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Most saturated OS Sq Km


Mallah
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http://coord.info/GC3CMXY

 

Is this the OS Sq Km with the most caches in it? Starting with this one there are 12 caches within the same OS Sq Km. Or is this a mere pretender to the honour!

The question is not well specifed, so I have made a few assumptions:

 

Listing sites - you say caches but don't say if it is to include all caches or only Groundspeak caches? Initially I included all listing sites but that threw up some anomalies because of cross listing. I could run it again for all sites but counting cross listed caches as only one, but for the present I restricted it to Groundspeak only.

 

All caches or only active caches? I have included only active caches.

 

Cache types? I have included traditionals, multis, letterboxes and wherigos, but not virtuals, earth caches, webcams, unknowns, events, etc. Initially I included unknowns but that introduces anomalies because some unknowns are set in clusters where the final locations obviously are more spread out. Same applies to multis, but to a MUCH lesser degree. For multis, of course, I've used the listed co-ordinates, not the finals.

 

The result is not certain because the data is of variable age up to 3 weeks or so.

 

The square with the highest number of caches using these parameters is 599000 225000, in Colchester, with 16. GC2YPM9 is near the middle of this square

 

Rgds, Andy

Edited by Amberel
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http://coord.info/GC3CMXY

 

Is this the OS Sq Km with the most caches in it? Starting with this one there are 12 caches within the same OS Sq Km. Or is this a mere pretender to the honour!

The question is not well specifed, so I have made a few assumptions:

 

Listing sites - you say caches but don't say if it is to include all caches or only Groundspeak caches? Initially I included all listing sites but that threw up some anomalies because of cross listing. I could run it again for all sites but counting cross listed caches as only one, but for the present I restricted it to Groundspeak only.

 

All caches or only active caches? I have included only active caches.

 

Cache types? I have included traditionals, multis, letterboxes and wherigos, but not virtuals, earth caches, webcams, unknowns, events, etc. Initially I included unknowns but that introduces anomalies because some unknowns are set in clusters where the final locations obviously are more spread out. Same applies to multis, but to a MUCH lesser degree. For multis, of course, I've used the listed co-ordinates, not the finals.

 

The result is not certain because the data is of variable age up to 3 weeks or so.

 

The square with the highest number of caches using these parameters is 599000 225000, in Colchester, with 16. GC2YPM9 is near the middle of this square

 

Rgds, Andy

As the OP used a GC.com example for the location, and as inactive caches really can't be counted (they might not even exist, and they're not supposed to be findable) I think a couple of answers are fairly obvious. Also, you can only use the coordinates of the cache listing (wherever the container actually turns out to be) as it will be pretty much an impossible task otherwise.

Logically I'd include virtuals, webcams, earthcaches and unknowns as they all appear on a search in the locations specified. I'd leave out waymarks and challenges though; just include caches that you see on a search based on the grid square location.

But I'd guess that 12 per grid square is fairly common and there's probably more than 16 in a few places.

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As the OP used a GC.com example for the location ... I think a couple of answers are fairly obvious.

By that reasoning we might say that only traditionals were to be counted, because the example was a trad. But the figure I gave was for GC only.

 

... and as inactive caches really can't be counted (they might not even exist, and they're not supposed to be findable)

Just to clarify, by "active" I mean neither archived nor temporarily unavailable.

 

Logically I'd include virtuals, webcams, earthcaches and unknowns as they all appear on a search in the locations specified ... But I'd guess that 12 per grid square is fairly common and there's probably more than 16 in a few places.
I left out virtuals, webcams and earthcaches (and events) because they aren't actually caches. It's easy enough for me to include them. I excluded unknowns because the published locations bear less relation to the final co-ordinates than most caches, and the "winner" included a large number of almost superimposed unknowns where the finals are almost certainly some distance away. But, again, I can easily include them.

 

BTW, using the original parameters there were 2 squares with 16, the other one was 312000, 372000, at Caerwys, e.g. GC2J00J.

 

Rgds, Andy

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Adding virtuals, webcams and earthcaches brings a 3rd one into the group of count 16, 531000, 181000, Central London, e.g. GC2MT4V

 

Including unknowns (as well as the above) produces the anomaly I mentioned before, where a large cluster of unknowns puts 512000, 147000, Wotton, at the top with count 22, e.g. GC1M100.

