EPT
- Feel free to discuss your thoughts, ideas. if you have solution, put it in + Show Spoiler +
here
- Feel free to post your own brainteaser/problem, use bold font so I can find them and paste into original post.
- Don't troll plz <3 enjoy!
1. (accessible to everyone) + Show Spoiler +
you have a 5-liter jug and a 3-liter jug and a pool of water. How can you produce exactly 4 liters of water? (a classic one, appeared in a "die hard" movie lol)
2. + Show Spoiler +
Suppose we have 10 bags, each bag contains 10 coins. One of the bags contains counterfeit coins, the other 9 bags contain real coins. Each counterfeit coin weighs 0.9 grams. Each real coin weighs 1.0 grams. If we have an accurate scale that give exact weight of whatever is placed on, could we determine which bag contains the counterfeit coins with just _one_ weighing?
2.b. + Show Spoiler +
Suppose we have 4 bags, each bag contains 10 coins. Some of the bags contains counterfeit all coins, some contain all real coins. We don't know how many bags of counterfeit coins there are. Each counterfeit coin weighs 0.9 grams. Each real coin weighs 1.0 grams. If we have an accurate scale that give exact weight of whatever is placed on, could we determine which bag(s) contains the counterfeit coins with just _one_ weighing?
3. (accessible) + Show Spoiler +
You have 2 hour-glasses, one measuring 7 minutes and the other 11 minutes. You want to boil an egg for exactly 15 minutes. Can you use the 2 hour-glasses to measure exactly 15 minutes? Note: your hands are so high APM it takes infinitely small amount of time to flip an hour glass.
4. (when will we meet again?) + Show Spoiler +
A very accurate clock has an hour hand and a minute hand. Both hands are (infinitely) thin. At 12 noon, the two hands coincide exactly. What is the next (exact) time at which the two hands will again coincide?
5. (my favorite :p)+ Show Spoiler +
Suppose a rectangle can be (in some way) entirely covered by 25 circular disks, each of radius 1. Can the same rectangle be entirely covered by 100 disks of radius 1/2? Prove your answer. Note: overlaps allowed of course.
6. What's your eyes color? (hard problem)
On April 10 2011 00:09 PepperoniPiZZa wrote:
http://xkcd.com/blue_eyes.html
http://xkcd.com/blue_eyes.html
7. (accessible) + Show Spoiler +
Suppose we have 9 coins that look the same and feel the same. But exactly one of them is counterfeit and it weighs less than a real coin. Can we identify the counterfeit coin among the 9 coins with just two weighings on an accurate balance scale?
8. (Day9 wants you to do this one)+ Show Spoiler +
On April 10 2011 00:29 Munk-E wrote:
Of course I must add,
If you have 2 pieces of string that when you light in fire take an hour to burn how do you measure 45 minutes?
Of course I must add,
If you have 2 pieces of string that when you light in fire take an hour to burn how do you measure 45 minutes?
Note: the string possibly burns unevenly.
9. (if you know what prime numbers are) + Show Spoiler +
When a prime number greater than 32 is divided by 30, you get a remainder R. If R is not equal to 1, must the remainder R be a prime number? Why or why not?
10. + Show Spoiler +
On April 10 2011 00:36 ILOVEKITTENS wrote:
Sultan summons all of his viziers. He says "Tomorrow I am going to put all of you in a line and place a hat on each of your heads. The hat will either be red or blue. You will not be able to see the hat on your head. However, because you are my royal viziers, you must be able to tell me what color hat is on your head. Only one of you may be wrong - otherwise, you all die. You can tell me the color of your hat in any order, and you are only allowed to say the color and nothing else - no communication with other viziers." How do the viziers keep their jobs and their lives (what is their strategy)?
Sultan summons all of his viziers. He says "Tomorrow I am going to put all of you in a line and place a hat on each of your heads. The hat will either be red or blue. You will not be able to see the hat on your head. However, because you are my royal viziers, you must be able to tell me what color hat is on your head. Only one of you may be wrong - otherwise, you all die. You can tell me the color of your hat in any order, and you are only allowed to say the color and nothing else - no communication with other viziers." How do the viziers keep their jobs and their lives (what is their strategy)?
