## Puzzle 200 (Nikoli Octathlon) [Unique]

Before I get to the rules and the puzzle itself, I’d like to say this first. I understand this puzzle is not for everyone, with some very complex rules and an absolutely enormous level of challenge. But if you’ve come here to enjoy puzzles, you would be missing out by avoiding this one. The solution to this puzzle is a sequence of pure logic, probably with more variety than almost any other grid-based logic puzzle there is, involving virtually no thinking ahead at all. I believe that anyone who perseveres to the end of this puzzle will feel very well rewarded for their efforts. Best of luck.

Now, puzzle 200:

This is a Sunday Nikoli Octathlon puzzle, a unique type. Eight different puzzles have been crunched together and interlocked in a cycle. Each puzzle’s clues are disguised somehow, and only by knowing the solution of the previous puzzle can you figure out the puzzle’s true state. Note that this “true state” may not be uniquely solvable itself, and it may be that you have to use constraints from the next puzzle in line to determine the solution. Detailed rules follow below the image.

Puzzle 200

Here is the same image, with some helpful extra grids and almost all of the rules written in brief notes outside the grids. Since these rules are kind of long and intimidating, you may wish to get started right away by using this image. The text is not comprehensive and not a full substitute, so you can use the rules below as a reference for the places where the image’s annotations are somewhat ambiguous. Thanks to Alan Curry for the idea of making the image, and also for testsolving the puzzle.

Akari (depends on Hitori, dependee of Shikaku)
See here for the rules to Akari.
The walls are not given to you in this puzzle. The black cells in the solution to the Hitori puzzle are exactly the locations of the walls. Any wall with a number represents a typical numeric clue in Akari. Any number without a wall is a fake clue and should be ignored. Light bulbs are allowed to be placed on top of fake numbers.

Shikaku (depends on Akari, dependee of Heyawake)
See here for the rules to Shikaku.
A lot of extra numbers are given in this puzzle. Overlay the light bulbs in the Akari solution on this puzzle. Only those numbers which have a lightbulb on top of them are true clues in this puzzle. All other numbers should be ignored; they may or may not denote the correct size of the rectangle that contains them.

Heyawake (depends on Shikaku, dependee of Nurikabe)
See here (flash) and here (better English) for the rules to Heyawake.
The rooms are not given to you in this puzzle. The rectangles in the solution to the Shikaku are where the rooms are. Only those numbers appearing in the top left cell of a room should be used as clues. All other numbers should be ignored.

Nurikabe, featuring Kurodoko (depends on Heyawake, dependee of Fillomino)
See here for the rules to Nurikabe. See here and here for the rules to Kurodoko (which is sometimes called Kuromasu).
A Nurikabe and a Kurodoko puzzle have been superimposed on each other. The solution to the Heyawake puzzle and the Kurodoko puzzle are identical. Each number in this puzzle is the location of a clue in both the Nurikabe and Kurodoko, and the number is the sum of the clues in each of the puzzles (i.e. if there is a Nurikabe 1 and a Kurodoko 6 in the same space, a 7 will appear in this puzzle).

Fillomino (depends on Nurikabe, dependee of Country Road)
See here for the rules to Fillomino.
A lot of extra numbers are given in this puzzle. Overlay the Nurikabe solution on this puzzle. All numbers covered by a black cell in the Nurikabe solution are liars and are not the correct number. All numbers covered by white cells are truth-tellers.

Country Road (depends on Fillomino, dependee of Corral)
See here for the rules to Country Road.
The rooms are not given to you in this puzzle. Overlay the Fillomino solution; it gives the shape of all of the rooms. Each room will contain no number or one number, which functions as a standard Country Road clue for that room. The number can appear in anywhere in the room.

