Puzzle Description:

Give yourself a pat on the back!

#1: Josh Greifer (joshgreifer) on Oct 26, 2011 [HINT]

In each row or column, the two's can only go in any of three positions. In column two, two of these three positions are relatively easy to see are impossible.

Fun solve! That's a pretty interesting concept, well done!

Fun! Thanks for not making it larger than 10x10! ;)

Interesting puzzle, fun solve.

So I guess the point is to prove that R2C2 cannot be black. If it was black, R2C1 would be white. So R3C1 and R4C1 would be black. So R3C2 and R4C2 would be black, which would be a contradiction since that gives three consecutive blacks in a column that can have only two at most. Thus R2C2 must be a dot, and after you have that dot, the whole thing line solves.

I'm trying to remember how many levels of look-ahead we allow for a puzzle to be considered "logically" solvable. But I think that is one level too many. So it's "logically solvable for really smart people" or something like that.

I had a few false starts, then I tried making R1 C1 black, and it all solved logically from there.

thats how i solved it jan

assuming r2c2 is black (with a mandatory dot on each side of it):
the first look ahead move is having to make r3c1 and r4c1 black
the second look ahead move is making r3c2 and r4c2 black (which gives the contradiction in c2)

this is definitely logically solvable with 2 move look ahead (unless you count placing the mandatory dots in r2c1 and r2c3 as the first look ahead step)

i still dont think it has ever been clearly defined as to what constitutes an actual "look ahead move"

is it all of the natural dots and black pixels that can be immediately, easily, or obviously placed placed as a direct result of any given black or dot that you initially place?

How about some affirmation logic?

Looking at column 1 the 2 clue can go in rows 1-4 only (or 1-2, 2-3, 3-4 - three possibilities). Looking at how column 2 is affected for each of these possibilities, we can see that R3C2-R4C2 will always be black. Checking each possibility is looking 1 or 2 moves ahead.

The rest solved with line logic.

Jan - two move look ahead is what I have been using to consider solvability.

bugaboo - the first mandatory dots would be the first look ahead.

Found to be logically solvable by gator.

I think the "mandatory dot on each side of it" should be counted as one of the look-ahead steps.

I don't really know exactly what the rule should be either. We are trying to pin down what constitutes a reasonable kind of puzzle to put out before the general public and expect them to be able to solve logically. Obviously some chains of reasoning are absurdly long. But at the same time we don't want to make our rules too restrictive, like the sites that only allow line-solvable puzzles. That just squeezes half the life out of pbn solving. I think the two moves look-ahead rule is a pretty good one.

But this kind of puzzle is clearly a special case. If I had to do this kind of logical step halfway through some big huge puzzle to be able to finish it, then I'd probably consider it a defect. But in this case you need to do it as step one. Finding it is obviously the *point* of the puzzle. So why should it be held to the same standards as other puzzles?

The 2-move look-ahead rule is not a bad standard to apply to normal puzzles, but not all puzzles are normal puzzles. When the goal is different, the standards should probably be different.

I've actually been thinking that it would be interesting to try to design some puzzles with multiple solutions. The idea would be to have column 1 be the "input" column where multiple patterns can be input, and right-most column be the "output" column, where the pattern would depend on the input column. You'd start by designing an AND-gate so that output cell C would be black if and only if input cells A and B are black. Then OR-gates and wires and cross-overs. Then you need to figure out how to combine elements so you can build up complex logic circuits like half-adders. In the end you could prove it possible to create a general computer in a pbn puzzle. That would be cool, though puzzles with multiple solutions usually aren't. Different standards for different kinds of puzzles.

So anyway, even if this doesn't necessarily fit our normal rule of logical solvability, that doesn't mean it's a bad puzzle. Just a different puzzle.

Thanks for comments, guys -- I've been playing a lot (far too much in fact!) with the online random pbn generator at http://mrl.nyu.edu/~hertzman/dots/ (which is *very* primitive, usually producing patterns with more than one solution). I found that the most enjoyable puzzles that it would come up with are similar to this one, which are solveable, although you can't use line logic to get started.

Great challenge - lots of fun! Thanks, Josh!

Jan - On the other site, they do allow what they call "Anomoly" puzzles. They have multiple solutions, but the title must give the intent of the puzzle which will often be necessary to get to the intended solution. Your description above made me think of this puzzle:
http://www.heroglyphix.com/play.php?upid=1329

I guessed. Sue me.

Cheat ;)

Deep ...

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