10b. + Show Spoiler +
On April 14 2011 09:41 sidr wrote:
For those who know a bit more math, I have a variation on #10. Suppose countably many prisoners (meaning we can assign each prisoner a natural number, ie there is a prisoner 1, prisoner 2, etc for all positive whole numbers) are given the following scenario: on the following day, an evil warden will assemble them in one (very large) room and give each of them a hat with a (not necessarily unique) natural number on it. Each prisoner will be able to see all hats except their own. Without any communication with other prisoners after receiving his or her hat, each prisoner will communicate with the warden what he or she thinks his or her number is. This communication occurs simultaneously; that is to say prisoner x has know knowledge of what prisoner y communicated to the warden (unless of course x=y...). The prisoners are all allowed free if and only if finitely many of them are wrong. Assume the prisoners know this will happen the following day, and are given a night to prepare a strategy. Is there a strategy which guarantees the prisoners all go free? Give the strategy or prove no such strategy exists.
For those who know a bit more math, I have a variation on #10. Suppose countably many prisoners (meaning we can assign each prisoner a natural number, ie there is a prisoner 1, prisoner 2, etc for all positive whole numbers) are given the following scenario: on the following day, an evil warden will assemble them in one (very large) room and give each of them a hat with a (not necessarily unique) natural number on it. Each prisoner will be able to see all hats except their own. Without any communication with other prisoners after receiving his or her hat, each prisoner will communicate with the warden what he or she thinks his or her number is. This communication occurs simultaneously; that is to say prisoner x has know knowledge of what prisoner y communicated to the warden (unless of course x=y...). The prisoners are all allowed free if and only if finitely many of them are wrong. Assume the prisoners know this will happen the following day, and are given a night to prepare a strategy. Is there a strategy which guarantees the prisoners all go free? Give the strategy or prove no such strategy exists.
11. + Show Spoiler +
Can a convex 13-gon be tiled (partitioned) by parallelograms? (A 13-gon is a solid polygon of 13 sides. "Convex" means the straight line segment connecting any 2 points of the polygon lie inside the polygon. "Tile" meaning the overlaps between parallelograms can only happen at their edges.)
12. (Monty Hall) + Show Spoiler +
On April 10 2011 02:00 Tunks wrote:
How about an all time classic, just for those who haven't come across it before. Very simple if you know anything about maths though.
You are in the final round of a game show and are shown 3 doors. You will win whatever is behind the door you eventually choose. Behind 1 door is a car, and behind the other 2 are goats. You make your original choice and the presenter opens one of the other 2 doors to reveal a goat. He then gives you the chance to switch to the other remaining closed door, or to open your original choice. Should you switch?
How about an all time classic, just for those who haven't come across it before. Very simple if you know anything about maths though.
You are in the final round of a game show and are shown 3 doors. You will win whatever is behind the door you eventually choose. Behind 1 door is a car, and behind the other 2 are goats. You make your original choice and the presenter opens one of the other 2 doors to reveal a goat. He then gives you the chance to switch to the other remaining closed door, or to open your original choice. Should you switch?
13.+ Show Spoiler +
Can every natural number (e.g.1,2,3,...) be expressed as a sum of distinct powers of 2 (e.g.1,2,4,8,...)? If so, is that expression unique (ignoring order of the terms in the sum)?
14. + Show Spoiler +
On April 10 2011 02:14 ghrur wrote:
Question:
What is the maximum number of times 10 lines can intersect in the same plane?
Question:
What is the maximum number of times 10 lines can intersect in the same plane?
paraphrased: What is the maximum number of intersection points between 10 distinct lines on a plane?
15.+ Show Spoiler +
Let A be a collection of 100 distinct integers. Can you select 15 integers from A so that the difference of any two numbers from this selected subset is divisible by 7?
16.
On April 10 2011 04:10 khanofmongols wrote:
this one is difficulty and interesting: http://gurmeet.net/puzzles/100-prisoners-and-100-boxes/
this one is difficulty and interesting: http://gurmeet.net/puzzles/100-prisoners-and-100-boxes/
+ Show Spoiler +
On April 10 2011 09:56 LastPrime wrote:
http://www.sciencenews.org/view/generic/id/7649/title/Puzzling_Names_in_Boxes
"Indeed, the probability that a random permutation of 2n objects has no cycle of length greater than n is at least 1 minus the natural logarithm of 2."
Does anyone know how this probability is calculated?
http://www.sciencenews.org/view/generic/id/7649/title/Puzzling_Names_in_Boxes
"Indeed, the probability that a random permutation of 2n objects has no cycle of length greater than n is at least 1 minus the natural logarithm of 2."
Does anyone know how this probability is calculated?
17. (3 princesses) + Show Spoiler +
On April 10 2011 05:16 cmpcmp wrote:
You are the most eligible bachelor in the kingdom, and as such the King has invited you to his castle so that you may choose one of his three daughters to marry. The eldest princess is honest and always tells the truth. The youngest princess is dishonest and always lies. The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.
