Web Paint-by-Number Forum
Topic #334: New Solvability Rating System
By Jan Wolter (jan)

#1: Jan Wolter (jan) on Jul 27, 2012

The rating system for solvability has been expanded.

The new categories are as follows:

FOR PUZZLES WITH A UNIQUE SOLUTION:

"Trivial"
Basically this is puzzles with no white space, or so little white space that there might as well be none. The checker will always identify these and automatically rule on them. If I remember right, it's actual criteria has to do with being able to solve the puzzle without ever looking at any line twice.

"Solvable with Line and Color Logic Only"
For two-color puzzles this just means that the puzzle is line solvable, that is, you can solve the whole puzzle without ever having to look at more than one line at a time. For multicolor puzzles, we also include puzzles that require some color logic in this category. See the Advanced Solving Techniques page for a short description of Line and Color solving. All these puzzles will be automatically flagged by the checker.

This includes all puzzles that can be solved using the kinds of techniques described in on the Advanced Solving Techniques page - edge logic, smile logic, summing, two-way logic, all that sort of thing. I think we've also sometimes referred to them as puzzles that don't require more than two levels of lookahead. These puzzles can be quite difficult, but generally if someone explains how they solved it, it'll be something most any experienced solver can understand and slap him/herself on the head for not spotting. This category, together with the two previous ones, includes all the puzzles we called "logically solvable" under the old system.

These are puzzles where someone has been able to find a logical solution procedure, and has posted it in the comments, but that procedure contains steps that require deeper lookahead and longer chains of reasoning than is typically required for our "Advanced Solving Techniques." These are puzzles that might well be considered "too hard" to solve by most people, but which are deeply loved by those rare solvers who really enjoy going to heroic lengths to solve a puzzle. These puzzles used to be included in the next two categories, but now, if someone finds a way to solve them, we have a new category to put them in.

"Solvable with Some Guessing"
If nobody has found a better solution technique than guessing something, keep going until you hit a contradiction, then hit the undo button until you've undone your guess, and then try something else, then we say the puzzle requires guessing. We divide the puzzles in that category by how hard they are to guess. If based on "picture logic" you can pretty easily find the solution, then this is the category for that puzzle. Puzzles in this category may will still be enjoyed by users who don't mind guessing when the going gets tough.

"Solvable with Much Guessing"
And if even by guessing and picture logic it proves really, really hard, or maybe impossible to arrive at the final solution, then this is the category they go in. Puzzles in this category are pretty much no fun for anyone.

FOR PUZZLES WITH MULTIPLE SOLUTIONS:

A puzzle with multiple solutions cannot be solved by logic. So the only two categories it can fit in are the last two listed above.

So we new have more categories. Two should always be identified by the checker. Puzzles in the other categories will be assigned based upon the majority opinion - whichever category most people think it is in will be the category. Eventually someone empowered to make a ruling (currently me or Gator) may come along and make a final assignment, after which people won't be asked to vote any more.

IMO, I would classify "Puzzles with a unique solution" only from the first 4 listed above. I don't believe there's such a thing as guessing with those puzzles, one will eventually arrive at the solution, even if it means VERY deep lookahead before hiting a contradiction. A unique solution puzzle that is not classified trivial or LLS (which I think is done automatically) could be tagged as Deep Lookahead until ruled to be Modest Lookahead.
You are right about multiple solutions puzzles, one has to guess, because the only contradiction one may hit is not getting the intended solution.

So basically, the last 4 listed are the 4 "?" marks.
#3: Jan Wolter (jan) on Jul 28, 2012
The following is a logical solving procedure:
1. Guess a color A for square X.
2. Work out all consequences.
3. If you find the solution, stop.
4. If you find a contradiction, undo all consequences of that guess. You now know square X is not color A.

Concerning this perfectly sound procedure note the following:

• The first word is "Guess". It involves guessing. The new terminology keeps the concept of "Guess" but no longer places it in stark contradiction to "Logical".
• This procedure is usable on both puzzles with unique solutions and puzzles with multiple solutions. On a puzzle with multiple solutions, you are always going to be forced to do this eventually. Some puzzles with unique solutions can only be solved this way. That's why I place all puzzles that need this solution technique in the "guessing" category, whether they have one solution or many.
• Unique puzzles that require many iterations of this procedure are very nearly as annoyingly awful as multiple solution puzzles that require it. They deserve to be tarred with the same brush. Good puzzles can be solved with an ink pen.
Am I to understand there will now be 6 possible "?" marks?
#5: Jan Wolter (jan) on Jul 28, 2012
For the "Deep Lookahead" puzzles, there is a "!" and since that only applies to unique puzzles, there is only one version of it.
FYI, when viewing infomation of "Solvable with Line and Color Logic Only" puzzles, we get this:
Logical: Definitely requires some guessing
#7: Jan Wolter (jan) on Jul 30, 2012
Oops. Guess I missed that screen. These changes had to be made in dozens of places.
#8: Jan Wolter (jan) on Jul 30, 2012
OK, that should be fixed now.
#9: Tom O'Connell (sensei69) on Jul 30, 2012
I like the new rating system, Jan
Here you write: "Solvable with Modest Lookahead".
The category is listed as "moderate lookahead" everywhere else on the site (view info, find puzzles, comments)!
#11: Jan Wolter (jan) on Jul 31, 2012
Oops. Typo. Will Fix.
How much white space can a puzzle have and is still be considered "Trivial"?
#14: Jan Wolter (jan) on Aug 7, 2012
If I remember correctly, if it can be solved under these rules, then it gets labeled trivial:

(1) It is line solvable.
(2) Every time you solve a line, you can fill the whole line in, leaving no unknown spaces behind.

You could probably have quite a bit of white space, probably as much as 50% white (an odd-sized checkerboard, for example). Maybe more. It just means that there is always at least one line that has only one possible solution.
#15: Daniel Korn (talechaser) on Aug 28, 2012
When you do a puzzle search on the Find Puzzles tab, it would be nice if when you selected a Solvability, it found all puzzles *at or under* that rating, not just those that met the actual rating.

So, searching for "Moderate Lookahead" puzzles would also show "Trivial" and "Line and Color Logic Only" puzzles in the results.
#16: Janet Weiss (janetmweiss) on Dec 3, 2012
I just want to second talechaser's comment. I would really, really like to be able to set a solvability *range* instead of just picking one level.

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