Slitherlink

[Mel-o-rama]

There's a new puzzle in town that's caught my attention. It's called Slitherlink.

The idea is to form a closed loop that goes around the grid and the numbers in each cell represent the number of line segments touching that number.

Conceptis Puzzles provides some solving tips. It may be worth checking out these tips before reading on. (Or you may find it more fulfilling to start doing the puzzles and discover these tips on your own.)

The solving techniques involve placing x's on line segments that won't work. Then by process of elimination, you can figure out the whole puzzle. Everywhere I look on the web for solving techniques, it's the same stuff.

Also, I've another technique to speed things up, which I can't seem to find on the web. It involves the simple fact that a closed loop separates a plane into two pieces: an inside and an outside. As you solve the puzzle, you can color each cell. I use yellow for inside and pink for outside. (Alternatively, you can use circles and dots for inside/outside.)

--Stop here if you want to try to figure out the rest on your own.

A line segment on the very edge on the puzzle will put its adjacent cell on the "inside". If there's another line segment on the "inside" cell, then the cell on the other side of the segment has to be on the "outside".

In this way, line segments are parity-changing entities. In other words, when you cross a line, change colors.

Xs connect two cells together, so they'll be the same colors.

Inside cells must connect to each other, so as you determine what color each cell is, don't block off the insides. There is only one "inside" piece but you can have several "outside" pieces. Each "outside" piece must find its way to touch the edge of the puzzle. (Actually, if you think of the outside extending beyond the edges of the puzzle, it will connect all the outsides together - so they're really one piece as well.)

2s can only be surrounded by two yellows and two pinks. So, if you have two yellows and one pink around a 2, the 4th cell must be pink. The color of the 2 cell itself can be either yellow or pink.

3s must have three adjacent cells of color opposite the color of the 3 cell.

1s must have three adjacent cells of color the same as the color of the 1 cell.

If a 1, 2, or 3 are on the edge of the puzzle, you can think of there being pink "outside" cells beyond the edge.

If any of you have already come across these parity (inside/outside)techniques on the web, let me know. I'd like to see how they explain it.

And yes - I should be studying, but this late at night, I just need a break!

[Mel-o-rama]

Bump - has no one seen these puzzles before?

[llcooljabe]

Not till I read this thread 10 seconds ago.

[rekrap]

Should have called it "Linesweeper".

[Mel-o-rama]

- for those who missed this last time, and also to add this link:

http://home.windstream.net/windhams/...itherlink.html

This explains the parity method in more detail. Enjoy...