As you will be forever married to one of the princesses, you want to marry the eldest (truth-teller) or the youngest (liar) because at least you know where you stand with them.
The problem is that you cannot tell which sister is which just by their appearance, and the King will only grant you ONE yes or no question which you may only address to ONE of the sisters. What yes or no question can you ask which will ensure you do not marry the middle sister?
Clarification: The answer you get wil ONLY be “yes” or “no” and you cannot ask a question that seeks a different answer or communicate with the daughters in any other way.
You are the most eligible bachelor in the kingdom, and as such the King has invited you to his castle so that you may choose one of his three daughters to marry. The eldest princess is honest and always tells the truth. The youngest princess is dishonest and always lies. The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.
As you will be forever married to one of the princesses, you want to marry the eldest (truth-teller) or the youngest (liar) because at least you know where you stand with them.
The problem is that you cannot tell which sister is which just by their appearance, and the King will only grant you ONE yes or no question which you may only address to ONE of the sisters. What yes or no question can you ask which will ensure you do not marry the middle sister?
Clarification: The answer you get wil ONLY be “yes” or “no” and you cannot ask a question that seeks a different answer or communicate with the daughters in any other way.
18. + Show Spoiler +
On April 10 2011 05:44 Joe12 wrote:
A ship had distributed the crew names on the many lifeboats onboard. Each lifeboat had equally many men, and there were exactly the same amount of men in each boat as there were boats in all.
During a storm the ship began to sink, and 10 lifeboats were destroyed by the waves with an unknown amount of men. The remaining crew pulled an additional 10 men into each of the remaining lifeboats.
How many drowned?
Its a while since i heard this one, but im pretty sure the wording is correct..
A ship had distributed the crew names on the many lifeboats onboard. Each lifeboat had equally many men, and there were exactly the same amount of men in each boat as there were boats in all.
During a storm the ship began to sink, and 10 lifeboats were destroyed by the waves with an unknown amount of men. The remaining crew pulled an additional 10 men into each of the remaining lifeboats.
How many drowned?
Its a while since i heard this one, but im pretty sure the wording is correct..
19.(pirates, arrrr)+ Show Spoiler +
On April 10 2011 06:32 tomnov wrote:
10 pirates found a loot of 100 gold pieces, and decided to split it the following way:
the captain offers how to split it, then they hold a vote and if at least half of them agree that is the split, else (more than half disagree) they kill him and the next in command tries, they vote again, and so on.
the pirates want to stay alive, get the most gold, and kill the most of the other pirates in that order + Show Spoiler +
how do they split the money and how many pirates die?
10 pirates found a loot of 100 gold pieces, and decided to split it the following way:
the captain offers how to split it, then they hold a vote and if at least half of them agree that is the split, else (more than half disagree) they kill him and the next in command tries, they vote again, and so on.
the pirates want to stay alive, get the most gold, and kill the most of the other pirates in that order + Show Spoiler +
* a pirate will offer a split where he gets 0 gold if he knows that any other split will not get the votes and he will die
* a pirate will not vote for a split if he knows he can get the same gold from the next pirate to offer
* a pirate will not vote for a split if he knows he can get the same gold from the next pirate to offer
how do they split the money and how many pirates die?
20 and 21.+ Show Spoiler +
On April 10 2011 07:14 MusicalPulse wrote:
I like logic puzzles more than math puzzles so...
These are my two favorites :D
In a far away land, it was known that if you drank poison, the only way to save yourself is to drink a stronger poison, which neutralizes the weaker poison. The king that ruled the land wanted to make sure that he possessed the strongest poison in the kingdom, in order to ensure his survival, in any situation. So the king called the kingdom's pharmacist and the kingdom's treasurer, he gave each a week to make the strongest poison. Then, each would drink the other one's poison, then his own, and the one that will survive, will be the one that had the stronger poison.
The pharmacist went straight to work, but the treasurer knew he had no chance, for the pharmacist was much more experienced in this field, so instead, he made up a plan to survive and make sure the pharmacist dies. On the last day the pharmacist suddenly realized that the treasurer would know he had no chance, so he must have a plan. After a little thought, the pharmacist realized what the treasurer's plan must be, and he concocted a counter plan, to make sure he survives and the treasurer dies. When the time came, the king summoned both of them. They drank the poisons as planned, and the treasurer died, the pharmacist survived, and the king didn't get what he wanted.
What exactly happened there?
-----
The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.
