"October 2, 2001" in MMDDYYYY format is a palindrome (a string that reads the same forwards as it does backwards). Pretty cool, check it out: 10/02/2001 --> 10022001. When was the last date before October 2, 2001 that is also a palindrome?
tell as many palindrome dates as possilble
Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your common sense.
Thursday, June 30, 2011
DIFFERENTIATION DISASTER
We know that the derivative of x2 with respect to x is 2x. However, what if we rewrite x2 as the sum of x x's, and then take the derivative:
d/dx[ x2 ] = d/dx[ x + x + x + ... (x times) ]
= d/dx[x] + d/dx[x] + d/dx[x] ... (x times)
= 1 + 1 + 1 + ... (x times)
= x
This argument shows that the derivative of x2 with respect to x is actually x. So what's going on here?
Note: Most people with some math experience can show that some part of the argument is erroneous. As in simply, something doesn't follow. However, a full solution will explain why this argument attacks something that lies at the very heart of calculus itself, and that is what really explains why it's erroneous.
d/dx[ x2 ] = d/dx[ x + x + x + ... (x times) ]
= d/dx[x] + d/dx[x] + d/dx[x] ... (x times)
= 1 + 1 + 1 + ... (x times)
= x
This argument shows that the derivative of x2 with respect to x is actually x. So what's going on here?
Note: Most people with some math experience can show that some part of the argument is erroneous. As in simply, something doesn't follow. However, a full solution will explain why this argument attacks something that lies at the very heart of calculus itself, and that is what really explains why it's erroneous.
VANISHING DOLLAR
Three men go to a cheap motel, and the desk clerk charges them a sum of $30.00 for the night. The three of them split the cost ten dollars each. Later the manager comes over and tells the desk clerk that he overcharged the men, since the actual cost should have been $25.00. The manager gives the bellboy $5.00 and tells him to give it to the men. The bellboy, however, decides to cheat the men and pockets $2.00, giving each of the men only one dollar.
Now each man has paid $9.00 to stay for the night, and 3 x $9.00 = $27.00. The bellboy has pocketed $2.00. But $27.00 + $2.00 = $29.00. Where is the missing $1.00? WTF?
Now each man has paid $9.00 to stay for the night, and 3 x $9.00 = $27.00. The bellboy has pocketed $2.00. But $27.00 + $2.00 = $29.00. Where is the missing $1.00? WTF?
INFINITE QUARTER SEQUENCE
You are wearing a blindfold and thick gloves. An infinite number of quarters are laid out before you on a table of infinite area. Someone tells you that 20 of these quarters are tails and the rest are heads. He says that if you can split the quarters into 2 piles where the number of tails quarters is the same in both piles, then you win all of the quarters. You are allowed to move the quarters and to flip them over, but you can never tell what state a quarter is currently in (the blindfold prevents you from seeing, and the gloves prevent you from feeling which side is heads or tails). How do you partition the quarters so that you can win them all?
Hint 1: If an infinite number of quarters confuses you, try 100.
Click here to see the answer
Hint 1: If an infinite number of quarters confuses you, try 100.
Click here to see the answer
CAMEL BANANA TRANSPORT
You have 3,000 bananas and a camel which can carry at most 1,000 bananas at a time. The camel eats a banana before moving a unit. You want to transport the bananas 1,000 units. What is the maximum number of uneaten bananas that you can move 1,000 units?
TRIANGLIA
Trianglia is a jacked-up island where no road has a dead end, and all the crossroads are "Y" shaped. The young prince of Trianglia mounts his horse, and is about to go on a quest to explore the land of Trianglia. He gets to the road by his palace, when the mother queen comes out and shouts: "But Charles, how will you find your way back?". "Don't worry Elizabeth", the prince replies, "I will turn right in every second crossroad to which I arrive, and left otherwise. Thus I shall surely return to the palace sooner or later." Is the prince right?
explain
explain
DAUGHTERS' AGES
Local Berkeley professors Dr. Demmel and Dr. Shewchuk bump into each other on Telegraph Ave. They haven't seen each other since Vietnam.
Shewchuk hey! how have you been?
Demmel great! i got married and i have three daughters now
Shewchuk really? how old are they?
Demmel well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..