Corral, featuring Masyu (depends on Country Road, dependee of Hitori)
See here for the rules to Corral. See here for the rules to Masyu.
The grid is filled with Corral clues in black or white circles, but not all of the Corral clues are correct. Overlay the solution to the Country Road puzzle on this one. Cross off all of the circled numbers for which that colored circle would not be a valid Masyu clue in the Country Road solution. All of the numbers that are left are the clues to the Corral puzzle. (the numbers that are crossed off may or may not be correct)

Hitori, featuring Slitherlink (depends on Corral, dependee of Akari)
See here (flash) and here (better English) for the rules to Hitori. See here for the rules to Slitherlink.
A Hitori and a Slitherlink puzzle have been superimposed on each other. The solution to the Corral puzzle and the Slitherlink puzzle are identical. The Slitherlink puzzle gives a number in every square, just as the Hitori does. All of the Hitori clues are numbers from 1 to 10. Each number that appears in this puzzle is the units digit of the sum of the Hitori and Slitherlink clues. For instance, in a space where the Slitherlink has a 3 and the Hitori has an 8, a 1 would be written in this puzzle.

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### 26 Responses to “Puzzle 200 (Nikoli Octathlon) [Unique]”

1. motris Says:

In the midst of this. Since I saw your country road rules are different than I’m used to I wanted to check that your region numbering goes as I’m expecting. Namely, is the number in a region always in the leftmost cell of the topmost row in which any region appears?

2. MellowMelon Says:

No, that’s not necessarily the case here. The number can appear in any square, but there can only be one. Clarified above.

3. motris Says:

Thanks – I’ve now proved it to myself but its good to have the clarifying note since otherwise it can be used as a break-in. Loving it so far.

4. motris Says:

Finished this tonight after working off and on since yesterday. I certainly had a mistake or two percolating in the set while solving, and had almost the right corral for a long time (it seemed super reasonable all around but had one major thing wrong) but could reverse out the mistakes by working down the line for where it needed adjustment. It did take a couple copies of the puzzle though.

It really is an impressive (and impressively hard) construction, and the choice of how puzzles flow into each other really well done. The “blow-out” extra notes sheet is certainly the one to solve on and this success of formatting was good foresight on your part. The only thing I found myself doing was adding one more 10×10 empty grid to actually solve the fillomino in since writing over the existing numbers was more difficult than desired. Anyway, thanks for sharing this fun challenge.

5. MellowMelon Says:

The annotated grid was good foresight on Alan Curry’s part, as opposed to mine.

I figured a WPC expert would be able to knock this one out without tremendous trouble, since the rules and solving style seemed to be fairly close to that. Thanks for the comment, and glad you enjoyed the puzzle. Easily replaces 100 as my personal favorite… it’s ridiculous how many tricks one can pull off with rules like these.

6. motris Says:

Its certainly a style of puzzle done in the WPC frequently (recent years have had combinations where you got “pieces” that assembled to make 5 different puzzle types, and you needed to think about how one puzzle type solves versus another to finish it, or got a bunch of grids and a set of potential rules for puzzles on them and had to figure out what went with what). I actually like this octathlon (I’d argue nonathlon with the kurodoko) style more than those as it really does have a lot of opportunities for forward and backward thinking between the grids and as I said the choice of what puzzles to go into the next grid always felt natural and well-planned so indeed this is a great feat of puzzle construction.

7. Anon Says:

In country roads, are you using the restriction that each box must be visited?

• MellowMelon Says:

No, none of my Country Road puzzles use that rule after I accidentally omitted it in earlier constructions and made some puzzles that rely heavily on that not having to be the case. I think the possibilities are much greater without that rule. The fact that this rule doesn’t apply here should be clear from the fact that there’s a 0 in the grid.

8. aclayton Says:

Wow! Like your great Country Road #21 puzzle, I carried this one around in my back pocket for a few days, pulling it out whenever I had a few spare minutes to solve.

Even with having a lot of experience solving each individual puzzle type (like most here I’m sure), I found the interactions between them revealed some surprising new techniques and aspects of each puzzle.. And along the way I could tell I was on the ‘intended path’, every time I got stuck for a while and finally found a break or new technique, it was obviously placed on purpose.. This is something I really appreciate about your puzzles, most seem to have a clear idea or theme that is communicated well to solvers.