"In the prison there is a switch room which contains two light switches labeled A and B, each of which can be in either the 'on' or the 'off' position. The switches are not connected to anything.
"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must move one, but only one of the switches. He can't move both but he can't move none either. Then he'll be led back to his cell."
"No one else will enter the switch room until I lead the next prisoner there, and he'll be instructed to do the same thing. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back."
"But, given enough time, everyone will eventually visit the switch room as many times as everyone else. At any time any one of you may declare to me, 'We have all visited the switch room.'
"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will be fed to the alligators."
*note - the only difference from Scenario B, the original position of the 2 switches are known.
Assuming that:
A) There is no restriction on the amount of time the prisoners could take before sending the notice to the warden that everyone has been to the switch room at least once.
B) There is no restriction on the number of time each prisoner can visit the switch room
C) The warden will not attempt any foul moves, such as intentionally not bringing a certain prisoner to the switch room forever.
I like logic puzzles more than math puzzles so...
These are my two favorites :D
In a far away land, it was known that if you drank poison, the only way to save yourself is to drink a stronger poison, which neutralizes the weaker poison. The king that ruled the land wanted to make sure that he possessed the strongest poison in the kingdom, in order to ensure his survival, in any situation. So the king called the kingdom's pharmacist and the kingdom's treasurer, he gave each a week to make the strongest poison. Then, each would drink the other one's poison, then his own, and the one that will survive, will be the one that had the stronger poison.
The pharmacist went straight to work, but the treasurer knew he had no chance, for the pharmacist was much more experienced in this field, so instead, he made up a plan to survive and make sure the pharmacist dies. On the last day the pharmacist suddenly realized that the treasurer would know he had no chance, so he must have a plan. After a little thought, the pharmacist realized what the treasurer's plan must be, and he concocted a counter plan, to make sure he survives and the treasurer dies. When the time came, the king summoned both of them. They drank the poisons as planned, and the treasurer died, the pharmacist survived, and the king didn't get what he wanted.
What exactly happened there?
-----
The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.
"In the prison there is a switch room which contains two light switches labeled A and B, each of which can be in either the 'on' or the 'off' position. The switches are not connected to anything.
"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must move one, but only one of the switches. He can't move both but he can't move none either. Then he'll be led back to his cell."
"No one else will enter the switch room until I lead the next prisoner there, and he'll be instructed to do the same thing. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back."
"But, given enough time, everyone will eventually visit the switch room as many times as everyone else. At any time any one of you may declare to me, 'We have all visited the switch room.'
"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will be fed to the alligators."
*note - the only difference from Scenario B, the original position of the 2 switches are known.
Assuming that:
A) There is no restriction on the amount of time the prisoners could take before sending the notice to the warden that everyone has been to the switch room at least once.
B) There is no restriction on the number of time each prisoner can visit the switch room
C) The warden will not attempt any foul moves, such as intentionally not bringing a certain prisoner to the switch room forever.
22. (nydus graph)+ Show Spoiler +
On April 10 2011 07:59 LastPrime wrote:
A young zergling hero from Zerus wants to explore the land his race has conquered. To do this, he wants to visit every zerg planet exactly once using nydus canals and return to his home planet. Every one of these planets is connected to exactly three other planets by nydus canals. He has already planned a route but does not like it for some reason. Is there another route he can take? If so prove its existence. *Note the new route cannot just be the reverse of the original route.
A young zergling hero from Zerus wants to explore the land his race has conquered. To do this, he wants to visit every zerg planet exactly once using nydus canals and return to his home planet. Every one of these planets is connected to exactly three other planets by nydus canals. He has already planned a route but does not like it for some reason. Is there another route he can take? If so prove its existence. *Note the new route cannot just be the reverse of the original route.
23,24,25.+ Show Spoiler +
On April 10 2011 08:43 Darkren wrote:
Ive got a couple love those things
For the people that found this one here is the harder version, suppose u have 12 coins now, one of them is still conterfeit but u don't know if it's heavier or if it weight less than the others. U have 3 weighings on an accurate balance scale, find the counterfeit coint?
4 people cross the bridge, Number one crosses in 1 min, Number two crosses in 2 min, Number 3 croses in 5 mins, Number 4 crosses in 10 mins. Now it's really dark and their scared of the dark, they have only one flashlight so they decide to go 2 by 2 to cross the bridge then one persons comes back and gives the flashlight to the others. What order must they go to cross the bridge in 17 minutes.
