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On May 11 2012 07:14 CptZouglou wrote:Enjoy this new (quite difficult) riddle: You are a russian bomber, and you want to send a bomb on a nuclear submarine. The submarine is located on a line and has an integer position (can be negative). It moves at a constant integer speed (can be negative too) each second. The good part is that you have an unlimited amount of bombs, and you can send one each second at a any position. The problem is that you don't know where is the submarine at time 0, and what its speed is. Is there a way to ensure that you can send hit the submarine in a finite amount of time ? If yes, what is your strategy ? hint: + Show Spoiler +
Yes! Consider the problem as finding two parameters initial position (p) and speed (s). After t seconds, the submarine is at position p + t*s. Try and find a way to explore all possible initial positions and speeds !
I'm actually curious about the answer for this... Is there another hint?
On the ball problem-
+ Show Spoiler +Ok, I think I realize how I got myself confused on why the answer is 1/2 and why some people are saying that the answer is 1/2.
Suppose that instead of you, your friend is the one in the problem, and you are being posed the problem. Now, your friend chooses a random pocket. Your friend looks into the pocket (so he knows the combination of the two balls). If, it's WW, then discard the trial. However, if it's a pocket with at least one orange ball- count the trial. Your friend looks into the pocket and pulls out an orange ball. Now you are asked what the probability of the other ball is orange. In this case the answer is 1/2.
However, I think the way the answer is posed, is that you don't know that you are pulling an orange ball until you pull it out, which is crucial to the reason why the answer is 2/3.
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On May 12 2012 03:11 Misder wrote:On the ball problem- + Show Spoiler +Ok, I think I realize how I got myself confused on why the answer is 1/2 and why some people are saying that the answer is 1/2.
Suppose that instead of you, your friend is the one in the problem, and you are being posed the problem. Now, your friend chooses a random pocket. Your friend looks into the pocket (so he knows the combination of the two balls). If, it's WW, then discard the trial. However, if it's a pocket with at least one orange ball- count the trial. Your friend looks into the pocket and pulls out an orange ball. Now you are asked what the probability of the other ball is orange. In this case the answer is 1/2.
However, I think the way the answer is posed, is that you don't know that you are pulling an orange ball until you pull it out, which is crucial to the reason why the answer is 2/3.
The first is indeed what I think.
You pick a pocket, then pull out an/the orange ball.
I think the question is posed so that you always pull out an/the orange ball, and never the white ball in the OW pocket.
You reach into one random pocket and pull out an orange ping pong ball.
I think that this means that you randomly pick a pocket, but then must pick an/the orange ball if possible.
If it said "one of the two balls", "randomly pick a ball out of the pocket" or something with the same meaning i would agree with it being 2/3rd, but it doesn't.
I guess that this is dependant on how you read it though, and I'm not too confident we'll agree soon. I say that we just leave this riddle for what it is now, and don't clutter the thread up about it anymore.
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I won't comment on this any further, but the problem is very explicit in wording. It never mentions prioritizing orange, or looking into the bag after picking one.
A friend packed six ping pong balls for you, 3 orange, 3 white. He's placed them in three pockets of your sports bag. One pocket has two orange balls. One pocket has two white balls. One pocket has one white and one orange. You reach into one random pocket and pull out an orange ping pong ball. What's the probability of the other ball in the pocket being orange?
A different way to phrase the same question is, someone else "reached into one random pocket and pulled out an orange ping pong ball." If you were now to place money on the color of the other ball in the bag, the bet with the higher statistical probability, at 2/3, is orange.
The question does not need to say that he picked a random ball in the bag, because he does not know the contents of the bag and therefore the ball selection must be random. And the result was orange. Change the wording if you like, but then you're not answering the same problem. I don't see how you can possibly think the question is saying, "you pick a bag, you look into it, you see at least one orange ball, you take an orange ball out, and now what's the probability of the other ball being orange [even though you plainly can see it]"?
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On May 12 2012 03:11 Misder wrote:Show nested quote +On May 11 2012 07:14 CptZouglou wrote:Enjoy this new (quite difficult) riddle: You are a russian bomber, and you want to send a bomb on a nuclear submarine. The submarine is located on a line and has an integer position (can be negative). It moves at a constant integer speed (can be negative too) each second. The good part is that you have an unlimited amount of bombs, and you can send one each second at a any position. The problem is that you don't know where is the submarine at time 0, and what its speed is. Is there a way to ensure that you can send hit the submarine in a finite amount of time ? If yes, what is your strategy ? hint: + Show Spoiler +
Yes! Consider the problem as finding two parameters initial position (p) and speed (s). After t seconds, the submarine is at position p + t*s. Try and find a way to explore all possible initial positions and speeds !