A great accomplishment, and a rarity in that when I was done, I looked forward to revisiting and solving it again someday.. I was expecting and hoping for more of an explosion of comments on this one, perhaps some are still working through it. π Thanks again for all the amazing puzzles!

(btw I agree with your dropping the ‘visit every room’ rule in Country Road; I was introduced to this type by the puzzles here, and I don’t see what adding that rule would really contribute, aside from being unnecessarily restrictive construction-wise)

• MellowMelon Says:

I did suspect there would not be a comment explosion on this one, mostly because all of the super hard puzzles posted here didn’t have them even if they were the best thing I had put out by far (100 for instance). I think there are two reasons for this: that some people don’t bother with any of the nightmarishly hard puzzles I post because they get frustrated with them, and others who do wait for a large block of free time to sit down and work on it. I personally do the latter with a lot of puzzles on other sites including mathgrant’s 31x45s and nikoli.com time trials, and evidently you did the same here too. But a puzzle like 183 or 199 on the other hand is something you can sit down and work on right away, and it still can leave a very distinct impression. Those are the ones that I notice tend to get more discussion, at least immediately.

Alan Curry, who test-solved the puzzle, gave me a detailed description of his steps (apparently partly so he could trace back any mistakes he made) and they matched the intended solution perfectly until the cleanup at the end. I had no idea this would happen, and when it did I knew this was without a doubt the best puzzle I had constructed to this point. So I knew when this puzzle was published that people would be following the path I had laid down. All the better here because that path contains all sorts of craziness I wouldn’t want anyone to miss.

As you’ve noticed I do try really hard to use a particular idea or theme in a puzzle. Long ago my rule of thumb was to make sure that no one would suspect the puzzle was computer-generated. Nowadays I think of a puzzle like that as at worst a “good” human-made puzzle, but the ones I put out today I always try to make “great”. I think there’s a visible difference between the quality of my recent puzzles and the ones before 75 or so that indicate this. Although a lot of the early puzzles are stuff I’d be embarassed to put out today, I like the idea of having a record of how far I’ve come in construction. And of course some of the early ones, like 21, turned out incredibly well despite my inexperience at the time.

Thanks a bunch for the comment, and I hope you continue to enjoy the work I put up here.

On the parenthetical note: One potential advantage I can see in the Country Road “forced visit” rule is for entrance/exit counting logic, because it establishes that every room has to have exactly two exits. But whenever I want to pull off logic like that I make a Double Back puzzle, which can do that kind of logic and other things so much better. Placed next to Double Back, the beauty of Country Road comes more from the rule that one of two adjacent squares in different rooms must be visited, and that rule is made much more powerful by allowing unvisited rooms.

9. Nix Says:

After being totally hooked on your puzzles and solving all 265 in reverse order after finding them a month ago, I decided to drop a comment on the one I enjoyed the most. Now there’s heaps of brilliant puzzles competing for that title and the Two-Faced Yajilin (114) was almost taking the honor, but this has to be the most memorable one.

This had easily the greatest amount of enjoyment in a single puzzle, if it even can be called a single puzzle. That’s even with the painful number lookup+arithmetic of Slitherlink–Hitori, which I had to repeat too (along with the neighboring areas) after making the only deep error of the puzzle which thankfully didn’t spread all around. Some subsets of this puzzle type combination idea, especially in the Heyawake-Nurikabe/Kurodoko-Fillomino-Country Road axis could easily stand on their own and make for great regular puzzle types as well. Though maybe they would be a pain to construct to this quality.

