Puzzle Description:

Gemini Zodiac Symbol

#1: Web Paint-By-Number Robot (webpbn) on Jul 11, 2012

Found to require some guessing by gator.

I need at least 3 moves look-ahead to solve this, so I'm marking it as guessing.

I'm reclassifying this with our new category, deep-lookahead. In fact, it is deep-but-easy lookahead. Zigzags.


After the central rectangle is done with line logic, you're left with the four corners to do.

As I've pointed out in other puzzles, when you see a bunch of crossing 2s, you can either have a bunch of 2x2 squares, or a zigzag. With a 1 on one side, the bet is very good that it must be a zigzag.

In fact, try to place a 1 in r1. It must extend into r2. That must then extend sideways (either left or right) and then *that* must extend down into r3... . No matter where you start a 1 in r1, you end up with a zigzag.

Here's a very important note about proceeding from assumption: Only if you run into a conflict can you mark anything. Just because it works doesn't mean that it's right. However, if it *doesn't* work, we know that your initial assumption is *definitely* wrong. Note that it must be wrong in *all instances* -- so with a zigzag that means that *both* the "left zig" and the "right zig" must be proven false to be able to mark your starting assumption false.

So, try a zigzag starting at r1c1. It could fit there, but since we assumed the staring place we must leave it blank and try another.

Try r1c2. If it zigs left we get a conflict in r3 almost immediately. If it zigs right, we must follow the zigzag all the way down, and even then it could be possible. So leave it blank and move on.

Try r1c3. If it zigs left, we get a conflict in r4 where there will be a block of one cut off from the 16. If it zigs right, then we get a conflict in r3. Since both zigs are failures, r1c3 cannot be black. Give it a dot.

Try r1c4. It can only zig left, and again it will cause a block cut off from the 16. So r1c4 must white. Dot it.

Okay, now we will go around the puzzle and do the same in the other three corners. (They are all mirrors of the first, so r1c17-18, r20c3-4, and r20c17-18 are all white.)

Notice that now in all the columns and in rows 1-3 & 18-20, there must be one clue in each corner. The long clues in r4,5,16,&17 might go either way.

Some summing:
Again in the upper left corner, the column clues give us eight more pixels to be placed. The row clues in r1-3 account for five of those pixels. Eight minus five gives only three more pixels in r4&5.

Now assume that ALL three pixels go into r4. Even then, it could not reach c1, so r4c1 must be white.

Then do line logic.

Then, if you can see it, there is an uber-smile across the top. Don't worry if you can't as you can just do edge logic on the 1 in r1. It shows that it cannot be in c2 (it would cause a block of 1 in r3). Then line logic finishes the top.

The bottom is the same, mirrored.

Found to be solvable with deep lookahead by infrapinklizzard.

OR, instead of doing all that long-winded lookahead nonsense, you could just use the obvious left-right AND top-bottom symmetry to center the 14s and 16s, and let all the 2s fall into place, ending with the 1s. Solving might technically require lookahead, but it's silly to ignore shortcuts when they're so blatantly handed to you. Save the explanation for puzzles that actually need it.

Symmetry is not considered a logical solve on this site. It will not work on any puzzle that does not have a unique solution, and that is not guaranteed on this site.

Even when there is a unique solution, we do not have a proof that it will always work, only empirical evidence.
Plus it's boring.

The explanation of the logical solve for this puzzle is not for people like you who don't want to hear them. It is for people who would like to extend their logical thinking skills

Thank you, Joe.

There are MANY puzzles on this site, perhaps thousands, which require logical thinking skills, any of which would benefit from your explanation. This is not one of them.

I agree that left-right OR top-bottom symmetrical clues aren't a guarantee of puzzle symmetry or a unique solution, but when they're symmetrical in both at the same time, it generally is. In those very few where it might not be, like a checkerboard, solving it on the assumption that it is symmetrical IS a logical solve in that it requires recognition and utilization of patterns. And if it's one of those very few that aren't symmetrical and/or unique, it was a use of trial and error which is also a part of logically solving many of the more difficult puzzles.

This apparently comes as a surprise to you, but "people like me" actually DO enjoy "extending our logical thinking skills". We just find going through all the lookahead steps on a puzzle that is so clearly symmetrical to be a waste of time when there are so many others out there that require more work. I guess I'm just not one of those people who enjoys spending two hours doing a puzzle that can be solved in five minutes, just so I can pat myself on the back for having solved it the "right" way.

Here you are chastising me for imposing "my way" of solving on you (when in fact I don't care at all how you solve it), and then you end by saying that your way is clearly superior. C'mon.

I didn't say it was superior. Don't put words in my mouth. But it IS way more efficient for quickly getting past an easy to solve, and generally boring, symmetrical puzzle so as to have more time to enjoy those that require it, or that will produce more interesting pictures.

Goto next topic

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