3 guys are in a hotel, they rent a room 30$ so they each pay 10 $. In the middle of the night the manager thinks 30$ is too expensive so he gives his son 5$ and tells him to go give it to the three men. The son puts 2 $ in his pocket and gives 3$ back to the three guys. So resuming this it's like if the guys paid 9X3$=27$ and their is a 2$ in the boy pocket so thats 29 in total, where did that 1$ pass from the beggining.
Ive got a couple love those things
For the people that found this one here is the harder version, suppose u have 12 coins now, one of them is still conterfeit but u don't know if it's heavier or if it weight less than the others. U have 3 weighings on an accurate balance scale, find the counterfeit coint?
4 people cross the bridge, Number one crosses in 1 min, Number two crosses in 2 min, Number 3 croses in 5 mins, Number 4 crosses in 10 mins. Now it's really dark and their scared of the dark, they have only one flashlight so they decide to go 2 by 2 to cross the bridge then one persons comes back and gives the flashlight to the others. What order must they go to cross the bridge in 17 minutes.
3 guys are in a hotel, they rent a room 30$ so they each pay 10 $. In the middle of the night the manager thinks 30$ is too expensive so he gives his son 5$ and tells him to go give it to the three men. The son puts 2 $ in his pocket and gives 3$ back to the three guys. So resuming this it's like if the guys paid 9X3$=27$ and their is a 2$ in the boy pocket so thats 29 in total, where did that 1$ pass from the beggining.
26. (cut out chess board) + Show Spoiler +
suppose you have a chess board with 2 opposite corners cut out as in picture
![[image loading]](http://www.cl.cam.ac.uk/~mj201/images/mutilated-chess-board.gif)
there would be 62 squares in this cut out board. you have a set of domino pieces, each piece can cover exactly 2 adjacent squares of the chess board. Is it possible to cover (tile) the cut out chess board with exactly 31 pieces of dominos? if yes, how? if not, why not?
there would be 62 squares in this cut out board. you have a set of domino pieces, each piece can cover exactly 2 adjacent squares of the chess board. Is it possible to cover (tile) the cut out chess board with exactly 31 pieces of dominos? if yes, how? if not, why not?
27. (The last templar)+ Show Spoiler +
On April 10 2011 18:45 0x64 wrote:
In the Protoss Lore, every time an Archon is merged, their soul is also merged [BS].
Everytime that archon dies, that souls reincarnates into a new templar following these rules:
-A High Templar + High Templar archon reincarnates into a High Templar
-A Dark Templar + Dark Templar reincarnates also into a High Templar
-A High Templar + Dark Templar reincarnates into a Dark Templar
In the begining of Templar Time there was a known amount of each type of templar and no archons.
They will merge until there is only one left. How do you determine which type of Templar will be the last remaining.
+ Show Spoiler +
In the Protoss Lore, every time an Archon is merged, their soul is also merged [BS].
Everytime that archon dies, that souls reincarnates into a new templar following these rules:
-A High Templar + High Templar archon reincarnates into a High Templar
-A Dark Templar + Dark Templar reincarnates also into a High Templar
-A High Templar + Dark Templar reincarnates into a Dark Templar
In the begining of Templar Time there was a known amount of each type of templar and no archons.
They will merge until there is only one left. How do you determine which type of Templar will be the last remaining.
+ Show Spoiler +
Ref:
[BS]: BullShit or Blizzard website, you choose which one I took this fact from
[BS]: BullShit or Blizzard website, you choose which one I took this fact from
28, 29, 30.
+ Show Spoiler +
On April 11 2011 06:34 MusicalPulse wrote:
One that's similar to the liters of water problem.
Here's what you have:
-Two 8-liter jugs, filled with water
-One 3-liter jug, empty
-Four infinite size, empty pools
Here's what your objective is:
Fill each of the four pools with exactly 4 liters of water.
------
Typical "stars" are drawn in connected, but not repeated, line segments. For example, a 5-point star is drawn as such - line segments AC, CE, EB, BD, DA. The segments must always alternate a constant number of points (in the above case, skipping 1 point in between).
Given the information that there is only 1 way to draw a 5-point star, and that there is NO way to draw a 6-point star (in continuous lines, that is), and there are 2 ways to draw a 7-point star, how many different ways are there to draw a 1000-point star?
------
In Madadia, a rather strange and misguided assassin, from his hidden position, uses a high-powered rifle to shoot someone in the foot from 50 feet away. The bullet travels at 1300 feet per second. Both the person being shot at and the assassin are at sea level. What will be the first evidence to the person of the attack? (As in how will he know he as been shot.)
One that's similar to the liters of water problem.
