Author round-table 013

InterviewsAuthor round-table

Talking about hard problems and all the heartache they cause

The theme this time is hard problems. We hope that both people who like hard problems and also people who are weak at hard problems will read and listen along. Our guests this time are T.Karino and Miya. They make hard problems a lot. From Nikoli we have NyanBaz and Nob.

NyanBazYou always make hard problems. Do you like solving hard problems?

T.KarinoIf I am told to choose between easy and hard problems, I'll choose a hard problem. But actually, I like making easy problems too.


T.KarinoWhen I make a hard problem I'm sometimes surprised at how difficult an advanced method is. In an easy problem no such thing occurs, ever.

NyanBazYou like new discoveries. Are you the same, Miya?

MiyaI like hard problems, too. In particular, I like to solve hard problems. Recently I don't pay so much attention to difficulty when I make a problem. Previously, I made problems that were as difficult as I could think up.

NobThat's why we invited you to be here today.

MiyaHowever, that was in the old days. When I was a high school student. After that I didn't aim for difficulty. I aim at a problem you have to think about with your head. I want to convey that impression when you notice it.

T.KarinoI make puzzles without thinking about that kind of thing. It makes me aware that I am not nice really. I lack consideration.

NobI don't think so. Do you want to tell the method that you discovered to solvers?

T.KarinoYes I'll do that, but I sometimes give up on it. (laughs) When I read interviews or round-table talks with other authors, I feel that every other author has got it right, they're totally enlightened.


T.KarinoBut me I'm not enlightened like that yet. I give up when I think that it is difficult to tell about what I do. I'm wrong of course. I must think of how to explain things so it becomes more understandable. But I'm not quite up to it I think.

NyanBazYou are really conscious of what the solvers are up against. How about you, Miya?

MiyaSure, I'm conscious of the solvers.

NyanBazBack to hard problems, there are several types of hard problems.

MiyaSomebody has said it before, but generally speaking hard problems come in three kinds. One where it is hard because you have to think about the solution by inference. Another one is those which require trial and error. And the last one is where it is just hard to find the solution simply. The three kinds get twisted up in real problems though, so when a problem appears in some actual situation, I can't identify what kind it is. I have the most esteem for inferencing among the three. And I think that Nikoli feels the same way really. But for example, you can try to make a problem hard and put an unnecessary number, and that does it. Hitori puts in unnecessary numbers that are difficult to catch. Then the puzzle advances in a direction that is hard to follow. Because I like inferencing, I arrange numbers so that solvers can easily catch on about that.

NyanBazThat was well put.

T.KarinoI wonder if, related to what you just said, there are problems where, as you are solving them it all gets narrowed down, and then the options start to multiply again.

NobYou mean a problem that can not be solved unless you notice some point in one place?

T.KarinoJust that. I feel things like that are difficult. But there the evaluation standards with Nikoli don't considered that point very much.

NobWell. When the problem uses only easy methods but it's hard to find this point, we can't really evaluate it as a hard problem. Basically we evaluate difficulty from the difficulty of the used method. A problem that is solved only by easy methods is easy.

T.KarinoBut it would be really difficult to confirm whether a problem is solved only with easy methods. When I solve Sudoku, I use hard methods without giving it much thought.

NobSure. There is no way to judge difficulty unless I check whether I solved it without using a difficult method. We evaluate Sudoku as easy if we can finish solving it with only easy methods. When we can't solve by easy methods alone, we use intermediate methods. That's how we assign difficulty.

MiyaAhaa, then it would be awkward if you assign a problem to be solved only by easy methods as hard.

T.KarinoBut you actually do that. Not always easy to get it right.

NyanBazIt is one thing to judge difficulty, and another to think about enjoying solving.

NobEven when there is a cell where some rule would solve everything, and I keep thinking but miss the place where I should have been looking for the way ahead.

NyanBazLet's return to the story of classification as hard. Do you also think that this way to classify is right T.Karino?

T.KarinoYes, I may disagree on little things, but yes I think it is all right really. Trial and error is a way of thinking that supposes some cell to be some way for the moment, and if not there is another way ahead, that's what you are saying isn't it?

NobMore or less. It's the sort of thing we are not really recommending. There are very troublesome problems related to that. For example, I try one of two options and keep going till the end when it fails, then I have to go back to the start, and as a result it becomes very very troublesome.

MiyaI'd want to try to look over such a problem real closely. It's ultimately trial and error. (laughs) Of course that's very different from how we are supposed to be enjoying puzzles with Nikoli.

NyanBazI sometimes feel disagreeable about this trial and error of alternatives. If I choose the right way ahead by chance, and it can be solved till the end, then because I have a solution it's OK but should I really also test the other alternatives?

