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?
NyanBazYou like new discoveries. Are you the same, Miya?
NobThat's why we invited you to be here today.
NobI don't think so. Do you want to tell the method that you discovered to solvers?
NyanBazYou are really conscious of what the solvers are up against. How about you, Miya?
NyanBazBack to hard problems, there are several types of hard problems.
NyanBazThat was well put.
NobYou mean a problem that can not be solved unless you notice some point in one place?
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.
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.
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?
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.
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?
NobFor me, I go back right away and make sure that the other option is wrong then.
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.
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
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.
NyanBazLike the method with Slitherlink we talked about just now, too. It's difficult to know how far trial and error should be accepted.
NyanBazAre there puzzles where it is easy to make hard problems? Other than Hitori which we already talked about a while ago?
NobT.Karino has a method with facing 2s or 3s that works well.
A method with facing 3s. A united front?
NyanBazThat method is used a lot so maybe we should have a name for it, a sort of shorthand term.
NobThat may make it a look-ahead thing. But it sounds like it could be interesting.
NyanBazAll right, 3 is often set by a cell where you cannot put anything else. You sort of use reverse logic on it there .
NyanBazBut then, which puzzles do you find it difficult to make a hard problems with?
NobI can agree with that. You don't make a lot of Sudoku Miya, or do you?
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?
NobWell. That's difficult work for a beginner.
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