 

Rgds, Andy

 

Edited for mis-spelling of cache id

Edited by Amberel
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I didn't have any intention of making it complicated. Simply by using the 'map this location' on GC and not limiting anything on the filter to find which OS Sq had the most caches that can be loaded onto your GPSr and found.

 

Interesting that you've found 3 with 16 in.

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I didn't have any intention of making it complicated. Simply by using the 'map this location' on GC and not limiting anything on the filter to find which OS Sq had the most caches that can be loaded onto your GPSr and found.

 

Interesting that you've found 3 with 16 in.

Don't worry, even the simplest of things becomes complicated in here. :blink:

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I didn't have any intention of making it complicated.

It's OK, it wasn't complicated, it just wasn't well defined :lol: . I'm a programmer, I try to avoid making assumptions, but if I have to I usually explain what they are :lol: .

 

Simply by using the 'map this location' on GC and not limiting anything on the filter to find which OS Sq had the most caches that can be loaded onto your GPSr and found.
So do you want me to run it again but including events and disabled caches?

 

Interesting that you've found 3 with 16 in.
Quite a lot of squares with considerably more than 16 if you include unknowns, but this is because some setters seem to cluster the listing locations for unknowns to achieve a visual effect on the map, even thought the caches themselves are spread about.

 

Rgds, Andy

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I'm sure if I thought about I could work it out, but knowing there are clever folk out there than me, I decided to ask instead (plus I'm just lazy!) - What's the theoretical maximum of actual caches that can fit in a map sq? (not non-box ones obviously). Could make an interesting challenge to fill a grid square with caches! :ph34r:

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I'm sure if I thought about I could work it out, but knowing there are clever folk out there than me, I decided to ask instead (plus I'm just lazy!) - What's the theoretical maximum of actual caches that can fit in a map sq? (not non-box ones obviously). Could make an interesting challenge to fill a grid square with caches! :ph34r:

For traditionals, the sums are easy. 1000 metres per side, 161 metres minimum separation, so max 7 per side. Square that = 49.

 

If you use final locations it's the same for multis and unknown. You can't make any meaningful calculation if you use the listed locations for multis and unknowns.

 

Rgds, Andy

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For traditionals, the sums are easy. 1000 metres per side, 161 metres minimum separation, so max 7 per side. Square that = 49.

 

The sums are anything but easy because the caches do not have to be arranged in a square array.

 

It's possible to fit 53 caches into a 1km-square patch of land.

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For traditionals, the sums are easy. 1000 metres per side, 161 metres minimum separation, so max 7 per side. Square that = 49.

 

The sums are anything but easy because the caches do not have to be arranged in a square array.

 

It's possible to fit 53 caches into a 1km-square patch of land.

Well done :lol: . Should have thought before putting "pen to paper".

 

Rgds, Andy

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I'd say no to events as they only last a short while and are then gone. Disabled ones, yes as they are usually only disabled whilst they get repaired so are still valid i.e. will be enabled at some point.

OK, added in the disabled ones and it made no difference to the "winner", still just the one square with 22.

 

How are you finding this info out?
Running some SQL against an offline database. The reason numbers are approximate is because it takes just under 4 weeks to refresh all the Groundspeak caches.

 

Rgds, Andy

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For traditionals, the sums are easy. 1000 metres per side, 161 metres minimum separation, so max 7 per side. Square that = 49.

 

The sums are anything but easy because the caches do not have to be arranged in a square array.

 

It's possible to fit 53 caches into a 1km-square patch of land.

 

I was just about to say that but you beat me to it!

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For traditionals, the sums are easy. 1000 metres per side, 161 metres minimum separation, so max 7 per side. Square that = 49.

 

The sums are anything but easy because the caches do not have to be arranged in a square array.

 

It's possible to fit 53 caches into a 1km-square patch of land.

 

I was just about to say that but you beat me to it!

 

Is 53 based on putting the caches and their full proximity circle within the square? Or did you take into account the the outer edges of the square don't have to contain the whole proximity circle?

 

Jon.

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I just looked it up. See the N=53 case here.

I wasn't doubting you - when I said "Should have thought before putting "pen to paper"" I meant me!

 

But having looked at your link, might it not be more than 53? I haven't studied it but there are some shown with more than 53 - or are they smaller circles? I'd work it out, but having messed up once I'll leave it to someone else :lol: .