Here's what you have:
-Two 8-liter jugs, filled with water
-One 3-liter jug, empty
-Four infinite size, empty pools
Here's what your objective is:
Fill each of the four pools with exactly 4 liters of water.
------
Typical "stars" are drawn in connected, but not repeated, line segments. For example, a 5-point star is drawn as such - line segments AC, CE, EB, BD, DA. The segments must always alternate a constant number of points (in the above case, skipping 1 point in between).
Given the information that there is only 1 way to draw a 5-point star, and that there is NO way to draw a 6-point star (in continuous lines, that is), and there are 2 ways to draw a 7-point star, how many different ways are there to draw a 1000-point star?
------
In Madadia, a rather strange and misguided assassin, from his hidden position, uses a high-powered rifle to shoot someone in the foot from 50 feet away. The bullet travels at 1300 feet per second. Both the person being shot at and the assassin are at sea level. What will be the first evidence to the person of the attack? (As in how will he know he as been shot.)
31. (odd overlapping)+ Show Spoiler +
On April 11 2011 07:15 pikagrue wrote:
You have place 1001 unit squares on a coordinate plane. The squares can overlap (any number of squares can overlap in any fashion). Prove that the minimum amount of area where an odd number of squares overlap (amount of area covered by an odd number of squares) is equal to 1. The sides of the squares are parallel to the X and Y axes
This has a really nice 1-2 line solution.
EDIT: Single layer counts as an odd number btw.
You have place 1001 unit squares on a coordinate plane. The squares can overlap (any number of squares can overlap in any fashion). Prove that the minimum amount of area where an odd number of squares overlap (amount of area covered by an odd number of squares) is equal to 1. The sides of the squares are parallel to the X and Y axes
This has a really nice 1-2 line solution.
EDIT: Single layer counts as an odd number btw.
Rephrase: Put 1001 unit squares on a coordinate plane. The squares can overlap in any fashion. Let S be the region of the plane that is covered by an odd number of squares. Prove that the area of S is greater than or equal to 1. Note: the sides of the squares are parallel to X and Y axes.
32.(3-player ffa) + Show Spoiler +
On April 11 2011 07:45 Housemd wrote:
Okay, I think I'll add one that isn't on the thread.
To start off, a truel is exactly like a duel just with three people. One morning Mr. Black, Mr. Gray, and Mr. White decide to resolve a dispute by trueling with pistols until only one of them survives. Mr. Black is the worst shot, hitting once every three times (1/3). Mr. Gray is the second best shot, hitting his target twice out of every three times (2/3). Lastly, Mr. White always hits his target (1/1). To make it fair, Mr. Black will shot first, following by Mr. Gray (if he is still alive) and then Mr. White (provided that he is still alive). The Question is: Where should Mr. Black aim his first shot?
Okay, I think I'll add one that isn't on the thread.
To start off, a truel is exactly like a duel just with three people. One morning Mr. Black, Mr. Gray, and Mr. White decide to resolve a dispute by trueling with pistols until only one of them survives. Mr. Black is the worst shot, hitting once every three times (1/3). Mr. Gray is the second best shot, hitting his target twice out of every three times (2/3). Lastly, Mr. White always hits his target (1/1). To make it fair, Mr. Black will shot first, following by Mr. Gray (if he is still alive) and then Mr. White (provided that he is still alive). The Question is: Where should Mr. Black aim his first shot?
33. (going for gold) + Show Spoiler +
On April 11 2011 08:22 Zeroes wrote:
Threads like these make me think that the starcraft community is the smartest community! =D
There are 3 coins on the table Gold, Silver and copper. The man at the table will let you make one statement, if it is true he will give you a coin. If it is false you won't let you have a coin. What will you say to him to always ensure that you have the gold coin?
Threads like these make me think that the starcraft community is the smartest community! =D
There are 3 coins on the table Gold, Silver and copper. The man at the table will let you make one statement, if it is true he will give you a coin. If it is false you won't let you have a coin. What will you say to him to always ensure that you have the gold coin?
34. (face the wall) + Show Spoiler +
On April 11 2011 12:05 x-Catalyst wrote:
4 captives are buried in the ground. There are 3 people on one side of a solid brick wall, and one person on the other. They are all facing the brick wall. The people on the left are in a line, so they can see the people in front of them. Person 1 can see person 2 and 3. Person 2 can see person 3. But person 3 and 4 can only see the brick wall in front of them. The people who are holding the captives place a star on each of the hats on their heads. 2 red, and 2 blue. They tell all 4 captives this, but do not tell them what order the stars are in. They say that if one of the captives can guess his color star, they will let him free. But if he's wrong, they all die. The captives can not talk to each other. They can only see what's ahead of them, including the other peoples stars, but not their own. The brick wall is completely solid and tall/wide. There is nothing reflective, and they cannot turn their heads to look at the people behind them. Which one of these people know what star they have, and how do they know?
