be solved with chains, but it can be solved in a fraction of the time using the uniqueness principle – on r4c25 and r6c25 => r6c5 = 4.

Code: Select all
` *-----------------------------------------------------------------------------* | 2       468     3489    | 5679    4569    134569  | 13      178     147     | | 169     46      7       | 269     23469   8       | 5       123     134     | | 18      5       348     | 27      24      134     | 9       1278    6       | |-------------------------+-------------------------+-------------------------| | 4       79      1       | 3       79      2       | 8       6       5       | | 3       28      28      | 56      1       56      | 4       79      79      | | 5       79      6       | 8       479     49      | 2       13      13      | |-------------------------+-------------------------+-------------------------| | 689     3       5       | 1       689     69      | 7       4       2       | | 89      1       289     | 4       23589   7       | 6       359     39      | | 7       246     249     | 2569    2569    3569    | 13      159     8       | *-----------------------------------------------------------------------------* `

That’s the trouble with this forum – brainy people keep coming up with new solving methods – it’s hard to keep up!
emm

Posts: 987
Joined: 02 July 2005

basically i meant solving steps... I just confused complexity(=solving steps+logical reasoning) with possible solutions
Claw_gr

Posts: 9
Joined: 13 December 2005

Thanks for pointing out the uniqueness test, em. I almost decided to cheat....

So, with the solution:

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`2 8 9|5 6 1|3 7 46 4 7|9 3 8|5 2 11 5 3|7 2 4|9 8 6-----+-----+-----4 9 1|3 7 2|8 6 53 2 8|6 1 5|4 9 75 7 6|8 4 9|2 1 3-----+-----+-----9 3 5|1 8 6|7 4 28 1 2|4 5 7|6 3 97 6 4|2 9 3|1 5 8`

Come a new toughy from my collection:

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

Good luck with this one. Remember, no solver programs

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

Re: Difficult Games

Claw_gr wrote:-The use of computers and programs to give solution are forbidden because it ruins the fun to other players. (If u are going to cheat dont play cause others try seriously)

I sympathise with the intention, but .... If someone uses a solving program and simply rewords the solver output, how would you know?
r.e.s.

Posts: 337
Joined: 31 August 2005

Re: Difficult Games

r.e.s. wrote:I sympathise with the intention, but .... If someone uses a solving program and simply rewords the solver output, how would you know?
Well I cant tell but he doesnt gain anything by wasting his time and giving solutions...(He wont bother doing this 4 more than 1 time at least(except if he now wants to prove me wrong )) He wont do it all the time of course and i simply guess that since asked not to do it he will just view it... And thats why i ask for the time it took to someone to solve it also... I believe that people who arent interested will just pass-out. If they just want to solve it or see how difficult it actually is with computers they can but in fair way(=Not posting answer if cheated(= that apllies to solution only, seeing difficulty or if it worths trying it only and solving it after with pencil it is fair for me) which means they are interested in solving only and can simply w8 4 some1 else to answer). Well in both cases i Will know something, if his quiz isnt very complicated of course and if he replies too fast. (That means i check the puzzle b4 solving it actually because high complexity problem needs a lot of time generating it...(so he doesnt know anything good he just want to solve so he wont post). Well these are my thoughts but maybe the proof is that this topic that was posted today has many views but not many replies (that means nobody cheated (at least without trying first)). And if anyone isnt solving it after some time they can ask4 hints than cheating (like EM did actually and prevented cheating )
In anyway even if he cheats i will get a difficult puzzle if not i will just ignore it...
By the way the complexity of Rudd's puzzle is near 558 (its worth trying it)... Complexity lower than 150 means not actually very hard to generate but i dont think anyone will be interested to post these. (He will see the rules above about POSTING Difficult puzzles and pass) Soz 4 the long answer
Claw_gr

Posts: 9
Joined: 13 December 2005

Hi Claw, I don’t think anyone will cheat. The question is - will anyone play?

One complicating thing is that you specify solving by chains alone. There are different paths to any solution and there are new techniques that supersede chains. Susser solved Rudd’s puzzle (OK I did cheat a little but I’m not playing) in 34 moves using uniqueness, whereas you had it down for 558. So I think you’ll have to let go of the chains for one thing.

