Spider

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uzurpatorul
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Spider

Postby uzurpatorul » Sun Jun 21, 2009 9:41 am UTC

A rectangular room measures 7.5 meters in length and 3 meters in width. The room has a height of 3 meters. A spider sits 25 centimeters down from the ceiling at the middle of one of the short walls. A sleeping fly sits 25 centimeters up from the floor at the middle of the opposite wall. The spider wants to walk (i.e., move along the walls, floor, and ceiling only) to the fly to catch it.

Spoiler:
the solution can be verified here http://www.projecteureka.org/problem/question/156

Yat
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Re: Spider

Postby Yat » Sun Jun 21, 2009 10:15 am UTC

I see you are stuck on this one... If you give me a clue about the bear, I give you a clue about the spider !

Just kidding :wink:

Spoiler:
Unfold the room, everything will become straight forward.

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Re: Spider

Postby skeptical scientist » Sun Jun 21, 2009 10:51 am UTC

Reply to previous post, with further hint:
Spoiler:
Ah, but HOW do you unfold the room?

Solution:
Spoiler:
Clearly the spider must take a geodesic path, but there are several such paths to choose from. (In fact, there are infinitely many.) We can think of geodesic paths as straight lines in some "unfolding" of the room, to use the terminology of the previous poster, but there are many different ways of doing this. A little thinking reduces it to three possibilities, each of which might reasonably be the best:
A)
Image
B)
Image
C)
Image
It is easy to calculate the path lengths as:
A) [imath].25m+7.5m+2.75m=10.5m[/imath]
B) [imath]\sqrt{(9.25m)^2+(4.25m)^2} \approx 10.2m[/imath]
C) [imath]\sqrt{(8m)^2+(6m)^2}=10m[/imath]
Clearly, method C) is optimal, and this answer checks out on the project EUREKA site. In the optimal solution, the spider traverses parts of three of the four walls, and both the floor and the ceiling.

I think I first encountered this puzzle in middle school. I like how the numbers are cleverly arranged:
Spoiler:
The correct solution yields a 3-4-5 triangle.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

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Moonbeam
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Re: Spider

Postby Moonbeam » Sun Jun 21, 2009 11:26 am UTC

Yat wrote: If you give me a clue about the bear, I give you a clue about the spider !


I'm also stuck on the bear - I haven't got a clue what it's going on about !!!

By the way - what number is the spider puzzle - I can't seem to find it :? .

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Re: Spider

Postby skeptical scientist » Sun Jun 21, 2009 12:50 pm UTC

156. The link is in the "spoiler" in the first post, which isn't really a spoiler but a link to the ProjectEUREKA page.

Re: the bear-
Spoiler:
The standard version of this riddle is that a hunter walks one mile south, then west/east, then north, and winds up where he started. On his walk he meets a bear. What color is the bear? The solution is that he must be at the north pole or near the south pole, so the bear is a polar bear, and therefore white.

If we follow this pattern, we should figure out where we are, and what kind of bears live there, and draw conclusions based on that. The only information we have tells us that the bear is near a hole in the ground, and wherever he is the local gravitational acceleration is [imath]20 m/s^2\approx 2g[/imath]. But I can't think of anywhere which has a gravity of 2 gees and a bear population, so I'm stuck.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

Bravemuta
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Re: Spider

Postby Bravemuta » Sun Jun 21, 2009 3:42 pm UTC

Concerning the bear:

This is a rather stab-worthy question because
Spoiler:
The time is measure from when the bear enters the hole.

so,
Spoiler:
It's not the gravitational acceleration that is different from what you'd expect. The bear is on Planet Earth. Now, if the acceleration is 1g, what else ca must be different for the bear to reach the bottom of the pit in 1 second?

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Moonbeam
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Re: Spider

Postby Moonbeam » Sun Jun 21, 2009 4:50 pm UTC

Bravemuta wrote:Concerning the bear:

This is a rather stab-worthy question because
Spoiler:
The time is measure from when the bear enters the hole.

so,
Spoiler:
It's not the gravitational acceleration that is different from what you'd expect. The bear is on Planet Earth. Now, if the acceleration is 1g, what else ca must be different for the bear to reach the bottom of the pit in 1 second?


I'd already thought about:

Spoiler:
The acceleration may still be 1g - giving the bear an initial velcity of 5m per second.
So we have a bear the falls into a hole with an initial velocity of 5m per second ..... I'm still stumped :oops: .

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Re: Spider

Postby Cosmologicon » Sun Jun 21, 2009 4:59 pm UTC

Well, is there a bear that can...
Spoiler:
jump 1.25 meters in the air? Or one that's likely to fall out of a low tree?

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Moonbeam
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Re: Spider

Postby Moonbeam » Sun Jun 21, 2009 5:31 pm UTC

Cosmologicon wrote:Well, is there a bear that can...
Spoiler:
jump 1.25 meters in the air? Or one that's likely to fall out of a low tree?


I keep thinking up something, only to come on here and find that someone has beat me to it.

I also worked out that:

Spoiler:
If the bear falls in the hole from a distance of 1.25m above the hole, then everything holds true - still stumped though :evil:

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Re: Spider

Postby Bravemuta » Sun Jun 21, 2009 6:03 pm UTC

Spoiler:
Why would the bear fall from a height? Or, to put this in other words, what kind of bears aren't always on ground level?

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Moonbeam
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Re: Spider

Postby Moonbeam » Sun Jun 21, 2009 6:22 pm UTC

Bravemuta wrote:
Spoiler:
Why would the bear fall from a height? Or, to put this in other words, what kind of bears aren't always on ground level?


Well:

Spoiler:
I thought that all bears could climb trees - so technically speaking the bear could be black and white (panda), brown or black ??