 

Rgds, Andy

Edited by Amberel
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Is 53 based on putting the caches and their full proximity circle within the square? Or did you take into account the the outer edges of the square don't have to contain the whole proximity circle?

The latter.

 

That's alright then! Bloody tight squeeze isn't it!

 

There are exceptions to the proximity rule though, so it's certainly possible to get more than the mathematical maximum of caches in a square.

 

Jon.

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It works as follows.

 

This page tells you the largest-known radius of N circles that could fit fully into a unit square. I'll show in a moment that our circles have radius 0.06931244 "units", which according to the page is smaller than the max known for N=53 (0.06994725...) and larger than the max known for N=54 (0.06864554...). So you could fit 53 of them into a unit square.

 

OK, so our caches have exclusion radius R=0.1609344/2 km; what's that in "units"? If circles with radius U units can fit into a unit square then points (~caches) with exclusion-radius U units can fit into a square of side 1-2U; thus points with exclusion-radius U/(1-2U) units can fit into a unit square. If U/(1-2U) = 0.1609344/2 then we must have U = 0.06931244 as claimed.

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See, glad I asked! :lol:

 

I guess you could do this on a moor or in a wood. As the skull said: power squares! Oh no! :unsure:

 

There was, I remember, a cache set in 'the most empty OS grid square' a few years back. Just white space with a power line cutting through the corner. No contours, paths or buildings. East Anglia way IIRC. Shame it got archived as I thought it was a curious and interesting claim to fame.

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It would look something like this: B)

 

77f8455b-4dd8-4dae-bc42-1302e1f5f13a.jpg?rnd=0.3945124

 

Which looks like 52 to me!

 

Mark

And then what could be added permanently, within the rules. i.e. an earth cache on one corner that overlooks the errr first GB Sq Km full of caches? Perhaps two Earth caches. Are there any others that could fit in there without breaking any rules? Lets make it a Super Power Square :)
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See, glad I asked! :lol:

 

I guess you could do this on a moor or in a wood. As the skull said: power squares! Oh no! :unsure:

 

There was, I remember, a cache set in 'the most empty OS grid square' a few years back. Just white space with a power line cutting through the corner. No contours, paths or buildings. East Anglia way IIRC. Shame it got archived as I thought it was a curious and interesting claim to fame.

This was the cache: "The Most Boring Cache in Britain".

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Are there any others that could fit in there without breaking any rules? Lets make it a Super Power Square :)

Yes, is perfectly allowable to have 1000 caches in the one square, if you use the listed co-ordinates and not the final co-ordinates of a physical cache. That was the point I was making about unknowns and multis, and the ambiguities in the question.

 

Rgds, Andy

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Who knew?

Who knew what? Which square had the greatest number of caches?

 

I gave various answers depending on what criteria are used for selection, and with the minor reservation that my database takes about 25 days to update, I believe those answers are correct for each selection.

 

Rgds, Andy

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Amberel, are you mixing work and pleasure again ? :laughing:

I often do - it's one of the bonuses of working for myself :lol: . If you are ever down this way take a look at some of my Church Micros (especially Littleton), definite crossover between work and pleasure there :lol: .

 

Rgds, Andy

Edited by Amberel
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Are there any others that could fit in there without breaking any rules? Lets make it a Super Power Square :)

Yes, is perfectly allowable to have 1000 caches in the one square, if you use the listed co-ordinates and not the final co-ordinates of a physical cache. That was the point I was making about unknowns and multis, and the ambiguities in the question.

 

Rgds, Andy

I guess the cache or cache subject would have to actually be in the Sq. I see what you mean now by 'unknown', wasn't clear in your first post.
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I guess the cache or cache subject would have to actually be in the Sq. I see what you mean now by 'unknown', wasn't clear in your first post.
"unknown" is a cache type - some people call them "puzzle" but that is a bit misleading because there is no cache type of "puzzle", they are just a subset of "unknown".

 

You will find that some setters of "unknown" caches may set the listed co-ordinates of a group of "unknowns" for visual effect, e.g. a smiley face, or whatever. Obviously this is a bit of fun, but it illustrates that the listed co-ordinates are not a guide to the actual cache density in an OS square. Multi's aren't either, though they arguably have a slightly stronger link because they are (supposed to be) the actual co-ordinates of the first stage.