I'm actually curious about the answer for this... Is there another hint?
It would be hard for him to give another hint without giving away the answer.
Anyway, the answer is like this
+ Show Spoiler +
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Holy shit this is going far O.o
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come on guys, did we all forget what the OP stated already?
WARNING:
Do not argue - about anything - in this thread. Use PMs.
Only Post Riddles or answeres, all answeres must be in spoilers.
Try to include the answere for every riddle you write.
enough with the ping pong balls!!!
+ Show Spoiler +
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On May 12 2012 06:54 Slithe wrote:Show nested quote +On May 12 2012 03:11 Misder wrote:On May 11 2012 07:14 CptZouglou wrote:Enjoy this new (quite difficult) riddle: You are a russian bomber, and you want to send a bomb on a nuclear submarine. The submarine is located on a line and has an integer position (can be negative). It moves at a constant integer speed (can be negative too) each second. The good part is that you have an unlimited amount of bombs, and you can send one each second at a any position. The problem is that you don't know where is the submarine at time 0, and what its speed is. Is there a way to ensure that you can send hit the submarine in a finite amount of time ? If yes, what is your strategy ? hint: + Show Spoiler +
Yes! Consider the problem as finding two parameters initial position (p) and speed (s). After t seconds, the submarine is at position p + t*s. Try and find a way to explore all possible initial positions and speeds !
I'm actually curious about the answer for this... Is there another hint? It would be hard for him to give another hint without giving away the answer. Anyway, the answer is like this + Show Spoiler +
+ Show Spoiler +
Very nice! Good job! You described one of the solutions. Would you also solve it if the the submarine was on a N-dimensional plane with a N-dimensional speed?
If you find it, I have another generalized riddle ready for you...
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Maybe I'm just blind but I don't think this famous riddle has been posted yet
Einstein's riddle
1. In a street there are five houses, painted five different colours.
2. In each house lives a person of different nationality
3. These five homeowners each drink a different kind of beverage, smoke different brand of cigar and keep a different pet.
Who owns the FISH?
HINTS
1. The Brit lives in a red house.
2. The Swede keeps dogs as pets.
3. The Dane drinks tea.
4. The Green house is next to, and on the left of the White house.
5. The owner of the Green house drinks coffee.
6. The person who smokes Pall Mall rears birds.
7. The owner of the Yellow house smokes Dunhill.
8. The man living in the centre house drinks milk.
9. The Norwegian lives in the first house.
10. The man who smokes Blends lives next to the one who keeps cats.
11. The man who keeps horses lives next to the man who smokes Dunhill.
12. The man who smokes Blue Master drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The man who smokes Blends has a neighbour who drinks water.
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Sanya12364 Posts
On May 13 2012 03:23 StoRm_res wrote:
Maybe I'm just blind but I don't think this famous riddle has been posted yet
Einstein's riddle
1. In a street there are five houses, painted five different colours.
2. In each house lives a person of different nationality
3. These five homeowners each drink a different kind of beverage, smoke different brand of cigar and keep a different pet.
Who owns the FISH?
HINTS
1. The Brit lives in a red house.
2. The Swede keeps dogs as pets.
3. The Dane drinks tea.
4. The Green house is next to, and on the left of the White house.
5. The owner of the Green house drinks coffee.
6. The person who smokes Pall Mall rears birds.
7. The owner of the Yellow house smokes Dunhill.
8. The man living in the centre house drinks milk.
9. The Norwegian lives in the first house.
10. The man who smokes Blends lives next to the one who keeps cats.
11. The man who keeps horses lives next to the man who smokes Dunhill.
12. The man who smokes Blue Master drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The man who smokes Blends has a neighbour who drinks water.
+ Show Spoiler +Ze Germans provided someone has to own the fish.
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I'm pretty sure the so-called "Einstein Riddle" has been posted.
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On May 11 2012 21:35 CyDe wrote:I guess I'll just throw one of those lateral thinking problems into this mix of relatively intelligent arguing about probability and wording  A bridge has a weight limit of 10,000 KG. A truck weighing exactly 10,000 KG drives onto the bridge, and stops at the center, where a bird weighing 30g lands on it. Why doesn't the bridge collapse? Hint: + Show Spoiler + It has nothing to do with the manner that the bridge was constructed (support placements, etc). Answer: + Show Spoiler +The truck would have burned more than 30g of gasoline by the time it reached the center of the bridge.
