ArticlesIn response to a few questions, I will attempt to explain the heart of my meta-gaming issue in more detail with an example from Hitori.
Introducing Hitori
Here is a sample puzzle sheet for Hitori, stolen from the dangerously addictive Conceptis Puzzles web site.
The goal of Hitori is to either cross out or circle every cell, so the following constraints apply:
- No row or column includes the same number circled twice.
- No two crossed out cells are touching (horizontally or vertically).
- All of the circled numbers form a contiguous area of the grid.
You might like to attempt to solve this puzzle now. Conceptis Puzzles has some techniques in their Help pages that you can use.
Analysis: Re-wording the Rule
Let me break the rules down from the perspective of a single cell:
The first rule effectively says “If there is a circled number equal to you on the row or column, you are constrained to be crossed out.”
The second rule effectively says “If you are next to a crossed out square, you are constrained to be circled.”
The third rule effectively says “If some complex grid-wide constraint about contiguous areas would otherwise be broken, you are constrained to be circled.”
Cheating (?) With Meta-gaming
I could solve the Hitari the long and laborious way that the help file suggests – or I could cheat with meta-gaming. Let me show you how powerful meta-gaming is here.
If I find a cell that doesn’t have an equivalent number sharing its row or column, then the first rule doesn’t apply. The other two rules only constrain cells to be circled not crossed out.
So no rule constrains it to be crossed out, and two rules might constrain it to be circled.
Meta-game hand-waving suggests that the cell must eventually be constrained, and hence must be constrained to be circled.
Results
I very quickly went through this grid, and coloured every cell that could be instantly circled, just through meta-gaming.
Just one technique solved 29 of 64 cells, and all I had to do was check whether the cell had a matching value in the same row or column.
Further Results
What was not illustrated here was a far less common, but more powerful application of a similar rule.
If you ever find an unsolved cell surrounded by a (contiguous) set of circled numbers, then the opposite analysis applies. Rules 2 and 3 wouldn’t apply – nothing would force that cell to be circled. However, Rule 1 may apply. It might be forced to be crossed out.
Applying similar logic, I conclude it must be crossed out. Furthermore, it must be crossed out because of Rule 1, so if there is only one other cell in its row and column with an equal number, than cell must be circled to ensure Rule 1 applies.
Conclusion
So, meta-gaming in Hitori is powerful… but is it cheating?
Comment by Alastair on September 14, 2006
I like your reasoning, and wish I had thought of it myself.
I wouldn’t call it cheating, because you’re not using anything to gain advantage that other puzzle solvers wouldn’t also have.
Also, I disagree that this is metagaming, as per my previous comment.
Just out of interest, was this a particularly hard Hitori puzzle?
Comment by Julian on September 14, 2006
Alastair
Re: Metagaming definition – I have responded in the original thread.
Re: Difficulty – no, this particular puzzle was rated as “Easy”.
Re: Cheating
Effectively you are defining cheating as being gaining an unfair advantage that other people couldn’t also use. Sounds reasonable.
I can’t help but think I am cheating the poor imaginary people who live in an alternative, Hitori-based universe. Their mathematicians are struggling with each Hitori they encounter, postulating, but never being able to prove, that the reason that every Hitori they’ve seen so far is soluble is because of the existence of a Hitori God, “the Puzzle Master”.
It is normally when my train of thought gets to this point that I start wondering about whether I should have accepted that homemade cookie from my stoner friend.
Comment by Sunny Kalsi on September 18, 2006
Is this metagaming? It’s an interesting question. The thing here is that your decisions are “soft”. You’ve got an easy way of getting the answer, but it doesn’t always work. If it doesn’t you’ve got a quick(ish) way of figuring out that there is a problem, and at least a reasonable chance of confining the error space. I haven’t thought through it yet, but I think sometimes it may not help at all, and in fact may be completely counter-intuitive. Point is, you can always change your mind. So:
If you could only make the decision about a number once, and you made it based on the fact that the number is probably constrained, then in my opinion, you’re metagaming.