MiyaLike, now I am not sure if this is a good example, if I am thinking about a maze with a role playing game, at some point where the way ahead splits, I select one option and go up to the next stage and find that's the way, like that?

NobFor me, I go back right away and make sure that the other option is wrong then.

T.KarinoWhatever, when making it I try out all options there are. I have a duty to make sure that there are no other solutions.

NyanBazWell. It's the same for an editor. Here we are talking about what a solver is doing, someone who isn't an editor or the person creating the puzzle in the first place.

MiyaJust calling it trial and error or inference is really vague. There are many methods which came out of this kind of trial and error that are basic methods now.

NobSure. Especially, with Slitherlink there are many methods like that. The method where a 3 is next to another 3 started out as trial and error.

33 in Slitherlink
33 in Slitherlink

MiyaThat has to be right. To my thinking a problem that uses trial and error alternatives to understand a result right away, earnestly, has to be acceptable.

NyanBazT.Karino likes such trial and error situations. Especially with Hashiwokakero. A bridge built from this island has to go in this or that place. Then because it fails when it's in this place, the solution has to be the one to that place. There are so many problems with that kind of situations.

T.KarinoTrue enough. But if we don't have trial and error situations in Hashiwokakero we won't be able to make that kind of puzzles hard.

MiyaI can agree with that.

T.KarinoAlso for other puzzles than Hashiwokakero, I first think something is trial and error, but with use it becomes recognized as a method on its own.

NyanBazLike the method with Slitherlink we talked about just now, too. It's difficult to know how far trial and error should be accepted.

MiyaI'll work to explore the limits to where it can be done, and then see to make interesting problems right up to what we can get away with.

NyanBazAre there puzzles where it is easy to make hard problems? Other than Hitori which we already talked about a while ago?

MiyaThere's Akari. There it is the difficulty to find out what to do next, that becomes a bottleneck.

NobT.Karino has a method with facing 2s or 3s that works well.

A method with facing 3s. A united front?
A method with facing 3s. A united front?

T.KarinoThe method where they are in a line where they could both work. I use it a lot. Maybe because I don't know any other methods. (laughs)

NyanBazThat method is used a lot so maybe we should have a name for it, a sort of shorthand term.

NobUnited front?

MiyaIt's when it is easy to see that I can't put light bulbs in 2 cells at the same time. With that, and thinking a bit, then notice that is not possible to put light bulbs in other cells in the same line.

T.KarinoI once worked on how to expand that to make it work in a quadrangle on four lines.

NobThat may make it a look-ahead thing. But it sounds like it could be interesting.

MiyaI am careful about using 3s in Akari. Except at the starting point I avoid them, other than when there is a place where I can't put a light bulb in a cell, and there are three remaining cells to put light bulbs in. I like the flow that 3 light bulbs around a 3 are set up from another position and there is one remaining cell where we can't put a light bulb, it becomes necessary to think about how to get a light in there?

NyanBazAll right, 3 is often set by a cell where you cannot put anything else. You sort of use reverse logic on it there .

T.KarinoI don't think so deeply about it. (laughs)

NyanBazBut then, which puzzles do you find it difficult to make a hard problems with?

T.KarinoThat would be Sudoku. When it can easily be solved from a place that I didn't think about.

NobI can agree with that. You don't make a lot of Sudoku Miya, or do you?

MiyaI don't make Sudoku at all. I tried to made Sudoku when I was a high school student, but it was difficult to complete them.

NobThere are other authors who make a lot of puzzles but are poor at making Sudoku too. I have the impression that authors who try to control the solver are weak with Sudoku. Because control is difficult with Sudoku.

NyanBazToday's theme is hard problems. What is some advice to a person who is weak in doing hard problems?

MiyaThis is something about my problems. I make the puzzles so it is easy to find the clues. So you will be able to find the next hint if you keep searching. When you just can't solve something, you should give it more time.

T.KarinoBegin by writing down the methods that you understand and sort those out. For instance, Sudoku has such methods, Slitherlink also has such methods. That way you will be able to clear your head, and you will find it easy to discover new methods.

NobWell. That's difficult work for a beginner.

T.KarinoThen, Nikoli could sort out the methods and tell us about them.

NobI guess that is one way. But we want you to notice a new method for solving on your own. That's one of the powerful charms of puzzles, to discover a new method.

NyanBazIt is difficult to say where to do it like that and where to instruct and then where to leave off and let people think for themselves. At any rate, I agree with the opinion that a hard problem is easy to solve when you are aware of a method. Thank you for interesting stories today.

Discussion on Nov 2010 Published on Nov 27, 2013

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