 

But you obviously realise that "... the cache or cache subject would have to actually be in the Sq." is not possible for me to do, as I haven't done every multi and solved every puzzle in the country :lol: . So any calculation has to be on listed co-ordinates, and using an arbitrary set of cache types and cache states. HH felt that the choice of cache types and states was obvious, but only 3 of us have expressed what we thought should be included and we have at least 4 quite major differences of opinion, so it's not entirely straightforward.

 

Rgds, Andy

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I'll settle for 52 as above, but that wasn't my question. That was, which actual Sq in the UK has the most. And to clarify that's as viewed on GC maps - obviously using the Chrome/Firefox script that allows you to see OS maps. So a multi with published co ords IN the Sq would count as that is where the icon appears and tends to be where you start etc.

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I'll settle for 52 as above, but that wasn't my question. That was, which actual Sq in the UK has the most. And to clarify that's as viewed on GC maps - obviously using the Chrome/Firefox script that allows you to see OS maps. So a multi with published co ords IN the Sq would count as that is where the icon appears and tends to be where you start etc.

To recap, that was:

 

17 if you include trads, multis, letterboxes, wherigos, virtuals, webcams and earthcaches, but not unknowns, events, etc.

312000, 372000 comprising 16 trads and a multi (one of the trads currently is disabled).

 

22 if you also include "unknowns".

512000, 147000, these are nearly all unknowns with co-ordinates set in a radius of about 60 metres.

 

I should add one more qualifier - Groundspeak's listed OS grid refs use a very poor conversion algorithm, with a typical error of 5 or 6 metres, to calculate the totals above I use a conversion algorithm with an accuracy of about 1.5 metres, but it means on a boundary condition they might lie in a different square.

 

Rgds, Andy

Edited by Amberel
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I'll settle for 52 as above

Then you're settling for second best: 53 is possible, as described previously.

OK, 53 it is then :)

 

I'll settle for 52 as above, but that wasn't my question. That was, which actual Sq in the UK has the most. And to clarify that's as viewed on GC maps - obviously using the Chrome/Firefox script that allows you to see OS maps. So a multi with published co ords IN the Sq would count as that is where the icon appears and tends to be where you start etc.

To recap, that was:

 

17 if you include trads, multis, letterboxes, wherigos, virtuals, webcams and earthcaches, but not unknowns, events, etc.

312000, 372000 comprising 16 trads and a multi (one of the trads currently is disabled).

 

22 if you also include "unknowns".

512000, 147000, these are nearly all unknowns with co-ordinates set in a radius of about 60 metres.

 

I should add one more qualifier - Groundspeak's listed OS grid refs use a very poor conversion algorithm, with a typical error of 5 or 6 metres, to calculate the totals above I use a conversion algorithm with an accuracy of about 1.5 metres, but it means on a boundary condition they might lie in a different square.

 

Rgds, Andy

Andy, you are a serious Geek!, but well done for finding the answers although OS map co ords would be helpful with their alpha reference so that those of us with everyday map reading skills can find them - or just put a link of one of the caches in each Sq so we can go find it in GC?

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Andy, you are a serious Geek!

It's just my job. In the late eighties I was UK technical support for a GPSr chipset manufacturer, so I wrote the co-ordinate transforms more than 20 years ago. And my job now involves some database work, so if the data is already there, which it is, pulling this stuff out of it is easy.
... or just put a link of one of the caches in each Sq so we can go find it in GC?
GC2J00J is in 312000, 372000. GC1HH4J is in 512000, 147000.

 

Rgds, Andy

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OS map co ords would be helpful with their alpha reference

The conversion is easy: think of the entire grid as a graph with its origin at the OS false origin (southwest corner of square SV). Each 100km square then can be referred to as either x,y or by its alpha designation.

 

To use Andy's examples: 312000 372000 is square 3,3 which is SJ so the full reference is SJ 12000 72000; 512000, 147000 is in square 5,1 which is TQ so the full reference is TQ 12000 47000.

 

This image will probably makes things clear.