Shewchuk right, ok ... oh wait ... hmm, i still don't know
Demmel oh sorry, the oldest one just started to play the piano
Shewchuk wonderful! my oldest is the same age!
How old are the daughters?
Shewchuk hey! how have you been?
Demmel great! i got married and i have three daughters now
Shewchuk really? how old are they?
Demmel well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..
Shewchuk right, ok ... oh wait ... hmm, i still don't know
Demmel oh sorry, the oldest one just started to play the piano
Shewchuk wonderful! my oldest is the same age!
How old are the daughters?
GREEDY PIRATES
A pirate ship captures a treasure of 1000 golden coins. The treasure has to be split among the 5 pirates: 1, 2, 3, 4, and 5 in order of rank. The pirates have the following important characteristics: infinitely smart, bloodthirsty, greedy. Starting with pirate 5 they can make a proposal how to split up the treasure. This proposal can either be accepted or the pirate is thrown overboard. A proposal is accepted if and only if a majority of the pirates agrees on it. What proposal should pirate 5 make?
CALENDAR CUBES I
a corporate business man has two cubes on his office desk. every day he arranges both cubes so that the front faces show the current day of the month. what numbers are on the faces of the cubes to allow this?
Note: You can't represent the day "7" with a single cube with a side that says 7 on it. You have to use both cubes all the time. So the 7th day would be "07". I also should note that this is a really sly problem. Almost unfair.
There are many solutions
Note: You can't represent the day "7" with a single cube with a side that says 7 on it. You have to use both cubes all the time. So the 7th day would be "07". I also should note that this is a really sly problem. Almost unfair.
There are many solutions
THREE-WAY PISTOL DUEL
you're a cyborg in a pistol duel with two other cyborgs. you have been programmed to fire pistols with an accuracy of 33%. the other two cyborgs shoot with accuracies of 100% and 50%, respectively. the rules of the duel are one shot per-cyborg per-round. the shooting order is from worst shooter to best shooter. thus, you go first, the 50% guy goes second, and the 100% guy goes third; repeat. if a cyborg dies, we just skip his or her turn, obviously. what should you shoot at in round 1 to maximize your chances of survival over time?
5 CARD MAGIC TRICK
this is a magic trick performed by two magicians, A and B, with one regular, shuffled deck of 52 cards. A asks a member of the audience to randomly select 5 cards out of a deck. the audience member -- who we will refer to as C from here on -- then hands the 5 cards back to magician A. after looking at the 5 cards, A picks one of the 5 cards and gives it back to C. A then arranges the other four cards in some way, and gives those 4 cards face down, in a neat pile, to B. B looks at these 4 cards and then determines what card is in C's hand (the missing 5th card). how is this trick done?
Note 1: There's no secretive message communication in the solution, like encoded speech or ninja hand signals or ESP or whatever ... the only communication between the two magicians is in the logic of the 4 cards transferred from A to B. Think of these magicians as mathematicians.
Note 1: There's no secretive message communication in the solution, like encoded speech or ninja hand signals or ESP or whatever ... the only communication between the two magicians is in the logic of the 4 cards transferred from A to B. Think of these magicians as mathematicians.
SQUARE FORMATION
Using all five of the pieces shown below, make a new square.
Save the image. then print it. Then cut out the pieces and play with them on your desk.
Save the image. then print it. Then cut out the pieces and play with them on your desk.
100 PRISONERS AND A LIGHT BULB
100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb from his or her own cell. Each day, the warden picks a prisoner equally at random, and that prisoner visits the central living room; at the end of the day the prisoner is returned to his cell. While in the living room, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting the claim that all 100 prisoners have been to the living room. If this assertion is false (that is, some prisoners still haven't been to the living room), all 100 prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world can always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.
Before this whole procedure begins, the prisoners are allowed to get together in the courtyard to discuss a plan. What is the optimal plan they can agree on, so that eventually, someone will make a correct assertion?
Note 1: What is meant by optimal? If your solution is optimal, it means you can prove that no other algorithm can produce a lower average running time. This is usually very hard to do though, and I would be surprised if anyone ever sends me such a proof. So the best we can do in the meantime is try to beat the best average running time we know of. The number to beat so far is around 3500 days. So BEFORE YOU E-MAIL ME YOUR SOLUTION(a_red_Sani@yahoo.co.in), check its average time to see if beats the 4000 day ballpark. If you get a number around 27-28 years, then you've found the solution most people who solve the puzzle come up with. However, it's not optimal.