![[image loading]](http://imgur.com/3EJ14.jpg)
4 captives are buried in the ground. There are 3 people on one side of a solid brick wall, and one person on the other. They are all facing the brick wall. The people on the left are in a line, so they can see the people in front of them. Person 1 can see person 2 and 3. Person 2 can see person 3. But person 3 and 4 can only see the brick wall in front of them. The people who are holding the captives place a star on each of the hats on their heads. 2 red, and 2 blue. They tell all 4 captives this, but do not tell them what order the stars are in. They say that if one of the captives can guess his color star, they will let him free. But if he's wrong, they all die. The captives can not talk to each other. They can only see what's ahead of them, including the other peoples stars, but not their own. The brick wall is completely solid and tall/wide. There is nothing reflective, and they cannot turn their heads to look at the people behind them. Which one of these people know what star they have, and how do they know?
35, 36, 37. + Show Spoiler +
On April 11 2011 12:22 hacklebeast wrote:
Trying to think of some that fall under a "math" category...
easy:
+ Show Spoiler +
harder (not math related):
+ Show Spoiler +
harder:
+ Show Spoiler +
Trying to think of some that fall under a "math" category...
easy:
+ Show Spoiler +
You have a jar filled with 100 black marbles and a jar filled with 100 white marbles. You can rearrange the marbles any way you like as long as all of the marbles are in jars. After sorting, you randomly select one jar and then randomly select one marble from the jar. If the marble is white you win. What are your maximum odds for winning?
harder (not math related):
+ Show Spoiler +
You are blind folded and presented with 100 coins. You are told that 50 are heads and 50 are tails. How can you split them into two piles so that the two piles contain an equal amount of heads? You can not distinguish the orientation of the coins by touch.
harder:
+ Show Spoiler +
You have two cups with 10 teaspoons of tea in one and 10 teaspoons of coffee in the other. You take one teaspoon from the tea cup and put it in the coffee cup, then take a teaspoon of the coffee-tea mix and put it in the tea cup. Is there more coffee in the tea cup, or tea in the coffee cup?
38. (are you positive?) + Show Spoiler +
On April 11 2011 13:12 Akari Takai wrote:
Think I'll contribute my own as well....
Suppose you are being screened for a disease that affects 1 in 10,000 people statistically. You are to be given a test for the disease that is 99% sensitive and 99% specific, that is, that the test will correctly identify someone who has the disease as testing positive 99% of the time, and will correctly identify someone who does not have the disease as testing negative 99% of the time. How much more likely are you to have the disease given a positive test result than to not have the disease given a positive test result.
I'm going to give the answer below just because I might not be in this thread for a few days and it would be unfair of me to not give the answer! But you should try to solve it on your own first.
CAUTION! Answer below...
+ Show Spoiler +
Think I'll contribute my own as well....
Suppose you are being screened for a disease that affects 1 in 10,000 people statistically. You are to be given a test for the disease that is 99% sensitive and 99% specific, that is, that the test will correctly identify someone who has the disease as testing positive 99% of the time, and will correctly identify someone who does not have the disease as testing negative 99% of the time. How much more likely are you to have the disease given a positive test result than to not have the disease given a positive test result.
I'm going to give the answer below just because I might not be in this thread for a few days and it would be unfair of me to not give the answer! But you should try to solve it on your own first.
CAUTION! Answer below...
+ Show Spoiler +
Let
P(S) = the probability that you are sick (This is 0.0001 given that the incidence of disease is 1 in 10,000 people)
P(N) = the probability that you are not sick (This is 1-P(N) or 0.9999)
P(+|S) = the probability that the test is positive, given that you are sick (This is 0.99 since the test is 99% accurate)
P(+|N) = the probability that the test is positive, given that you are not sick (This is 0.01 since the test will produce a false positive for 1% of users)
P(+) = the probability of a positive test event, regardless of other information. (0.010098, which is found by adding the probability that a true positive result will appear (0.99*0.0001) plus the probability that a false positive will appear (0.01*0.9999).)
P(N|+) = the probability that a non sick person tested positive
P(N|+) = P(+|N)P(N)/P(+) = 0.01*0.9999/0.010098 ~ 0.9901960784313725
P(N|+) ~ 99%
P(S|+) = the probability that a sick person tested positive
P(S|+) = P(+|S)P(S)/P(+) = 0.99*0.0001/0.010098 ~ 0.0098039215686275
P(S|+) ~ 1%
P(N|+)/P(S|+) = 101.
