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#1: Gator (Gator) on Sep 2, 2009 [HINT]

And of course to get anywhere in this puzzle, you will need to use edge logic. :)

Found to be logically solvable by Gator.

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Fun little puzzle! Great use of edge logic! Loved it!

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I just love all your puzzles. Just the right size, and just the right difficulty. Keep 'em coming.

It is so much fun to solve your puzzles, Gator.

:-D Jan.

Thanks for your entry!

Thanks all.

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I don't understand what you mean about using edge logic. Are you just putting in blocks until the puzzle tells you "no"?

LOL. Yes and no. Look up the advanced puzzle solving techniques that Jan has created.

Here is another example of edge logic with an illustration and explanation:

http://www.heroglyphix.com/forum/viewtopic.php?p=811&highlight=boo#811

Let me try yet another more detailed description of edge logic. This puzzle happens to be a great example.

When you start a new puzzle, you start by looking for certain patterns. Lines with no clues. Lines with large numbers of clues or clues with large numbers. In this puzzle you'd fill in the top rows with dots and then you'd probably do something with row 14, which has some big numbers in it. However that doesn't really lead anywhere in this case so I'm going to ignore it and go straight to looking for a different kind of pattern: a good place to apply edge logic.

This puzzle is oozing with classic edge logic opportunities. What we are looking for is a big number along the edge of the puzzle, and some smaller numbers one row inward. And in this case, we have that on all four edges of the puzzle. On three edges we have fives with nothing but twos one row inward, and on the third side we have an eight, with fours. Bigger numbers are better, so we are going to start with the 8 on the right edge of the puzzle.

In normal line solving you focus your attention on just one line of the puzzle at a time. Edge logic requires a bit of a broader focus. We are going to be looking at the column with the 8 and the column with the 4s and just the last clue number for every row clue. Kind of like this:

I said that we are going to pay attention to those right-most clue numbers, but we really only care whether they are ones or not. It's the pattern of ones and non-ones that we care about.

So, we want to consider different possible positions of the 8, and what impact that would have one the column with the two 4s. Usually it's easiest to start by thinking about 8 being on one end or another. We'll start it at the bottom.

So, if the 8 were at the bottom of column 20, what would be in column 19? This is really easy to visualize, because the pattern it would make is exactly the pattern of ones and non-ones in the clue numbers. You don't really need to mark this on the puzzle to see it, but I'll draw a picture just to make it clear what I'm talking about:

OK, so it's hard to draw with a scratch pad. The X's are black squares and the dots are whites. What we are interested in is what's in column 19. The pattern s just like the ones and non-ones in the row clues, so it's easy to visualize. Just look at the row clues. And it's also easy to see that it doesn't come anywhere near being consistent with the "4 4" clue for column 19. So the 8 can't be all the way at the bottom.

So we'll have to move the eight upward. How far upward? Well, moving it up just one wouldn't help a bit. You'd still have the 1 black with dots on either side in row 15. So we have to move the eight up so the bottom is on row 15. Then we still get a black at R15C19, but it doesn't have to have a white under it any more, so it no longer contradicts the "4 4" clue. So we can put dots in the bottom 5 rows of column 20.

You can do the same thing from the top. If you try the 8 in the top 8 rows of column 20 (well, not counting the row 1 which is already dotted), then you get a similar problem. Rows 2 through 5 of column 19 have to be black, which is fine, but so R8C19 also has to be black, and the cells above and below it have to be white, which is bad. So we have to move the eight downward until that problem goes away. This lets us dot rows 2 through 7 of column 20.

This leaves only eight cells in column 20 undotted. We've completely located the 8, and are off to a good start to solving the puzzle.

It doesn't always work out as well as this. Sometimes you only can place a few dots, but every dot helps.

Sometimes you don't use the first row inward to check. Like you might check the "8" in column 20 against the "1 2" in column 17. Or you could check the 4's in column 19 against the "1 2 2" in column 18.

Thank you. That is very clear.

Once I understood the edge logic it was very easy. Thanks again for the help. Neat puzzle.

Edge logic, in general, can be a challenge to figure out conceptually (it was for me anyway), but once you have the hang of it, it's as easy as any other solving technique. I personally use it quite a bit, including in cases where it's not absolutely necessary. For me it's often less tedious than meticulously counting squares for line logic solving!

There should be a link to this exact puzzle with your detailed explanation, Jan.

Enjoyed solving this, Gator, thanks!

Great puzzle!

Thanks for the explanation of edge logic Jan!

agree 100% with #17.
fun solve...easier than some of yours! :) amazed, as Jan said, that you got this to solve ok with such a simple line drawing.

Thanks all.

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