Note 2: How to compute average running time? The preferred method is to do a probabilistic analysis using pencil and paper. But if you haven't learned about stuff like that, a much simpler way is to just program your solution and run it maybe 100 times, recording how many days elapsed in each invocation. Afterwards you should have an array of 100 numbers. Now take the average of all them, and you'll have an empirical average which is close to the theoretical one.
Note 3: The problem statement used to say "The prisoners are allowed to get together one night to discuss a plan." In the forum, quite a few people mentioned the clever solution of simply having the planning meeting in the central living room, and then asserting that everyone has been there on the first day of the random selection process. To assure that this problem is not so easily defeated, I have stipulated that the meeting happen in the courtyard.
Before this whole procedure begins, the prisoners are allowed to get together in the courtyard to discuss a plan. What is the optimal plan they can agree on, so that eventually, someone will make a correct assertion?
Note 1: What is meant by optimal? If your solution is optimal, it means you can prove that no other algorithm can produce a lower average running time. This is usually very hard to do though, and I would be surprised if anyone ever sends me such a proof. So the best we can do in the meantime is try to beat the best average running time we know of. The number to beat so far is around 3500 days. So BEFORE YOU E-MAIL ME YOUR SOLUTION(a_red_Sani@yahoo.co.in), check its average time to see if beats the 4000 day ballpark. If you get a number around 27-28 years, then you've found the solution most people who solve the puzzle come up with. However, it's not optimal.
Note 2: How to compute average running time? The preferred method is to do a probabilistic analysis using pencil and paper. But if you haven't learned about stuff like that, a much simpler way is to just program your solution and run it maybe 100 times, recording how many days elapsed in each invocation. Afterwards you should have an array of 100 numbers. Now take the average of all them, and you'll have an empirical average which is close to the theoretical one.
Note 3: The problem statement used to say "The prisoners are allowed to get together one night to discuss a plan." In the forum, quite a few people mentioned the clever solution of simply having the planning meeting in the central living room, and then asserting that everyone has been there on the first day of the random selection process. To assure that this problem is not so easily defeated, I have stipulated that the meeting happen in the courtyard.
CIRCULAR JAIL CELL
There is a circular jail with 100 cells numbered 1-100. Each cell has an inmate and the door is locked. One night the jailor gets drunk and starts running around the jail in circles. In his first round he opens each door. In his second round he visits every 2nd door (2,4,6---) and shuts the door. In the 3rd round he visits every 3rd door (3,6,9---) and if the door is shut he opens it, if it is open he shuts it. This continues for 100 rounds (i.e. 4,8,12 ---; 5,10,15 ---; ---; 49,98 etc.) and exhausted the jailor falls down. How many prisoners found their doors open after 100 rounds?
BIRTHDAY TWINS
Sheila and He-Man are twins; Sheila is the OLDER twin. Assume they were born immediately after each other, an infinitesimally small - but nonzero - amount of time apart. During one year in the course of their lives, Sheila celebrates her birthday two days AFTER He-Man does. How is this possible?
10/28/2002 3:58AM Bonus: What is the maximum amount of time by which Sheila and He-Man can be apart in their birthday celebrations during the same year? I think it's more than two days.
Note: For both Sheila and He-Man, these birthday celebrations happen on the actual birthday date -- it cannot be a celebration that occurs at a date earlier or later than the actual birthday date for whatever reasons of convenience. Also, the solution has nothing to do with the theory of relativity or any other over complicated nonsense like that.
10/28/2002 3:58AM Bonus: What is the maximum amount of time by which Sheila and He-Man can be apart in their birthday celebrations during the same year? I think it's more than two days.
Note: For both Sheila and He-Man, these birthday celebrations happen on the actual birthday date -- it cannot be a celebration that occurs at a date earlier or later than the actual birthday date for whatever reasons of convenience. Also, the solution has nothing to do with the theory of relativity or any other over complicated nonsense like that.