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Andy, you're finding this too easy, so I've got a harder challenge for you. Say that a collection of caches(*) is a "blot on the landscape" if they are so tightly clustered that the 0.1-mile exclusion rule forbids placement of anything else within their convex hull. The size of the blot is defined as the area of the convex hull. Your challenge: find the largest blot on the UK landscape. In other words: find the largest "rounded" area of land in which there's no room for any more caches.

 

(*) defined in whatever way is convenient.

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Andy, you're finding this too easy, so I've got a harder challenge for you. Say that a collection of caches(*) is a "blot on the landscape" if they are so tightly clustered that the 0.1-mile exclusion rule forbids placement of anything else within their convex hull. The size of the blot is defined as the area of the convex hull. Your challenge: find the largest blot on the UK landscape. In other words: find the largest "rounded" area of land in which there's no room for any more caches.

 

(*) defined in whatever way is convenient.

I haven't been ignoring you - took the campervan down to Dorset at dawn on Thursday morning for a spot of caching, and only got back 15 minutes ago so only just seen your question.

 

That is a MUCH harder problem. I don't have an instant algorithm for it, it will need a bit of thought, and I've got about 70 caches to log before I do that :lol: .

 

Rgds, Andy

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That is a MUCH harder problem.

Unfortunately, I think it's ill-defined: in many cases, the convex hull of a set of caches will be completely saturated (no new caches will fit) only if the "exclusion zone" around one or more caches outside of the convex hull is taken into consideration.

 

A simpler question, allowing for shapes other than rounded "blots", would be: show me the top ten largest "islands of exclusion" in the UK. The i.o.e. containing cache X is defined as: start with the exclusion zone around X; add all exclusion zones that overlap that; add all exclusion zones that overlap those; keep going until you can add no more. The area's calculated by application of the inclusion-exclusion principle.

 

If done in the U.S. then you'd get a lot of powertrails scoring highly, making long thin islands of exclusion: not so much "blots" as "scars" on the landscape.

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That is a MUCH harder problem.
A simpler question, allowing for shapes other than rounded "blots", would be: show me the top ten largest "islands of exclusion" in the UK. The i.o.e. containing cache X is defined as: start with the exclusion zone around X; add all exclusion zones that overlap that; add all exclusion zones that overlap those; keep going until you can add no more. The area's calculated by application of the inclusion-exclusion principle.

 

If done in the U.S. then you'd get a lot of powertrails scoring highly, making long thin islands of exclusion: not so much "blots" as "scars" on the landscape.

30 logs done, only another 41 to go. But I've also got some urgent work for a customer this morning.

 

The initial problem was very straightforward because it was a matter of simple addition. Even this "simplified" one is far trickier than the initial problem. The only practical way I can see to do it would be to quantize the surface, but as quantization is implicit in the fixed precision of the published data points I don't really see that as an issue.

 

As a diversion, after mentioning the fixed precision of the published data points, the Caravan Club web site greatly amuses me. They give the lat/long of CLs, but these are not provided by the farmer, they get them from somewhere else and the accuracy suggests they must compute them from the postcode :lol: . But despite the questionable accuracy, they publish the position to 15 decimal places :lol: . A case of the programmer not understanding the difference between accuracy and resolution, I think :lol: .

 

Rgds, Andy

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The initial problem was very straightforward because it was a matter of simple addition. Even this "simplified" one is far trickier than the initial problem. The only practical way I can see to do it would be to quantize the surface, but as quantization is implicit in the fixed precision of the published data points I don't really see that as an issue.

 

Quantisation should be unnecessary for finding the islands-of-exclusion. Calculating the area could get a little hairy, and you may well prefer to solve the overlapping-circles problem by discrete approximation.

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The initial problem was very straightforward because it was a matter of simple addition. Even this "simplified" one is far trickier than the initial problem. The only practical way I can see to do it would be to quantize the surface, but as quantization is implicit in the fixed precision of the published data points I don't really see that as an issue.

 

Quantisation should be unnecessary for finding the islands-of-exclusion. Calculating the area could get a little hairy, and you may well prefer to solve the overlapping-circles problem by discrete approximation.

It might not be necessary if you are a (lot) better at maths than I am, but it's way beyond my capabilities. The only way I can see to define the boundary would be by a list of arcs, but I don't know how to generate such a list, nor how to do anything useful with it even if I could :lol: .

 

Hopefully I might have a look at this later today, maybe while I'm watching the Ireland/France match.

 

Rgds, Andy

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