You are 101 times more likely to NOT be sick given a positive test result than to BE sick given a positive test result. (Even though the test is 99% sensitive and 99% specific!)
P(S) = the probability that you are sick (This is 0.0001 given that the incidence of disease is 1 in 10,000 people)
P(N) = the probability that you are not sick (This is 1-P(N) or 0.9999)
P(+|S) = the probability that the test is positive, given that you are sick (This is 0.99 since the test is 99% accurate)
P(+|N) = the probability that the test is positive, given that you are not sick (This is 0.01 since the test will produce a false positive for 1% of users)
P(+) = the probability of a positive test event, regardless of other information. (0.010098, which is found by adding the probability that a true positive result will appear (0.99*0.0001) plus the probability that a false positive will appear (0.01*0.9999).)
P(N|+) = the probability that a non sick person tested positive
P(N|+) = P(+|N)P(N)/P(+) = 0.01*0.9999/0.010098 ~ 0.9901960784313725
P(N|+) ~ 99%
P(S|+) = the probability that a sick person tested positive
P(S|+) = P(+|S)P(S)/P(+) = 0.99*0.0001/0.010098 ~ 0.0098039215686275
P(S|+) ~ 1%
P(N|+)/P(S|+) = 101.
You are 101 times more likely to NOT be sick given a positive test result than to BE sick given a positive test result. (Even though the test is 99% sensitive and 99% specific!)
39. (ask the zerglings)+ Show Spoiler +
On April 11 2011 14:26 Earll wrote:
This might be something everyone knows the answer to and might already have been posted(though I cant say I have seen it and I think i have read all of the 16 pages) But here goes.
You have to walk into 1 of 2 doors, where one will lead to certain instantenous death, and the other will lead to a life full of starcraft 2 and happy things. Each door is guarded by an all knowing all powerfull zergling(A crackling, if you will). One of the zerglings will always lie and the other will always tell the truth. You can ask One of them, 1 question. What do you ask to figure out what door to take? (You obviously do not know what zergling lies, and what door the zergling guards holds no relation to him lying or telling the truth.)
This might be something everyone knows the answer to and might already have been posted(though I cant say I have seen it and I think i have read all of the 16 pages) But here goes.
You have to walk into 1 of 2 doors, where one will lead to certain instantenous death, and the other will lead to a life full of starcraft 2 and happy things. Each door is guarded by an all knowing all powerfull zergling(A crackling, if you will). One of the zerglings will always lie and the other will always tell the truth. You can ask One of them, 1 question. What do you ask to figure out what door to take? (You obviously do not know what zergling lies, and what door the zergling guards holds no relation to him lying or telling the truth.)
40. (a round robin starcraft tournament) + Show Spoiler +
Suppose that 20 starcraft pros played in a tournament where each player competed against every other player exactly once. The result of each game is only win/lose, no draw. Is it always possible (regardless of results) to name the players 1,2,3,...,20 so that player 1 defeated player 2, player 2 defeated player 3,... player 19 defeated player 20? Give a proof or a counterexample.
41. + Show Spoiler +
On April 11 2011 20:41 ]343[ wrote:
Hmm, don't think this has been posted yet?
Let A be a finite set of (distinct) integers. Let A+A be the set of all sums a+b where a, b are in A, and similarly define A-A to be the set of all differences a-b where a, b are in A. a and b are not necessarily distinct. Prove or disprove: |A+A| <= |A-A|.
(Example: A = {1, 2, 3}. A+A = {2, 3, 4, 5, 6}. A-A = {-2, -1, 0, 1, 2}.)
Hmm, don't think this has been posted yet?
Let A be a finite set of (distinct) integers. Let A+A be the set of all sums a+b where a, b are in A, and similarly define A-A to be the set of all differences a-b where a, b are in A. a and b are not necessarily distinct. Prove or disprove: |A+A| <= |A-A|.
(Example: A = {1, 2, 3}. A+A = {2, 3, 4, 5, 6}. A-A = {-2, -1, 0, 1, 2}.)
42. + Show Spoiler +
Find a mathematical model that explains everything in the universe. Gogo glhf.
43. + Show Spoiler +
On April 13 2011 14:18 MusicalPulse wrote:
Friend asked me this one, kinda like the other 3 person truth/lie one.
Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which.
Friend asked me this one, kinda like the other 3 person truth/lie one.
Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which.
44.
I'll add more when I can.