Doublespeak Proverbs
The following proverb brainteasers represent well known old sayings that have been relied on for hundreds of years. You've probably used these proverbs, or at least have heard them used at some point in your life. But for this brainteaser quiz, they have been re-written using BIG WORDS that mean essentially the same thing, but sound a whole lot different.
If you can translate these camouflaged (but familiar) witticisms, you have a talent for making clear writing out of doublespeak. We think you'll agree that they sound much better and make a lot more sense in their original forms, which relied on plain and simple English
1) Neophyte's serendipity.
2) The stylus is more potent than the claymore.
3) It is fruitless to indoctrinate a super-annuated canine with innovative manoeuvres.
4) The person presenting the ultimate cachinnation possesses, thereby, the optimal cachinnation.
5) Sorting on the part of mendicants must be interdicted.
6) Exclusive dedication to necessary chores without interludes of hedonistic diversion renders John a heptudinous fellow.
7) Pulchritude possesses solely cutaneous profundity
8) Where there are visible vapours having their province in ignited carbonaceous material, there is conflagration
9) A plethora of individuals with expertise in culinary techniques vitiates the potable concoction produced by steeping comestibles.
10) Male cadavers are incapable of yielding testimony.
11) All articles that coruscate with resplendence are not truly auriferous.
12) Members of an avian species of identical plumage congregate.
13) Eschew the implement of corrections and vitiate the scion.
14) If a large solid-hoofed mammal becomes available to you without compensation, refrain from casting your faculty for seeing into the oral cavity of such a creature.
15) Each vaporous mass suspended in the firmament has an interior decoration of metallic hue.
16) It is not advantageous to place the sum total of your barnyard collections into the same wicker receptacle
17) Feathered bipeds of a kindred mind in their segregated environment associate with a high degree of amiability.
18) Deviation from the ordinary or common routine of existence is that which gives zest to man's cycle of existence.
19) He who locks himself into the arms of Morpheus promptly at eventide, and starts the day before it is officially announced by the rising sun, excels in physical fitness, increases his economic assets and celebrates with remarkable efficiency.
20) Do not traverse a structure erected to afford passage over a waterway until the time of drawing nigh unto it.
21) Superfluous chronological dispatch institutes riddance of value defects.
22) There’s no value to be derived from demanding attention by loud screeches over fallen white liquid derived from the lactic glands of a female bovine.
23) An excess of culinary experts impairs the quality of a thin derivative of meat.
24) A body of persons abiding in a domicile of silica combined with metallic oxides should not carelessly project small geological specimens.
If you can translate these camouflaged (but familiar) witticisms, you have a talent for making clear writing out of doublespeak. We think you'll agree that they sound much better and make a lot more sense in their original forms, which relied on plain and simple English
1) Neophyte's serendipity.
2) The stylus is more potent than the claymore.
3) It is fruitless to indoctrinate a super-annuated canine with innovative manoeuvres.
4) The person presenting the ultimate cachinnation possesses, thereby, the optimal cachinnation.
5) Sorting on the part of mendicants must be interdicted.
6) Exclusive dedication to necessary chores without interludes of hedonistic diversion renders John a heptudinous fellow.
7) Pulchritude possesses solely cutaneous profundity
8) Where there are visible vapours having their province in ignited carbonaceous material, there is conflagration
9) A plethora of individuals with expertise in culinary techniques vitiates the potable concoction produced by steeping comestibles.
10) Male cadavers are incapable of yielding testimony.
11) All articles that coruscate with resplendence are not truly auriferous.
12) Members of an avian species of identical plumage congregate.
13) Eschew the implement of corrections and vitiate the scion.
14) If a large solid-hoofed mammal becomes available to you without compensation, refrain from casting your faculty for seeing into the oral cavity of such a creature.
15) Each vaporous mass suspended in the firmament has an interior decoration of metallic hue.
16) It is not advantageous to place the sum total of your barnyard collections into the same wicker receptacle
17) Feathered bipeds of a kindred mind in their segregated environment associate with a high degree of amiability.
18) Deviation from the ordinary or common routine of existence is that which gives zest to man's cycle of existence.
19) He who locks himself into the arms of Morpheus promptly at eventide, and starts the day before it is officially announced by the rising sun, excels in physical fitness, increases his economic assets and celebrates with remarkable efficiency.
20) Do not traverse a structure erected to afford passage over a waterway until the time of drawing nigh unto it.