Wow this is a really clever riddle, which unfortunately I had to look at the answer for
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Sanya12364 Posts
Cowboy road into town on Friday. He stayed two nights and a day. Then he road out on Friday. What happened?
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On May 12 2012 09:50 CptZouglou wrote:+ Show Spoiler +
Very nice! Good job! You described one of the solutions. Would you also solve it if the the submarine was on a N-dimensional plane with a N-dimensional speed?
If you find it, I have another generalized riddle ready for you...
Wait.. how does that work? + Show Spoiler +If you let its initial position be arbitrarily large, and it's speed be arbitrarily large, then you're never going to find it by starting in the middle and moving out at a rate of 1/1, because the ship'll outrun the bombs forever. On the other hand, if the boat has a speed of 0, and you're skipping integers, you have a chance of never finding it ever. Even if bombs are persistent, you have to hope you manage to choose a integer arbitrarily large enough on your first couple guesses that it makes the position/speed of the sub look arbitrarily small. Which is impossible to guess, even if we start talking about grahm's numbers - tiny compared to infinity..
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On May 07 2012 04:31 NTTemplar wrote:Show nested quote +On May 07 2012 01:22 amd098 wrote:On May 07 2012 00:29 frogrubdown wrote:On May 06 2012 23:53 NTTemplar wrote:
How about this:
What is the largest natural number you can create with only two 9's you are not allowed any more digits, but you can use any mathematical symbols. No upper bound. You can just keep adding parentheses and factorials likes so: 9(9!), 9((9!)!), 9(((9!)!)!), ... or repeat the factorials in (9!)^(9!) + Show Spoiler +Pretty much it, wanna give the actual number though? ;P
+ Show Spoiler +9! ↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑ 9!
edit: wait wait + Show Spoiler + sum (n - > infinity) 9! ↑<sup>n</sup> 9!
edit: ok that was cheating + Show Spoiler +
f(a) = sum (n - > f(a-1)) f(a-1) ↑<sup>n</sup> f(a-1)
when a=9! and f(a-1) = 9!
totally cheating now woooooooooo
edit: this one should be legit
+ Show Spoiler +
a=9!
b= a ↑a a
sum (n->b) b ↑n b
Big.
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On May 24 2012 13:45 GoldenH wrote:Show nested quote +On May 12 2012 09:50 CptZouglou wrote:+ Show Spoiler +
Very nice! Good job! You described one of the solutions. Would you also solve it if the the submarine was on a N-dimensional plane with a N-dimensional speed?
If you find it, I have another generalized riddle ready for you...
Wait.. how does that work? + Show Spoiler +If you let its initial position be arbitrarily large, and it's speed be arbitrarily large, then you're never going to find it by starting in the middle and moving out at a rate of 1/1, because the ship'll outrun the bombs forever. On the other hand, if the boat has a speed of 0, and you're skipping integers, you have a chance of never finding it ever. Even if bombs are persistent, you have to hope you manage to choose a integer arbitrarily large enough on your first couple guesses that it makes the position/speed of the sub look arbitrarily small. Which is impossible to guess, even if we start talking about grahm's numbers - tiny compared to infinity..
+ Show Spoiler +No matter how large its initial position and velocity are, they are still finite once decided, and constant for all time >= 0. So what you are essentially doing is not searching for the submarine, but searching for the submarine's initial condition in the x_0 v_0 phasespace, which will terminate in finite time. The solution is again NOT searching for the submarine, but searching for the submarines initial position and velocity. The N dimensional problem is the exact same, except you need to find an onto mapping from Z (the integers) to Z^(2N), which exists since they have the same cardinality. If you let the submarine change its speed or direction... that's obviously intractable for an infinite line.
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On May 24 2012 19:02 vega12 wrote:Show nested quote +On May 24 2012 13:45 GoldenH wrote:On May 12 2012 09:50 CptZouglou wrote:+ Show Spoiler +
Very nice! Good job! You described one of the solutions. Would you also solve it if the the submarine was on a N-dimensional plane with a N-dimensional speed?
If you find it, I have another generalized riddle ready for you...