And even if you don’t get many replies, you can find good difficult puzzles for yourself – millions of them in fact – at this great website http://www.menneske.no/sudoku/eng/
emm

Posts: 987
Joined: 02 July 2005

I did the Ruud's puzzle and it took me less than 10 minutes to solve. even though I was an above-average scoring guy at math, it has never been my passion. I don't know if those 10 minutes represent a good or less than good timing, but with due respect, I failed to see any complexity in that puzzle. what puzzle me is that you guys come up with all sort of algorithms and try to rationalize what common sense can solve in a reasonable amount of time.

claw_gr are you the same guy as chp?
elf

Posts: 3
Joined: 15 December 2005

Hmm yeah thats right... At the start i thought that difficult games are for anyone but it depends on the solution methods anyone use... It is different for every person the way he use it as i see it and the steps are different... The program that counts complexity counts how many different methods can be used to solve it perhaps (My program is bad) but when i solved ruud's puzzle i stuck somewhere that could only be solved with x-wings or T&E... Well i hoped that there are not many other ways to solve them but know i understood that the priority of the methods someone use can make the steps smaller or different. To tell you the truth i hoped that there is a way to see the "priority" u sould use, before solving it (without computer) but it cant be done... Oh yeah and maths doesnt matter in this game all it matters is logic. thanks 4 that site... I was searching games that need a specific chain "in logic" to solve them but know i know it cant be done... Now i will search games who need T&E to solve and cannot be solved by any other method. (Computers cant generate those hopefully without a new method) if i find any of those i will post it. If anyone has a clue about where i can find those and all the known methods up to now,post them or pm me
Claw_gr

Posts: 9
Joined: 13 December 2005

Claw_gr wrote:Now i will search games who need T&E to solve and cannot be solved by any other method. (Computers cant generate those hopefully without a new method) if i find any of those i will post it. If anyone has a clue about where i can find those and all the known methods up to now,post them or pm me

The most comprehensive list of solving methods is at Sudoku Susser but you have to download the manual for explanations. Find it here - http://www.madoverlord.com/projects/sudoku.t . It’s free but you can make a donation! The manual explains all the techniques.

You sound like you’re not too interested in computer solvers but if you were to download one eg SS - it can make puzzles that require any method you choose. You can solve the puzzle yourself and/or get hints or get the solver to solve it for you and list the order of techniques it used.

I’m not sure what you mean by T&E - it covers a lot of things, I hope you don't mean guessing! I agree with you about Ruud’s puzzle – it’s not easy. If you're still there elf I’d be interested to know how you got past this point?

Code: Select all
`*-----------------------------------------------------------* | 3     1     7     | 4     58    258   | 6     9     28    | | 4     6     89    | 189   7     1289  | 23    5     238   | | 5     2     89    | 3     6     89    | 1     7     4     | |-------------------+-------------------+-------------------| | 6     39    5     | 7     39    4     | 8     2     1     | | 8     4     1     | 59    2     359   | 7     6     39    | | 7     39    2     | 6     18    18    | 39    4     5     | |-------------------+-------------------+-------------------| | 129   7     4     | 1289  138   6     | 5     38    29    | | 129   5     6     | 128   4     138   | 29    38    7     | | 29    8     3     | 259   59    7     | 4     1     6     | *-----------------------------------------------------------*`
emm

Posts: 987
Joined: 02 July 2005

What T&E is excactly

em wrote:I’m not sure what you mean by T&E - it covers a lot of things, I hope you don't mean guessing! I agree with you about Ruud’s puzzle – it’s not easy. If you're still there elf I’d be interested to know how you got past this point?

With T&E you can solve it only now... Look we say if r1c9= 2 (we will prove its not)<=>...<=> and i am sure u will end up that r5c9=9 and r6c7=9 which is imposible... (so its not 2 of course and the other and only candidate is 8). When i solved it i found more values and x-wings was possible but now i found this...
This is T&E and its non guessing...

Many people say its guess or similar but there are some differences...
We must start from something that its not the expected answer (to prove wrong... In that case we can easily prove that 2 cant be there actually)
If we say IF its 8 then => ... =>corect so its 8 then its guess... and its not T&E we prove that this is function and nothing more... WE didnt prove the possibility that it aint 2... we must also say if its 2 then => incorect so its 8
(because in logic the following sentences and the nature of => is like that
T=>T Correct
T=>F Incorrect (there must be a mistake in steps if we concluded like that
F=>T Correct!
F=>F Correct!
As you can see from something that is false we can either end up on false or correct results

but in this game its not only =>... Its <=> actually (the results can be reverted) so
F<=>T is incorrect actually (remember T=>F is incorect)
so we only use the F<=>F (which is correct always logically)
Thats T&E... I cant explain it better but if you check about differences of => and <=> and when we can say that the results are revertable (<=>) and not only => then you can figure it out yourself. But now the important thing is that because all the logical correct and there arent any other possibilities we can say that <=> is free to use for this game (sorry i dont know good english and describe it like that)
Claw_gr