21) Superfluous chronological dispatch institutes riddance of value defects.
22) There’s no value to be derived from demanding attention by loud screeches over fallen white liquid derived from the lactic glands of a female bovine.
23) An excess of culinary experts impairs the quality of a thin derivative of meat.
24) A body of persons abiding in a domicile of silica combined with metallic oxides should not carelessly project small geological specimens.
Introducing "Challenge Questions"
Every week we are gonna post one Challenge question starting from 15th June and the winner( the person who gets the correct answer) will be rewarded with free goodies(the goodies will depend on the Blogs earnings). so the more we earn the more GET so share the blog with your friends.
Terms and conditions -:
1) in case of a tie there will be a lucky draw where the the answer which was givin will be given priority.
2) All answers have to be sent to a_red_sani@yahoo.co.in and should have the topic "Challenge question no - ## ")
3) The decision of the blog is final
4) Multiple entries are not allowed
5) You need to prove ur identity to receive the reward
6) your answer should contain
a) name
b) age
c) gender
d) contact info
Terms and conditions -:
1) in case of a tie there will be a lucky draw where the the answer which was givin will be given priority.
2) All answers have to be sent to a_red_sani@yahoo.co.in and should have the topic "Challenge question no - ## ")
3) The decision of the blog is final
4) Multiple entries are not allowed
5) You need to prove ur identity to receive the reward
6) your answer should contain
a) name
b) age
c) gender
d) contact info
POPULATION OF FUNKYTOWN
In the city of Funkytown, the following facts are true:
No two inhabitants have exactly the same number of hairs.
No inhabitant has exactly 483,207 hairs.
There are more inhabitants than there are hairs on the head of any one inhabitant.
What is the largest possible number of inhabitants of Funkytown?
No two inhabitants have exactly the same number of hairs.
No inhabitant has exactly 483,207 hairs.
There are more inhabitants than there are hairs on the head of any one inhabitant.
What is the largest possible number of inhabitants of Funkytown?
PAPER CUTTING
LIGHT BULBS AND SWITCHES
You are in a room with three light switches, each of which controls one of three light bulbs in the next room. Your task is to determine which switch controls which bulb. All lights are initially off, and you can't see into one room from the other. You are allowed only one chance to enter the room with the light bulbs. How can you determine which lightswitch goes with which light bulb?
EQUILATERAL TRIANGLE DIVISION
draw an equilateral triangle (all sides same length). divide it into four identical shapes. remove the bottom left hand shape. now divide the resulting shape into four identical shapes.
SQUARE DIVISION
draw a square. divide it into four identical squares. remove the bottom left hand square. now divide the resulting shape into four identical shapes.
GHETTO ENCRYPTION II
Three coworkers would like to know their average salary. However, they are self-conscious and don't want to tell each other their own salaries, for fear of either being ridiculed or getting their houses robbed. How can they find their average salary, without disclosing their own salaries? and there is no other person computer or any type of gadget
and these guys are mathematicians and will do anything to get to know others income
and these guys are mathematicians and will do anything to get to know others income
GHETTO ENCRYPTION I
You want to send a valuable object to a friend securely. You have a box which can be fitted with multiple locks, and you have several locks and their corresponding keys. However, your friend does not have any keys to your locks, and if you send a key in an unlocked box, the key could be copied en route. How can you send the object securely?
Alternative, more precise phrasing: Andy and Grant are staying in different rooms in the same hotel. Andy needs to give a gold pendant to Grant, but spies are trying to assassinate Andy and Grant so neither of them can leave their room. The only way they can transfer objects is by using the bellhops. Both Andy and Grant have a safe with a large clasp that can be secured with a padlock. Both Andy and Grant have a padlock and a corresponding key. (So 1 gold pendant, 2 safes, 2 padlocks, and 2 keys.) But the bellhops are thieves. Anything that is not padlocked in the safe will be stolen by the bellhops - including any unlocked padlocks, the keys or the pendant. How can Andy transfer the gold pendant to Grant without it being stolen? (where both sides have encryption capability, and where unsecured items are taken away rather than just copied?)