All your puzzles have been enjoyable, but I just love all the special variations. I totally wish you made more of them, even more puzzles of the same variation; too many great ideas you’ve left with a single unique example. To mention some of the very best in numerical order: All Threes Slitherlink (86; 199 too in its own way), Crossways Yajilin (141), Pairs Nurikabe (162), Nonconsecutive Fillomino (183), Where is Black Cells? Masyu (190), Minefield Double Back (192), Alternator Double Back (226), and the Swapped Slitherlink (253). Next in line: 120, 132, 135 and 163. From non-specials, the hellish Akari EX 189 springs to mind. I may have missed some of the best in the newer puzzles due to solving them the longest ago. Also, puzzles with one great idea aren’t remembered as well as ones that were nice and fresh all the way, as well as identifiable with the type for the unique ones.

Most of the Liars Slitherlinks have been great as well, as well as Numerical Stairs and Castle Walls as whole types. Not to ignore the great things you’ve done with the Nikoli types, but your new puzzle ideas have been wonderful.

Thank you so much for the best month of puzzling I’ve ever had! Shame your extensive collection had to go so quickly, but I just couldn’t help myself with the addiction. I’ll be solving many of the best again.

• MellowMelon Says:

Thanks for the comment. Congratulations on doing all 265, in one month even; that’s a pretty major accomplishment. Thanks a bunch for mentioning your favorites too, which will help me figure out what to construct for this blog next (once I finish current projects). I’ll be sure to revisit some of the special variations you mentioned.

I’m not the least bit surprised to hear that 200 trumped all of the others, as I also consider it far and away my best (although, like you, I also find the Slitherlink-Hitori a bit irritating). I am surprised to hear 114 was up there, which in my opinion was good but not outstanding. 100 would probably be my personal second favorite.

In my personal opinion virtually all the puzzles somewhere around 190 and beyond exceed the quality of most of the ones before it, so I would guess there are at least a few recent ones that could be added to your list, although your lack of mentioning them may be because I haven’t been doing “Extra Variation”s as much recently as with the 2xx puzzles.

• Nix Says:

I’m not sure why I liked 114 so much. It’s probably far from the best in a kind of objective quality, and especially suffers for having multiple places to enter and solving much of the way both left-to-right and right-to-left but the other one much stickier. I solved it the easier way after messing it up going the harder way. Still I happened to like solving it very much. Maybe I was just having a good day.

From the marathons, I liked solving every one more than 100. In “quality” 100 could well be better than the others though. I guess I have solved too many hard Akari before, therefore failing to find any tricks novel enough and it feeling more like work than other types.

Same goes for me generally devaluing Slitherlink because it feels like I’ve seen it all. I’m even surprised that you consider 5 so hard; I found it nothing compared to the hard puzzles of other types. Shading the inside and outside of the loop and looking at it in colors more than fences helps for the hard ones. Any variations obviously always spice things up nicely. The easiest Colorlink (except the well separated one) took easily more staring from me than #5. But Crosslinks also seem easy, near enough to classic.

10. David Says:

With the slew of new puzzles over the past month-and-a-half (or thereabouts), I’m back to having more than 50 puzzles to solve. Sigh. Must remember to make a start on this (and #300) tonight.

I’m actually surprised, considering their presence in this puzzle, that you haven’t done more Kurodoko, Hitori, or Shikaku.

I sort of agree with Nix — with how few exploitable tricks there are in Akari, 100 felt (certainly towards the end at least) as though it was less of a challenge and more “let’s get this done and move on”. Was a nice puzzle, but being a bit smaller (whether 50×50 like #50 or even something like 75×75) would have made the tricks used stand out a bit more. Admittedly, I’ve only actually sat down and finished two of the six marathon/unique puzzles, but #250 felt more original than #100 did.

There are a few genres that feel as though everything you can possibly do with them has already been done — in addition to Nix’s Akari and Slitherlink, I’d also add Sudoku (heck, every possible step you can use in it has a lame nickname) and Kakuro to the list, but thankfully you haven’t gone down those paths yet. There’s probably a few minor tricks left in basic Slitherlink, but it seems increasingly likely that variations are the only real ways to make the four genres have any degree of originality. (And even then, Akari and Kakuro only have one, maybe two, possible variations that could recur.)