Posts: 9
Joined: 13 December 2005

of course there might be a way to solve them with swordfish or T&E+X-Wing (two 8 in a row will remain in the same example i used T&E...) but those arent spoted easily... So when you are stuck and think that there isnt other method left use T&E... I think X-Wing and Swordfish are methods that are based on T&E, but i didnt found an explanation WHY they work somewhere... (Computer cannot aply T&E but can aply some "forms" of it like swordfish or x-wing). Anyway that was a good example for me and was intresting...
Claw_gr

Posts: 9
Joined: 13 December 2005

em wrote:I’d be interested to know how you got past this point?

Claw_gr wrote:Look we say if r1c9= 2 (we will prove its not)

Testing R1C9=2 is OK, but testing R1C5=8 is a little shorter. I'l use R1C9=2 anyway. These are the candidates:

Code: Select all
` *-----------------------------------------------------------*  | 3     1     7     | 4     58    258   | 6     9     28    |  | 4     6     89    | 189   7     1289  | 23    5     238   |  | 5     2     89    | 3     6     89    | 1     7     4     |  |-------------------+-------------------+-------------------|  | 6     39    5     | 7     39    4     | 8     2     1     |  | 8     4     1     | 59    2     359   | 7     6     39    |  | 7     39    2     | 6     18    18    | 39    4     5     |  |-------------------+-------------------+-------------------|  | 129   7     4     | 1289  138   6     | 5     38    29    |  | 129   5     6     | 128   4     138   | 29    38    7     |  | 29    8     3     | 259   59    7     | 4     1     6     |  *-----------------------------------------------------------*`

so, When R1C9=2:

-> box 3 completes: R2C7=3, R2C9=8
-> column 9 completes: R5C9=3, R7C9=9;
----> box 5: R5C6<>3 ==> R4C5=3
----> column 7 completes: R6C7=9, R8C7=2
-> R1C6<>2; naked pair in box 2, setting R2C4<>8, R2C6<>8, R3C6<>8;
----> column 3 completes: R3C3=8, R2C3=9
----> row 2 completes: R2C4=1, R2C6=2
----> column 6 completes: R5C6=5, R1C6=8, R6C6=1, R8C6=3
----> column 5 completes: R1C5=5, R6C5=8, R7C5=1, R9C5=9
-------> column 1 completes: R9C1=2

conflict in R7C9: All candidates (1,2,9) eliminated.

Code: Select all
` *-----------------------------------------------------------*  | 3     1     7     | 4     5-    --8   | 6     9    =2-    |  | 4     6     -9    | 1--   7     -2--  | -3    5     --8   |  | 5     2     8-    | 3     6     -9    | 1     7     4     |  |-------------------+-------------------+-------------------|  | 6     39    5     | 7     3-    4     | 8     2     1     |  | 8     4     1     | 59    2     -5-   | 7     6     3-    |  | 7     39    2     | 6     -8    1-    | -9    4     5     |  |-------------------+-------------------+-------------------|  |#---   7     4     | 1289  1--   6     | 5     38    -9    |  | 129   5     6     | 128   4     -3-   | 2-    38    7     |  | 2-    8     3     | 259   -9    7     | 4     1     6     |  *-----------------------------------------------------------*`

Amazing to see how testing a candidate in the right-top causes a conflict in the left-bottom, using almost the entire candidate grid. It took me longer than 10 minutes to work this out by hand. Did elf find a shorter path? Elf?

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

Ruud wrote:Testing R1C9=2 is OK, but testing R1C5=8 is a little shorter. Amazing to see how testing a candidate in the right-top causes a conflict in the left-bottom, using almost the entire candidate grid. It took me longer than 10 minutes to work this out by hand. Did elf find a shorter path? Elf?
Well But AS i explained you cant test 8 (Because you will end up correct and you prove nothing... (you prove only that u did correct logic to get these results nothing more.(You dont prove that these are finals results cause there is the possibility to be 2... (That is because you dont know if there are two solutions 4 this puzzle... except if you prove it that is only one first which is imposible )... So you must always start with something that is not correct and prove its wrong... Anyway i dont think elf solved it without cheating a little (coloring or filtering or swordfish) ,isnt that true elf? You cant possibly see all that by a glimpse... you need 5mins at least for that and only after reaching to that step. If you really solved it without a bit cheating in 10 mins then congradulations but i think its impossible
Claw_gr

Posts: 9
Joined: 13 December 2005

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