Alternative, more precise phrasing: Andy and Grant are staying in different rooms in the same hotel. Andy needs to give a gold pendant to Grant, but spies are trying to assassinate Andy and Grant so neither of them can leave their room. The only way they can transfer objects is by using the bellhops. Both Andy and Grant have a safe with a large clasp that can be secured with a padlock. Both Andy and Grant have a padlock and a corresponding key. (So 1 gold pendant, 2 safes, 2 padlocks, and 2 keys.) But the bellhops are thieves. Anything that is not padlocked in the safe will be stolen by the bellhops - including any unlocked padlocks, the keys or the pendant. How can Andy transfer the gold pendant to Grant without it being stolen? (where both sides have encryption capability, and where unsecured items are taken away rather than just copied?)
GLOBE TRAVERSAL
how many places are there on the earth that one could walk one mile south, then one mile west, then one mile north and end up in the same spot? to be precise, let's assume the earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere. also, the rotation of the earth has nothing to do with the solution; you can assume you're walking on a static sphere if that makes the problem less complicated to you.
Get solution here
Get solution here
Wednesday, June 29, 2011
WHO AM I? (10)
The person who makes it, sells it. The person who buys it never uses it and the person who uses it doesn't know they are. What is it?
Get solution now just for a tweet
Get solution now just for a tweet
WHO AM I? (9)
Think of words ending in -GRY. Angry and hungry are two of them. There are only three words in the English language. What is the third word? The word is something that everyone uses every day. If you have listened carefully, I have already told you what it is.
Get solution now
Get solution now
WHO AM I? (8)
What is in seasons, seconds, centuries and minutes but not in decades, years or days?
Get solution now
Get solution now
WHO AM I? (7)
There was a green house. Inside the green house there was a white house. Inside the white house there was a red house. Inside the red house there were lots of babies. What is it?
Get solution now
Get solution now
WHO AM I? (6)
At night they come without being fetched. By day they are lost without being stolen. What are they?
Get solution now
Get solution now
WHO AM I? (5)
I never was, am always to be. No one ever saw me, nor ever will. And yet I am the confidence of all, To live and breath on this terrestrial ball. What am I?
Get solution now
Get solution now
WHO AM I? (4)
What always runs but never walks, often murmurs, never talks, has a bed but never sleeps, has a mouth but never eats?
Get solution now
Get solution now
WHO AM I? (3)
I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?
Get solution now
Get solution now
WHO AM I? (2)
It walks on four legs in the morning, two legs at noon and three legs in the evening. What is it?
Get solution now
Get solution now
WHO AM I? (1)
I am greater than God, and more evil than the devil. Poor people have me. Rich people want me. And if you eat me, you'll die. What am I?
Get solution now
Get solution now
COIN UNBIASING
You and your arch rival are competing for the same girl. After years of battling, you both decide to settle it by tossing a coin.
Your rival produces a coin, but you don't happen to have one on you. You are certain that the coin your rival has produced is loaded, ie. it will come up with heads more than 50% of the time on average.
How do you arrange a fair contest, based purely on chance and not skill, by flipping this coin?
Variation: (COIN BIASING) You and your rival are competing for the same girl, and decide to settle it with a coin toss. Your rival has known the girl longer than you have, so you agree that it is fair for him to have a chance of winning equal to P, where P > 0.5. However, you only have a fair coin. How can you conduct this contest such that the biased probability is manifested? What is the average number of coin flips needed to determine a winner?
Get solution now
Your rival produces a coin, but you don't happen to have one on you. You are certain that the coin your rival has produced is loaded, ie. it will come up with heads more than 50% of the time on average.
How do you arrange a fair contest, based purely on chance and not skill, by flipping this coin?
Variation: (COIN BIASING) You and your rival are competing for the same girl, and decide to settle it with a coin toss. Your rival has known the girl longer than you have, so you agree that it is fair for him to have a chance of winning equal to P, where P > 0.5. However, you only have a fair coin. How can you conduct this contest such that the biased probability is manifested? What is the average number of coin flips needed to determine a winner?
Get solution now
KNIGHT VS. DRAGON
A dragon and knight live on an island. This island has seven poisoned wells, numbered 1 to 7. If you drink from a well, you can only save yourself by drinking from a higher numbered well. Well 7 is located at the top of a high mountain, so only the dragon can reach it.