However, if you’re using it simply to short-circuit an easy problem (something you can change your mind about if you’re wrong), then you’re not metagaming in my opinion, just taking advantage of “the Puzzle Master’s” idiocy.
Incidentally, I was thinking of using a similar trick for sudoku.
Comment by Christopher on September 20, 2006
It’s not chating, just using techniques. I discoverd hitori puzzles just yesterday, and found out these “tricks” at the first puzzle, and i could add other 2 very simple and very useful in harder puzzles.
1 if in a column or line there is a colpue of a number and then other same numbers all the ones out of the couple are surley filled.
2 If there are to same numbers in one column or line with just one other number in the middle that number must bhe circled.
Aniway techniques that are not explicit in the ruls are used for solving all kind of puzzles like hitori, kakuro or sudoku. It is not cheating, in my advice they are not directly explaind in the rules because A) they are techinques and not rules, and B) it is a fun part of the game for most peole to discover solving techniques with their one brains.
Comment by Neil on September 23, 2006
Another hitori site you might be interested in checking out is:
http://www.hitoriconquest.com
that I put together recently.
Hope you enjoy..
I agree with the other commenters that using such techniques ‘beyond the rules’ is not cheating and in fact almost required to solve many hitori puzzles.
Neil
Comment by Kekoa on December 20, 2007
I don’t think this technique is cheating. The ultimate goal of Hitori is to correctly mark the black cells, and circling the white cells you mention doesn’t help mark ANY black cells!
Comment by Julian on December 27, 2007
Kekoa,
I have been rolling the nuances of your comment around for a few days, and have decided, nah, it doesn’t hold.
In the game Minesweeper, you know upfront how many mines there are. Once you have marked that many mines, you can stop.
In Hitori, you don’t know how many black cells there are. It is only by circling all the remaining white cells that you have finished. This helps circle the white squares, so it is helping solve the puzzle.
Of course, none of this goes to the actual point of the post. Whether I am cheating by meta-gaming isn’t related to whether this particular instance of meta-gaming can be nuanced away with sophistry.
Comment by Kekoa on January 4, 2008
Hi Julian,
At the time I made my post, I was looking for fast ways to solve Hitori. My background here is that I joined Nikoli.com, and there are people out there who can solve Hitori very quickly without marking any white cells at all! (I discovered this by watching some of their solution histories.)
While I was looking for more information on fast techniques, I found your blog post, but realized it didn’t help me solve the puzzles any quicker. You can spend the time to mark the cells you mention, but you won’t find the black cells any faster by doing this — white cells don’t constrain the location of any black cells if their circled numbers are alone in their respective rows/columns. Also, I have since learned that it’s pretty easy to track the white cells without marking them: the only white cells that matter are the ones next to the black cells and the ones that keep the white cells connected. Both of these can be “seen” pretty easily. Also, the puzzles by definition can’t be ambiguous, so every cell will eventually be mentally marked this way.
Going back to solving Hitori quickly, I didn’t find any good info, but after practicing for a bit without marking any white cells, I have gotten much better and faster. (The Hitori game for the Nintendo DS helped a lot.) The most important technique I found was knowing when to search for additional black cells after discovering a white cell. I’ve found a good rule of thumb is to search for black cells only after finding a “non-trivial” white cell, where the trivial white cells are the ones that are directly adjacent to black cells and not dividing the white cells. (In your puzzle, you can start by marking the two 8s in the lower left black. After doing this, I’d consider the 2, 1, 2, 4 leading out of that corner non-trivial white cells and the 7, 5, and 3 trivial at this point.) Sometimes this leads to mistakes, and in that case I usually find the black cells by looking at a cell and looking for white cells in its row/column, rather than the other way around, since usually it’s easy to identify the cells you’d like to mark as black. Also, checking for black cells after marking EVERY white cell is a huge waste of time.
I don’t know if solving Hitori quickly interests you at all, but maybe in the future this information will help somebody else who does a similar search for solving Hitori quickly. (Your site currently ranks #2 on Google for this query, maybe this post will help it rank higher. 🙂 )