Counter intuitive puzzle

No, that's because the question was created by someone who based their conception of universal physics around classical/Newtonian physics rather than General Relativity. :p
 
So basically you just wanted to show off how much you knew about relativity?
 
For the airplane treadmill question, the problem is with two different interpretations of the reference frame for determining speed. There are two correct interpretations of the question. One of them makes sense, the other is stupid. But people are stupid.

The first interpretation, and the one which actually makes sense, all speeds are taken relative to the universal ground (the earth). The speed of the plane is measured against the ground, not against the treadmill. So when the plane moves forward relative to the earth, the treadmill moves backwards relative to the earth at the same speed. The result is that the wheels spin twice as fast as normal and the plane takes off.

The second stupider interpretation is that the plane's speed is measured relative to the treadmill. Because the plane speed and treadmill speed are linked. Their is only one stable state (the plane is not moving relative to the earth) So as the plane applies a finite amount of thrust, the theoretical treadmill must accelerate constantly in order to constantly accelerate the rotational mass of the wheels in order to counter the thrust of the plane. This results in a treadmill speed which approaches infinity for any finite forward thrust the plane generates. In reality, such a treadmill would begin to cause the air above it to move at some percentage of its speed. This would eventually create enough relative air speed to let the airplane fly, or the wheels would melt and the plane would not fly.
 
There are three prisoners on death row. They are told that one of them has been chosen at random to be executed the next day, and that the other two will be freed. One of the prisoners privately begs the warden to tell him the name of at least one of the people who will be freed. The warden says "Susie will be freed."

What is the chance that that the prisoner who asked the question will be the one executed?
Click to expand...
100% Because the warden doesn't like being asked stupid questions by prisoners.

There is a single path up a mountain. A climber begins his ascent at 6:00am and reaches the top at 6:00pm. The next morning he begins his descent at 6:00am and reaches the bottom at 6:00pm. Each day of climbing he travels at different speeds during the climb, resting in different areas, stopping for lunch, etcetera. What are the chances that there is a spot that he passes at the exact same time both days?
Click to expand...
100%. Imagine a ghost of yourself climbing up the mountain as you climb down it. Kind of like the best time records from Mario Kart. At some point in the day, you will pass your ghost going upwards as you go downwards. At that time, you are both at the same point.

A shopkeeper has two new baby beagles thats she is trying to give away, but she doesnt know the genders of either one. You tell her you only want a male, and she phones the person who is bathing them and asks "Is at least one a male?" to which he responds "yes."

What is the probability that the other one is male?
Click to expand...
59% because dog litters are naturally skewed towards males.
 
This is an old one.

You have 4 small islands arranges in a perfect square 200 feet on each side. What is the shortest length of bridge you can build to connect all 4 islands and what does the result look like?
It's less than 565 feet
 
Dan said:
This is an old one.

You have 4 small islands arranges in a perfect square 200 feet on each side. What is the shortest length of bridge you can build to connect all 4 islands and what does the result look like?
It's less than 565 feet
Click to expand...
First thing that comes to mind is a X between them all?
 
Shit I got it I think
)-(

Edit: )( is smaller. that must be it
 
Krynn, post the answers. I'm very curious if I'm correct on some of them.
 
Solaris said:
Shit I got it I think
)-(

Edit: )( is smaller. that must be it
Click to expand...

Is it? If the islands are 200 feet apart, the full circle would have a radius of 100 feet, or a length of pi * 100 = 314 feet, times two for the other arch = 628 feet. Dan already said that it's less than 565 feet, which is the length of building that X shaped bridge between the islands.
 
Tacoeaterguy said:
Krynn, post the answers. I'm very curious if I'm correct on some of them.
Click to expand...

Post yours first :D No cheating and saying you were right after I post the answers.

And I'll post them when I get home.
 
If I remember correctly from Geometry class 7 years ago the answer is something like this:

140jmh0.jpg
 
PvtRyan said:
Is it? If the islands are 200 feet apart, the full circle would have a radius of 100 feet, or a length of pi * 100 = 314 feet, times two for the other arch = 628 feet. Dan already said that it's less than 565 feet, which is the length of building that X shaped bridge between the islands.
Click to expand...

You're formulas wrong but it would be a bit too big.

I think vegetas an improvement on mine. I think he might have it.
 
If the line in the middle is 100 feet long then it would give 547.something feet altogether.
 
1. No. The initial lottery was 20/32 (Reduced 5/8). The second lottery was 1/13.

2. Well, logically, if you're on death row, there's no way you are getting out of an execution, so I would assume that the warden was just lying to them. But since that's probably not it, I would say 50%.

3. There's really no way of knowing.

4. 50%

5. This one is frustrating.
 
Dan said:
100%. Imagine a ghost of yourself climbing up the mountain as you climb down it. Kind of like the best time records from Mario Kart. At some point in the day, you will pass your ghost going upwards as you go downwards. At that time, you are both at the same point.
Click to expand...

