Author |
Message |
08/05/2008 16:33:01
|
connect4
Joined: 04/03/2008 05:04:39
Messages: 250
Location: USA
Offline
|
In my (thus far unsuccessful) attempt to comprehend Cogwheels puzzles, I came across the following typo:
http://www.puzzlepicnic.com/genre?cogwheels
"As an example we will solve a small instance of these puzzles. Assume we're dealing with a puzzle with two wheels of size 3 and three of size 1. "
The example, however, has only one wheel of size 3.
|
|
|
08/05/2008 19:10:19
|
Johan
Joined: 22/12/2006 20:08:51
Messages: 1046
Offline
|
Thank you, it has been fixed.
Maybe I can put it in a less cryptic (more mathematically oriented perhaps) way for you: We are essentially placing non overlapping squares in the diagram, whose sizes are 1x1, 3x3 and 5x5. If we observe an undirected graph in which those squares are the vertices, then there is an edge between two vertices iff the corresponding squares touch and have their centers on a line parallel to one of the grids' axes. The graph is required to be connected.
Small note: the graph is easily shown to be bipartite, so there are no cycles of odd length to worry about concerning the remark that every wheel has to spin when you spin one of them.
|
|
|
08/05/2008 21:57:57
|
connect4
Joined: 04/03/2008 05:04:39
Messages: 250
Location: USA
Offline
|
Thanks for that reply Johan (never would guess you're a TopCoder from teh alternative explanation!) I like that method of thinking of the puzzles. I just now need a way to figure out some of the strategies (probably some of which will involve me doing it out with pencil and paper, like I've discovered I need to do with Spiral Galaxies and Neighbors). Maybe that'll help me figure out how to get started on those 3-4* puzzles that I haven't done yet!
|
|
|
17/05/2008 17:11:25
|
connect4
Joined: 04/03/2008 05:04:39
Messages: 250
Location: USA
Offline
|
Just wanted to thank you again for that explanation! Thanks to thinking of it that way, I've managed to shut down 3 cogs in the last few days.
|
|
|
19/05/2008 19:56:59
|
Johan
Joined: 22/12/2006 20:08:51
Messages: 1046
Offline
|
You're very welcome. I need to reword the explanation given on the website (I just noticed it isn't even mentioned that the wheel sizes are 1x1, 3x3 and 5x5 ), but TopCoder style is not suitable for many users. Any suggestions concerning what not to forget to put in there?
|
|
|
|