Wait.. how does that work? + Show Spoiler +If you let its initial position be arbitrarily large, and it's speed be arbitrarily large, then you're never going to find it by starting in the middle and moving out at a rate of 1/1, because the ship'll outrun the bombs forever. On the other hand, if the boat has a speed of 0, and you're skipping integers, you have a chance of never finding it ever. Even if bombs are persistent, you have to hope you manage to choose a integer arbitrarily large enough on your first couple guesses that it makes the position/speed of the sub look arbitrarily small. Which is impossible to guess, even if we start talking about grahm's numbers - tiny compared to infinity.. + Show Spoiler +No matter how large its initial position and velocity are, they are still finite once decided, and constant for all time >= 0. So what you are essentially doing is not searching for the submarine, but searching for the submarine's initial condition in the x_0 v_0 phasespace, which will terminate in finite time. The solution is again NOT searching for the submarine, but searching for the submarines initial position and velocity. The N dimensional problem is the exact same, except you need to find an onto mapping from Z (the integers) to Z^(2N), which exists since they have the same cardinality. If you let the submarine change its speed or direction... that's obviously intractable for an infinite line.
+ Show Spoiler +How are you going to detect the initial position though? It's just empty space, and a bomb isn't some fancy 'ooh, a submarine was here an hour ago' detector. The submarine isn't everywhere on the line at once, just one point on the line. It seems like if you drew a graph of the rate of the submarine's possible movement vs the rate of testing every possible location, it would be at least equal for all non-zero values of the submarine's velocity. And that's even ignoring a negative value for movement, which means the submarine could at any time cross over into your already searched space. Yes, at infinity, they will converge, but not before then.
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On May 24 2012 19:02 vega12 wrote:Show nested quote +On May 24 2012 13:45 GoldenH wrote:On May 12 2012 09:50 CptZouglou wrote:+ Show Spoiler +
Very nice! Good job! You described one of the solutions. Would you also solve it if the the submarine was on a N-dimensional plane with a N-dimensional speed?
If you find it, I have another generalized riddle ready for you...
Wait.. how does that work? + Show Spoiler +If you let its initial position be arbitrarily large, and it's speed be arbitrarily large, then you're never going to find it by starting in the middle and moving out at a rate of 1/1, because the ship'll outrun the bombs forever. On the other hand, if the boat has a speed of 0, and you're skipping integers, you have a chance of never finding it ever. Even if bombs are persistent, you have to hope you manage to choose a integer arbitrarily large enough on your first couple guesses that it makes the position/speed of the sub look arbitrarily small. Which is impossible to guess, even if we start talking about grahm's numbers - tiny compared to infinity.. + Show Spoiler +No matter how large its initial position and velocity are, they are still finite once decided, and constant for all time >= 0. So what you are essentially doing is not searching for the submarine, but searching for the submarine's initial condition in the x_0 v_0 phasespace, which will terminate in finite time. The solution is again NOT searching for the submarine, but searching for the submarines initial position and velocity. The N dimensional problem is the exact same, except you need to find an onto mapping from Z (the integers) to Z^(2N), which exists since they have the same cardinality. If you let the submarine change its speed or direction... that's obviously intractable for an infinite line.
About the submarine...
+ Show Spoiler +
That isnt what the problem said at all. The way the problem is written is impossible...plus how would you use the bombs to find out the speed of the submarine?
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On May 24 2012 10:44 LeapofFaith wrote:Show nested quote +On May 11 2012 21:35 CyDe wrote:I guess I'll just throw one of those lateral thinking problems into this mix of relatively intelligent arguing about probability and wording A bridge has a weight limit of 10,000 KG. A truck weighing exactly 10,000 KG drives onto the bridge, and stops at the center, where a bird weighing 30g lands on it. Why doesn't the bridge collapse? Hint: + Show Spoiler + It has nothing to do with the manner that the bridge was constructed (support placements, etc). Answer: + Show Spoiler +The truck would have burned more than 30g of gasoline by the time it reached the center of the bridge.
Wow this is a really clever riddle, which unfortunately I had to look at the answer for
There's another civil engineering way of thinking about this: weight limits aren't the actual load that the bridge can bear. It's actually higher but not shown in case of poor construction/idiots who try to cross the line. The actual load that the bridge can bear is about 2-3x higher. So a flock of birds can land on the truck no problem.
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On May 25 2012 00:10 pugowar wrote:Show nested quote +On May 24 2012 19:02 vega12 wrote:On May 24 2012 13:45 GoldenH wrote:On May 12 2012 09:50 CptZouglou wrote:+ Show Spoiler +
Very nice! Good job! You described one of the solutions. Would you also solve it if the the submarine was on a N-dimensional plane with a N-dimensional speed?
