Eketech Games

This is a logic puzzle based on linking squares.

The Rules: Shaded cells (with numbers) must be connected.  the number in the upper-left hand corner is the length of the connecting line.  The number in the lower-right hand corner is the number of intersecting lines (self-intersections count as two).  Each [connecting] line must start at one cell and end at a different cell with the same marks (2/4 -> 2/4).   Shaded cells can not be connected to themselves.

http://www.eketech.com/games/eketekonnect.html

OrThought is a 3d block-pushing puzzle game.

It is intended to be challenging, but not frustrating. When a puzzle seems difficult, the best advice is to stop and think your way through the challenge. A lot of puzzles are a lot less difficult than they appear, once you can see through the gimmick.

The game also comes with a map editor which permits anyone to create and publish their own OrThought map-packs (or singles).

OrThought

EDIT:  For site admins, bloggers, and whoever else might want a piece of the action, not only is OrThought free to play, it is free to redistribute (as is):

http://eketech.com/files/orthought.zip

Please, do your best to keep it at 700×600 – it runs better that way!

This is a part of The EketeKonnect Tutorial.

Part I

Part II

—————————

In many EketeKonnect puzzles, odds are very good that you will end up having a few links pass through an area where they must intersect each other several times.

For the purpose of this tutorial, I have created a custom level:

Note:  Here is the code for the level — just copy and paste it into the custom level dialog, then click play:

eNodzlkSQyEIRNEWUYHkZdr/XpNw/TjV1VLK8+P6/s+SUr6lu/xIN3nQJxb6aAMTC6dxi2EqeZILbTKDOXXJiixvBxoWavUmtcibmd1vFlmHBu30nkVW0EfvX2QlTfIjWUWDhhMdF248GJhY+HhpSNe7/QEkyaJb

This level was contrived for simplicity — getting proper length and intersection parity is a non-issue here:

From there, I decided to work on fixing line 13/6, so I used the most obvious change:

Almost Solved!  Actually, no, there is still the matter of 9/4 not having any intersections (and no ability to self-intersect, since there is no slack available).

I decided to have links 10/4 and 11/4 each double-intersect 9/4, in the process, taking 4 intersections away from 13/4:

The solution, at this point, is now obvious.  For convenience, here is a slightly adjusted form of the same setup:

The two points where links 13/6 and 12/4 meet, but do not intersect, are now very useful.  Normally, by switching two such points from a double-bend to an intersect, you increase the number of intersections for both lines by two (a simple way to resolve a lot of situations).  However, since the change will also remove link 14/4′s two intersections with 9/4, the net change will be zero.  Those two intersections will go to link 13/4, for a net change of 4:

Solved!

Double-curves and intersections are key to shifting links around on a board.  It can help you find empty space to put extra slack, correct intersections errors, and other useful changes.

This is a part of The EketeKonnect Tutorial.

Part I

Part II

Many puzzles in EketeKonnect, especially the large ones with complex paths, can not easily be easily solved without using a technique I call “Parity Matching.”  Parity Matching can be used to quickly reveal the puzzle’s basic structure.   For this tutorial, I will use level #3 — a level that seems difficult, but with parity matching, is easily solved.

(Note:  For the purpose of this tutorial, parity is the even/odd-ness of a number)

Here is puzzle #3:

There are two kinds of parity involved in parity matching:  Length and the Number of Intersections.

Length is quite simple — if you imagine the puzzle grid as a checkerboard, a line with an even parity connects a light square to a dark square, and a line with an odd parity connects two dark squares to each other (or two light squares). The line parity helps is an easy way to determine which squares can not be connected, when they otherwise appear compatible – the two 14/6 cells in the northeast can not be linked because the parity of the length is odd, not even.

The Intersection Parity is, for the purpose of determining structure, much more important.  You can quickly determine whether or not a link can pass through part of the puzzle (or whether some other link should be routed into or around the area).  Once you have all links drawn with correct Intersection parity, it becomes much easier to manipulate the puzzle nearby them.  You can make a link with correct intersection parity self-intersect or intersect another line twice without changing the basic layout of a puzzle.  You can likewise remove self-intersections and double-intersections.

For most puzzles, intersection parity is easy to achieve with all lines.  I recommend you draw short and simple links between each pair of compatible shaded cells.  After that, check each link for intersection parity.  If a link does not have it, either re-route it or reroute some other link in or out.  If you can, use the adjustment to correct intersection parity elsewhere in the puzzle.

Here is puzzle #3 with proper intersection parity:

Notice, he only concern here was intersection & length parity – no attempt was made to match the actual number of intersections or the full length of each line.

Aside from anything else that’s obvious, the next step should be to extend each link to match the length indicated by the shaded cells.  Ideally, the extended parts of each link should be drawn into edges and areas which are not crowded.

Puzzle #3 with all links I could extend extended.

In particular, pay attention to how link 12/3 is extended at the top into an area no other link can enter (due to parity issues) and a side-area where there was not much to crowd it out, as well as how link 14/3 is wrapped around its own isolated cell (though after one of the 14/6 links was bumped over).  By routing as much as possible into otherwise empty space, that gives you more room to work with in the crowded areas.

There is an error with the link between the top-most 14/6 cells.  Here is puzzle #3 with the problem highlighted:

In my haste to do parity-matching, I got *greedy and failed to notice I made an invalid link!  While it has 6 straight sections to handle 6 intersections, one of them can only be accessed by one link.  Furthermore, there are so few options available for the 9/5 link, I was forced to make the upper 14/6 link as is.

However, remember how I said this level is easy, and how parity-matching also applies to length?  By linking to the 14/6 cell two spaces to the south, the same 14/6 link now has enough slack to do this:

Solved!  And of course, the other 14/6 link, which I could not [easily] find enough space or intersections for before easily has enough space and provides the two missing intersections for the other 14/6 link.

* Truth be told, it was a contrived error

I’ve got a new game a few days from complete.  Its a logic puzzle!

The Rules: Shaded cells (with numbers) must be connected.  the number in the upper-left hand corner is the length of the connecting line.  The number in the lower-right hand corner is the number of intersecting lines (self-intersections count as two).  Each [connecting] line must start at one cell and end at a different cell with the same marks (2/4 -> 2/4).   Shaded cells can not be connected to themselves.