And Numerical Stairs are indeed f**king awesome. (Endless Labyrinth too.)

• MellowMelon Says:

I can’t argue with Akari, Slitherlink, Sudoku, and Kakuro being somewhat saturated in terms of new logical tricks. Of course, there’s probably lots of room left for doing clever things with the flow or aesthetics, but as you certainly know that’s not as much my thing. You’ve basically nailed the reason I rarely publish anything vanilla in those types these days.

I think a big part of the drudge feeling on 100 comes from the tedium any Akari has when done on paper or in MSPaint or whatever (it probably feels worse for a puzzle that size). If I could have provided an applet or something to do automatic bulb lighting, I think it might have been a bit more entertaining.

Shikaku is something that will probably get posted. Kurodoko maybe, but I have toyed around with it before and had a tough time coming up with something I liked. Hitori? No. Figuring out how to fill the grid with numbers in this puzzle after all the logic was placed was such a pain in the ass that I can still remember it being a pain in the ass. Out of Sight was intended to be my own version of it anyway, as many people have valid beef with Hitori as a type.

11. David Says:

Agreed. I’d rather a standard puzzle with an interesting solving trick than a beautiful puzzle that solves the same way any other puzzle would, which I would in turn prefer to a Hitori.

Yeah, the shading was a huge issue with #100 — especially when I decided to solve on the smaller grid. π

12. Giovanni P. Says:

Okay, so I saw the next step to this one the other day after not working on 200 for a while, and I ended up making a bit of progress before hitting a snag.

I just had one question before I proceeded; I hope you don’t mind, as I’m trying to avoid another mistake and figure out where I went wrong. If a clue in the Fillomino is found to have a wrong value, does that automatically mean the same space in the Nurikabe will have a black square? In other words, is the reverse situation of what the rules state (all fillomino clues covered by shaded squares are liars) necessarily true?

• MellowMelon Says:

As soon as you deduce a Fillomino clue is a liar, the corresponding Nurikabe space is black. The relationship between cells in Fillomino and Nurikabe goes both ways.

• Giovanni P. Says:

Thanks for clearing that up. I realized that you had accounted for that when writing the puzzle after your message. Loving it so far, although I might be e-mailing you soon to check I haven’t fallen off the path.

13. Laura Says:

I’m really enjoying this puzzle even though I’m barely making inroads on it. I can’t find an entry point on — basically the left half, and I think that’s what’s keeping me stuck. But I love this sort of dependent puzzle, and I’ve never seen one using so many different types. well done, and thank you!

• Laura Says:

By the by, greetings from a Scrippsie (alum)! And where in the name of sanity do you find the time to do these things with a Mudd courseload?! π

• MellowMelon Says:

Glad to see a new name. Having to keep up with Mudd’s classes and making one of these everyday didn’t leave a lot of hours in the day, but that was fine with me since making these is something I really enjoy doing. I don’t post stuff daily anymore, of course. One reason was to make time for other pursuits, like making puzzles to be used in places other than my blog.

Here’s a hint for getting started on this one (decode at http://www.rot13.com/): URLNJNXRGBCYRSG
Good luck; this is one of the toughest puzzles this blog has to offer, and that’s really saying something.

14. Bram Says:

I’m almost ready to stop trying this one. I can’t seem to not make a mistake and run into an impossibility. And of course it’s impossible to track back where the mistake lies, so constantly have to restart.
I already managed to track back a few dumb mistakes (like starting with the assumption that every heyawake cage would have a clue number in it or adding instead of subtracting slitherlink clues)
I think my main mistake probably lies in making wrong conclusions in counterclockwise grid interactions.

15. Scott Handelman Says:

My white whale has finally been defeated! I’ve been putting this one off, but finally gave this one a go. It took me the better part of a day, and I was very scared I had made an error at one point, but I got through it cleanly. Phew.