One day they decide that the island isn't big enough for the two of them, and they have a duel. Each of them brings a glass of water to the duel, they exchange glasses, and drink. After the duel, the knight lives and the dragon dies.
Why did the knight live? Why did the dragon die?
Get solution now
One day they decide that the island isn't big enough for the two of them, and they have a duel. Each of them brings a glass of water to the duel, they exchange glasses, and drink. After the duel, the knight lives and the dragon dies.
Why did the knight live? Why did the dragon die?
Get solution now
MYSTERIOUS TRIANGLE AREA
LOGICAL SIGNS I
You are an archaeologist that has just unearthed a long-sought pair of ancient treasure chests. One chest is plated with silver, and the other is plated with gold. According to legend, one of the two chests is filled with great treasure, whereas the other chest houses a man-eating python that can rip your head off. Faced with a dilemma, you then notice that there are inscriptions on the chests:
Silver Chest
This chest contains the python.
Gold Chest
One of these two inscriptions is true.
Based on these inscriptions, which chest should you open?
Get solution now
Silver Chest
This chest contains the python.
Gold Chest
One of these two inscriptions is true.
Based on these inscriptions, which chest should you open?
Get solution now
HOURGLASSES
You have two hourglasses: a 7 minute one and an 11 minute one. Using just these hourglasses, accurately time 15 minutes.
Get solution now
Get solution now
ARAB SHEIKH CAMELS
An Arab sheikh is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line last will win the fortune for its owner. During the race, the two brothers wander aimlessly for days, neither willing to cross the finish line. In desperation, they ask a wise man for advice. He tells them something; then the brothers leap onto the camels and charge toward the finish line. What did the wise man say?
Get solution now
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MARBLE JARS
you are a prisoner in a foreign land. your fate will be determined by a little game. there are two jars, one with 50 white marbles, and one with 50 black marbles. at this point, you are allowed to redistribute the marbles however you wish (e.g. swap a black marble with a white marble, etc.): the only requirement is that after you are done with the redistribution, every marble must be in one of the two jars. afterwards, both jars will be shaken up, and you will be blindfolded and presented with one of the jars at random. then you pick one marble out of the jar given to you. if the marble you pull out is white, you live; if black, you die. how should you redistribute the marbles to maximize the probability that you live; what is this maximum probability (roughly)?
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Poisened Drink Puzzle
A rich old man has died. After his death, his children are surprised to learn that he has left all of his money to his oldest son Jeremiah, who loved him dearly, and ignored his other children, who hated him.
So, the funeral is a day or two later, and the other sons and daughters have decided to kill Jeremiah and take his inheritance. Since his father's death, Jeremiah has taken to drinking, and they know that, at the wake, he's going to be gulping down the liquor like it was nectar of the gods. So they decide to poison the drinks. One of the other sons, Wallace, tends bar, and gets the poison all ready.
So Jeremiah comes up, crying and depressed, and orders a scotch on the rocks. Wallace serves him one, and he chugs it down in two seconds. "Give me another." Wallace gives him a second glass of scotch, which he also drinks in a matter of moments. The other siblings are puzzled...the poison is fast-acting; Jeremiah should be convulsing on the floor and retching his guts out. Finally, fifteen minutes later, a rather inebriated and very much alive Jeremiah orders one last glass of scotch, but as Wallace hands it to him, he changes his mind and leaves, sobbing. The other siblings come over to Wallace, and wonder what's going on. They talk about what could have gone wrong for a few minutes, and figure the poison's harmless. So Wallace sips the drink he poured for Jeremiah, and is pronounced DOA thirty minutes later.
Why did Jeremiah live? (He had no immunity to the poison, he didn't know it was coming, and the poison was obviously deadly.)
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So, the funeral is a day or two later, and the other sons and daughters have decided to kill Jeremiah and take his inheritance. Since his father's death, Jeremiah has taken to drinking, and they know that, at the wake, he's going to be gulping down the liquor like it was nectar of the gods. So they decide to poison the drinks. One of the other sons, Wallace, tends bar, and gets the poison all ready.