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Re: Spider

Postby Cosmologicon » Sun Jun 21, 2009 6:43 pm UTC

Clearly I don't know enough about bears.
Spoiler:
According to Wikipedia, "The Giant Panda is able to climb and take shelter in hollow trees or rock crevices", whereas American Black Bears "climb trees to escape danger", and Polar Bears "depend on sea ice as a platform for hunting". Brown Bears are apparently too big to climb trees, but surely they go up on rocks from time to time.

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Re: Spider

Postby skeptical scientist » Sun Jun 21, 2009 6:47 pm UTC

I have a solution which is completely satisfying to me, but which doesn't seem to satisfy projectEUREKA. (Bravemuta, check your PMs.) Since I don't want to throw people off on the wrong track if I'm thinking in the wrong direction, I'll hold off posting it for now.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

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Moonbeam
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Re: Spider

Postby Moonbeam » Sun Jun 21, 2009 6:49 pm UTC

Well, the answer isn't:

Spoiler:
Red (covered in blood from falling a great height), white, black or brown - 'cos I just tried inputting these as the answer and all came out as incorrect.

uzurpatorul
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Re: Spider

Postby uzurpatorul » Sun Jun 21, 2009 7:03 pm UTC

for the bear problem:
Spoiler:
the answer is black and white (aka panda). The bear problem requires a solution that may be interpretable, the idea is as follows:

because the bear gets to the bottom of the hole in 1s (10m), assuming g = 10m/s^2, d = gt^2/2 = 5m (without initial speed), hence the bear is falling from above the ground (it can be anything).

Now, most likely the bear fell from a tree, so it must be a panda (hence black and white).

I know the answer is debatable and there are plenty of bears that climb trees (including black ones).

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Re: Spider

Postby skeptical scientist » Sun Jun 21, 2009 7:19 pm UTC

Aw, I think that answer is kind of lame.
Spoiler:
After all, many species of bears climb trees, or could otherwise fall from a few feet above ground into a hole, so none of the details of the puzzle help you identify the species of bear at all.

I like the solution I came up with better:
Spoiler:
Physics tells us that the bear fell from a height of about 1.3 meters into a 10 meter hole. I asked myself, where are you likely to find a 10 meter hole in the ground? The first thing that came to mind was a well. And since 1.3 meters is about the height of a man's arm, I immediately pictured someone dropping a coin into a well (to make a wish). So naturally I thought that the bear was likely to be a device on a coin, such as the toonie, making the correct answer, "gold."
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

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Moonbeam
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Re: Spider

Postby Moonbeam » Sun Jun 21, 2009 7:53 pm UTC

skeptical scientist wrote:Aw, I think that answer is kind of lame.


Ditto.

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quintopia
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Re: Spider

Postby quintopia » Mon Jun 22, 2009 2:26 pm UTC

It's even lamer when you take into account the fact that
Spoiler:
pandas aren't bears :(

Bravemuta
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Re: Spider

Postby Bravemuta » Mon Jun 22, 2009 3:01 pm UTC


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Re: Spider

Postby Cosmologicon » Mon Jun 22, 2009 6:14 pm UTC

They used to be raccoons, but I guess they changed their mind.

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Moonbeam
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Re: Spider

Postby Moonbeam » Mon Jun 22, 2009 7:32 pm UTC

I emailed them yesterday telling them how lame I though the answer was.

Got a reply today:

Hi James,

I knew right from the beginning that there are multiple solutions, you forgot also about Koala Bear (technically not a bear). I will rephrase the problem ;-), I think Pandas are the only vegetarian bears. I will change the problem like this:

"A vegetarian bear falls into a hole in the ground. The hole is 10 meters deep. After one second the bear reaches the bottom of the hole. What color is the bear?"

What do u think?, probably is too easy now.

Cheers,
R.


I thought they were kidding, but they have actually changed the wording of the puzzle:

http://www.projecteureka.org/problem/question/335

The mind boggles :? :shock: .

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quintopia
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Re: Spider

Postby quintopia » Mon Jun 22, 2009 9:49 pm UTC

wikipedia wrote:For many decades the precise taxonomic classification of the Giant Panda was under debate as both it and the distantly related Red Panda share characteristics of both bears and raccoons. However, molecular studies suggest that the Giant Panda is a true bear and part of the Ursidae family,[21][22] though it differentiated early in history from the main ursine stock. The Giant Panda's closest ursine relative is the Spectacled Bear of South America. Disagreement still remains about whether or not the Red Panda belongs in Ursidae, the raccoon family Procyonidae, or in its own family, Ailuridae. The Giant Panda has been referred to as a living fossil.[23]


Well, I guess I was wrong, but at least it's still disputed. . .

uzurpatorul
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Re: Spider

Postby uzurpatorul » Tue Jun 23, 2009 8:39 am UTC

Did you also know that
The giant panda remains the world's most threatened bear species, according to a new World Conservation Union (IUCN) report released November 12, 2007.
The assessment found that six of the world's eight bear species—75 percent—are threatened with extinction, with Asia and South America being "the areas most in need of urgent conservation action."
Confined to south-central China, the giant panda is the only bear species that the IUCN lists as endangered, meaning it faces "a very high risk of extinction in the wild."


This problem is part of a shameless marketing campaign to raise awareness about panda endangerment.

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VectorZero
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Re: Spider

Postby VectorZero » Sun Mar 21, 2010 12:48 pm UTC

uzurpatorul wrote:This problem is part of a shameless marketing campaign to raise awareness about panda endangerment.
To be fair they did use up a lot of pandas gathering the experimental data for the puzzle.
Van wrote:Fireballs don't lie.


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