Ah, duh. Thanks for explaining that, I was really stumped. But that makes perfect sense now.

Riom, it's not about finding the most efficient path to any destination, it's about using the least amount of bridge.
 
"There are three prisoners on death row. They are told that one of them has been chosen at random to be executed the next day, and that the other two will be freed. One of the prisoners privately begs the warden to tell him the name of at least one of the people who will be freed. The warden says "Susie will be freed."

What is the chance that that the prisoner who asked the question will be the one executed?"
Click to expand...

Okay, so there are three people. The man with the warden, Susie still in her cell, and another, gender unknown person we'll call Jamie.

So there are two people, one randomly to die. So it's 50/50. What's hard about that?
 
Solaris said:
You're formulas wrong but it would be a bit too big.

I think vegetas an improvement on mine. I think he might have it.
Click to expand...

My formula is correct?

But Vegeta is probably right. According to my program, the ideal length for the center bridge is 84.42 which would give the bridge a total length of 546.41.
 
Solaris said:
Okay, so there are three people. The man with the warden, Susie still in her cell, and another, gender unknown person we'll call Jamie.

So there are two people, one randomly to die. So it's 50/50. What's hard about that?
Click to expand...

I think the question is missing a crucial piece of info, it has to be stated that the Warden will not tell the prisoner about his own fate.

It's a reversed version of this: http://en.wikipedia.org/wiki/Three_Prisoners_problem
 
Haha, the prisoner asking the question is not Susie. And vegeta is sort of correct, but he has it backwards. Theres still only a 1/3 chance that the prisoner who asked the question will be executed, while the other prisoner (not susie obviously) has a 2/3 chance.
 
PvtRyan said:
My formula is correct?

But Vegeta is probably right. According to my program, the ideal length for the center bridge is 84.42 which would give the bridge a total length of 546.41.
Click to expand...


Circumferance is Pi*d

Area is pi*r^2
 
1. Obvious, 1/13 compared to 5/8 which has been said already.

2.The one with the prisoners is the monty hall problem all over again. You "pick" a prisoner and there's a 1/3 chance that you'll get executed (win the prize). Then you ask the warden to reveal the name of one of the prisoners who won't be executed (reveal one of the "goats"). Now you still have 1/3 chance of being executed but the other guy went up to 2/3 chance.

3. Like Dan said: Imagine two people, one starting at the top and one starting at the bottom. If they walk on the same path and the one on the top walks to the bottom and vice versa they will meet at one point. So 100% chance.

4.It's 1/3.
At first the possible combinations are:

Male Female
Male Male
Female Female
Female Male

But since at least one of them is male leaves us with:

Male Female
Male Male
Female Male

and out of those 3 combinations only 1 is male/male which gives it a 1 in 3 chance.

5. Impossible. If he drives 60mph, he'll finish the track twice as fast as if he was driving 30mph. The average speed will then be (30 + 30 + 60)/3 = 40mph. If he drives at 90mph, he'll finish it 3 times faster and the average speed would be (30 + 30 + 30 + 90)/4 = 45mph. The formula would be (30*n + 30*n)/(n+1). Simplified (60*n)/(n+1). And if we want 60mph that would give us:
(60*n)/(n+1) = 60
60*n = 60 * (n+1)
60*n = 60*n + 60
n = n+1

wat.
 
PvtRyan said:
I know. But since it was two semi-circles, their length/circumference is pi * (d/2) or in other words: pi * r.
Click to expand...

Haha but there's two of them, so it makes no difference :p

Anyway, we demand answers!!!!!!"!
 
Kisze knocked it out of the park. Everything he said is correct.

Smith and Jones started off walking together to a nearby town. Smith walked the first half-mile at one mile per hour faster than Jones. Smith then walks the second half of the mile at one mile per hour slower than Jones. Jones walks a constant speed the entire way. Who arrives first?
Click to expand...
 
There are three prisoners on death row. They are told that one of them has been chosen at random to be executed the next day, and that the other two will be freed. One of the prisoners privately begs the warden to tell him the name of at least one of the people who will be freed. The warden says "Susie will be freed."

What is the chance that that the prisoner who asked the question will be the one executed?
Click to expand...

This is not the monty hall problem re-worded.

This still doesn't feel right. Let me re-write it in terms of the Monty hall problem with the 'prisoner' becoming a door, and being executed means 'having a car behind it'.

There are three doors, one has a car behind chosen at random. The gameshow host tells this door, that at least one of the other doors is empty.

What is the chance that the door has the car in it.

No, it's definitely 50/50.

Somethings different, I'll do a probability tree and come back.
 
Krynn72 said:
Smith and Jones started off walking together to a nearby town. Smith walked the first half-mile at one mile per hour faster than Jones. Smith then walks the second half of the mile at one mile per hour slower than Jones. Jones walks a constant speed the entire way. Who arrives first?
Click to expand...

Jones. Smith moves faster for less than half the journey, since he reaches the halfway/slowdown point before Jones.
 
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