The Glade 4.0

Ok, first I must preface this with I AM NOT OCD. I swear.

Moving on...

The carpet in our office is made up of square carpet "tiles". Each as a quarter circle design:



The circle is subtle, and beneath the design on the carpet itself. But, you can see it.

Now, the tiles are placed with random (seemingly) orientation. Therefore, one can expect in any group of 4 tiles, there is a small chance that a circle is formed, an equal chance that a curvy "+" sign is formed, and a great chance that some other dismissible pattern is formed.

So first, when walking around the office, I immediately notice when there's a circle. So much so that I have thus far found 5 circles and I remember where they are. So there's that.

Secondly, I find myself wanting to calculate the odds of a circle, and thereby extrapolate to predict how many circles are in the building. However, it's not as easy as you might thing. While you could quickly calculate how often an isolated group of 4 tiles would make a circle, the building is not made up of isolated groups of 4 tiles. Each tile that fails to contribute to a specific group of 4's circle is necessarily contributing to another group.

This is solvable, but I refuse to pick up a pencil and a calculator, because, well, that would be OCD - and as I said I'm not OCD. Instead, I am left to try and figure this out in my head as I walk around the office (this is the non-OCD alternative), which I have not devoted enough energy to being able to do.

So, instead, it's just distracting and annoying.

.

Choose an arbitrary tile. That tile will contribute to one block's circle, if the appropriately chosen other 3 tiles are also oriented in the correct 1 direction out of 4 possible directions.

(1/4)^3, then, no? 1/128

This doesn't account for disruptions in the probability caused by edges of the tile space, etc.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

You could probably formulate a query on WolframAlpha that would tell you.

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LOL I mentioned this to my father. His response:

This is easily solvable without mathematics. Every time you find a circle, spill coffee on it. Over time, these tiles will be replaced, assumably with a random pattern. The number of circles in the building will converge on zero.

Wouldn't the number of possible combinations of 4) 4 sided objects be 4^4, and since only 1 confirms to a circle ... 1 out of 256?

Then, you'd need to know the number of instances in the room where there are 4 adjacent tiles...and that depends on the room.

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In time, this too shall pass.

You're calculating the probability of a given 4-tile square containing a circle.

I'm calculating the probability that a given tile will be part of a circle.

I don't need to calculate the size of the room -- I've calculated for an infinitely tiled plane, and stated that I'm not accounting for boundaries.

It's like that old joke among physicists.. "Assuming a spherical cow..."

_________________
"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

Right, but each 4x4 group that fails to form a circle increases the odds of a circle being formed adjacent, since at least one quarter circle must be turned away and toward the next potential group. And thus, the two groups in question overlap.

I'm not following you with this. I get the premise, but what's with the then, no?

The "then, no?" is a negatively framed question format. Why did I choose that? I have no idea.

_________________
"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

It is more OCD to go on about how you're not OCD enough to get out a pencil and paper and work out the problem while you wander around being distracted and irritated by the problem than it would be to actually do the math.

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Buckle your pants or they might fall down.

Someone needs to purchase a sense of humor.

I'm sorry, but I have to do this to you:

http://www.reddit.com/r/mildlyinfuriating
http://www.reddit.com/r/mildlyinteresting

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Sail forth! steer for the deep waters only!
Reckless, O soul, exploring, I with thee, and thou with me;
For we are bound where mariner has not yet dared to go,
And we will risk the ship, ourselves and all.

OMG NO!!!!

Some carpet layer really hates bishops.

_________________
"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

At least, he hates the black bishop.

_________________
Buckle your pants or they might fall down.

Racism!

_________________
"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades