Having reviewed my numbers from last night, I see that I made an error on the vertical, and "re-used" some space for neighboring vertical squares (still good on the horizontal though.  Therefore, I have to drop a single row of 10 and the number becomes 115.

I also worked up my numbers per the stated criteria of a 0.05 buffer on all edges.  For this style, I get 106, as follows:

row     num  cumulative side length   
 1       10          0.000
 2       10        528.000
 3       10       1056.000
 4        9       1513.261
 5       10       1970.523
 6        9       2427.784
 7       10       2885.046
 8        9       3342.307
 9       10       3799.568
10        9       4256.830
11       10       4714.091
        106

With the new max side length of 4,752 feet, approx 38 feet remains, not enough to convert another row.

Bill... I think all the other kids left for the playground (AKA a cache).

Tim

Your answer is more accurate than mine, but does not technically meet the stated criteria of a ".05 mile buffer zone."  Of course, as you point out, a "floating" buffer zone, while not meeting the stated goal, does allow for more points.

Same problem we were solving before, just with a square that is 528' shorter on a side, so it is 4752 on a side.  That means you get 10 in the long rows and 9 in the short rows (triangle pattern for max density).  Rows are still 457.261' apart, except you can put a couple the full 528 apart and get extra rows of 10.  I think 96 is right.
 
Bill in Willcox
 

From: az-geocaching-bounces@listserv.azgeocaching.com [mailto:az-geocaching-bounces@listserv.azgeocaching.com] On Behalf Of Tim Giron
Sent: Monday, March 14, 2005 9:02 PM
To: listserv@azgeocaching.com
Subject: Re: [Az-Geocaching] Maximum square mile cache density
 
With this new constraint (which I will call interlocking horizontal neighbors), I will offer 2 answers to be debated.  The first is 120, since now the rows are all 10 "dots" wide and they just shift back and forth, forming triangles.  However, this leaves approx 250 feet wasted at the top of the square (since there is no longer a benefit to "squaring up" the sides.  So, I will throw out another, softer number of 125 which is the average for two squares stacked vertically (the 250 feet from each add up to enough to make another row which takes 457 feet, and they split the number in the row).
 
Tim
Team AZFastFeet
 
Okay, maybe I opened a can of worms here...
 
I should be more specific...I was trying to figure out how many caches can fit into a square mile, leaving enough buffer zone (.05 mile) around the edges, so each square mile around the area in question can also have the same amount of caches?
 
Any math geniuses out there? Anyone?
 
Scott and I were discussing this today, and also called it a "Power Grid"...
 
Maybe on Terracaching.com....thinking, thinking.....