If you find it, I have another generalized riddle ready for you...
Wait.. how does that work? + Show Spoiler +If you let its initial position be arbitrarily large, and it's speed be arbitrarily large, then you're never going to find it by starting in the middle and moving out at a rate of 1/1, because the ship'll outrun the bombs forever. On the other hand, if the boat has a speed of 0, and you're skipping integers, you have a chance of never finding it ever. Even if bombs are persistent, you have to hope you manage to choose a integer arbitrarily large enough on your first couple guesses that it makes the position/speed of the sub look arbitrarily small. Which is impossible to guess, even if we start talking about grahm's numbers - tiny compared to infinity.. + Show Spoiler +No matter how large its initial position and velocity are, they are still finite once decided, and constant for all time >= 0. So what you are essentially doing is not searching for the submarine, but searching for the submarine's initial condition in the x_0 v_0 phasespace, which will terminate in finite time. The solution is again NOT searching for the submarine, but searching for the submarines initial position and velocity. The N dimensional problem is the exact same, except you need to find an onto mapping from Z (the integers) to Z^(2N), which exists since they have the same cardinality. If you let the submarine change its speed or direction... that's obviously intractable for an infinite line. About the submarine... + Show Spoiler +
That isnt what the problem said at all. The way the problem is written is impossible...plus how would you use the bombs to find out the speed of the submarine?
+ Show Spoiler +It's not impossible. If the submarine has, say, initial position 3 and constant speed 2, it will be at point 3, then 5, then 7, and so on for time 0, 1, 2. So once you have a function from n=1...inf to the plane of points (the initial conditions phasespace), call it x(n) and v(n) if you want, then all you need to do is chose the functions so that you cover every possible position in the Z^2 plane. If you have say x(10) = 3 and v(10) = 2, corresponding to the correct initial conditions, then you will send your bomb to 3 + 10*2 = 23, which is exactly where the submarine will be at time 10 for starting location 3 and velocity 2. Doing it this way you try every possible set of initial conditions. This is guaranteed to terminate in a finite way. If the initial submarine position was 8276 with speed -99810, you will still eventually get to that set of points on the phasespace in a finite time.
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On May 12 2012 09:50 CptZouglou wrote:Show nested quote +On May 12 2012 06:54 Slithe wrote:On May 12 2012 03:11 Misder wrote:On May 11 2012 07:14 CptZouglou wrote:Enjoy this new (quite difficult) riddle: You are a russian bomber, and you want to send a bomb on a nuclear submarine. The submarine is located on a line and has an integer position (can be negative). It moves at a constant integer speed (can be negative too) each second. The good part is that you have an unlimited amount of bombs, and you can send one each second at a any position. The problem is that you don't know where is the submarine at time 0, and what its speed is. Is there a way to ensure that you can send hit the submarine in a finite amount of time ? If yes, what is your strategy ? hint: + Show Spoiler +
Yes! Consider the problem as finding two parameters initial position (p) and speed (s). After t seconds, the submarine is at position p + t*s. Try and find a way to explore all possible initial positions and speeds !
I'm actually curious about the answer for this... Is there another hint? It would be hard for him to give another hint without giving away the answer. Anyway, the answer is like this + Show Spoiler + + Show Spoiler +
Very nice! Good job! You described one of the solutions. Would you also solve it if the the submarine was on a N-dimensional plane with a N-dimensional speed?
If you find it, I have another generalized riddle ready for you...
+ Show Spoiler +Here's a solution to the original problem that suggests the generalization.
Let f(n) = pn + r be the position of the submarine at time n. Let g(n) be the bombed position at time n. The problem is to find a function g(n) that for any integers p, r there exists an integer N>0, such that f(N)=g(N).
First let's map any pair (p,r) from Z^2 to an integer N>0 bijectively*. Now let g(N) = pN+r. So for any pair p,r there exists a number N such that f(N)=g(N).
I didn't prove that such a bijection exists. I'll refer to the theorem that the Cartesian product of finitely many countable sets is countable. As long as the position of the submarine can be described with a function of a finite number of parameters taken from countable sets we can hit the submarine. Just map every possible function to a certain time N where the bomb will hit at exactly at the position that the function takes.
In the extreme case we can assure a hit even if the submarine has arbitrary rational speed and starting position in N dimensions.
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EPT![[image loading]](http://img167.imageshack.us/img167/24/infinityyd1.jpg)