So Jeremiah comes up, crying and depressed, and orders a scotch on the rocks. Wallace serves him one, and he chugs it down in two seconds. "Give me another." Wallace gives him a second glass of scotch, which he also drinks in a matter of moments. The other siblings are puzzled...the poison is fast-acting; Jeremiah should be convulsing on the floor and retching his guts out. Finally, fifteen minutes later, a rather inebriated and very much alive Jeremiah orders one last glass of scotch, but as Wallace hands it to him, he changes his mind and leaves, sobbing. The other siblings come over to Wallace, and wonder what's going on. They talk about what could have gone wrong for a few minutes, and figure the poison's harmless. So Wallace sips the drink he poured for Jeremiah, and is pronounced DOA thirty minutes later.
Why did Jeremiah live? (He had no immunity to the poison, he didn't know it was coming, and the poison was obviously deadly.)
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Rungs under water puzzle
A boat has a ladder that has six rungs, each rung is one foot apart. The bottom rung is one foot from the water. The tide rises at 12 inches every 15 minutes. Assume high tide peaks in one hour.
When the tide is at it's highest, how many rungs are under water?
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When the tide is at it's highest, how many rungs are under water?
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Prime Number Upside down
If you type the prime 3217001 on a calculator and hold it upside down, you can read the word "IDOLIZE", provided you accept that '0' can be both "D" and "O". Are there any larger primes that become a meaningful word when read upside down like this?
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The count puzzle
The puzzle is too simple, you just need to fill in the blanks below.
The number of 0 in this whole puzzle is ......
The number of 1 in this whole puzzle is ......
The number of 2 in this whole puzzle is ......
The number of 3 in this whole puzzle is ......
The number of 4 in this whole puzzle is ......
The number of 5 in this whole puzzle is ......
The number of 6 in this whole puzzle is ......
The number of 7 in this whole puzzle is ......
The number of 8 in this whole puzzle is ......
The number of 9 in this whole puzzle is ......
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The number of 0 in this whole puzzle is ......
The number of 1 in this whole puzzle is ......
The number of 2 in this whole puzzle is ......
The number of 3 in this whole puzzle is ......
The number of 4 in this whole puzzle is ......
The number of 5 in this whole puzzle is ......
The number of 6 in this whole puzzle is ......
The number of 7 in this whole puzzle is ......
The number of 8 in this whole puzzle is ......
The number of 9 in this whole puzzle is ......
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Lateral Thinking - The Elevator Puzzle
A man lives on the twelfth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator -- or if it was raining that day -- he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up two flights of stairs to his apartment.
Why does the person follow such a way to go to his apartment?
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Why does the person follow such a way to go to his apartment?
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Prisoner's Hat Puzzle
Four prisoners are caught and are to be punished. The judge allows them to be freed if they can solve a puzzle. If they do not, they will be hanged. They all agree.
The four prisoners are lined up on some steps (shown below). They are all facing in the same direction. A wall separates the fourth prisoner from the other three.
To summarize:-
Man 1 can see men 2 and 3.
Man 2 can see man 3.
Man 3 can see none of the others.
Man 4 can see none of the others.
The prisoners are wearing hats. They are told that there are two white hats and two black hats. The men initially don't know what colour hat they are wearing. They are told to shout out the color of the hat that they are wearing as soon as they know for certain what colour it is.
They are not allowed to turn round or move.
They are not allowed to talk to each other.
They are not allowed to take their hats off.
Who is the first person to shout out and why?
Difficult form of the puzzle -:
A group of N players, at least 3, are each wearing a hat. The hats are coloured black and white, and there is at least one hat of each colour. Each player can see the colour of every other player's hat, but not that of their own. Without communicating with any other player, some of the players must make a guess as to the colour of their hat. How accurate can the guesses of the players be?
The answer to this question depends on how the players are expected to make their guesses.
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The four prisoners are lined up on some steps (shown below). They are all facing in the same direction. A wall separates the fourth prisoner from the other three.
To summarize:-
Man 1 can see men 2 and 3.
Man 2 can see man 3.
Man 3 can see none of the others.
Man 4 can see none of the others.
The prisoners are wearing hats. They are told that there are two white hats and two black hats. The men initially don't know what colour hat they are wearing. They are told to shout out the color of the hat that they are wearing as soon as they know for certain what colour it is.
They are not allowed to turn round or move.
They are not allowed to talk to each other.
They are not allowed to take their hats off.
Who is the first person to shout out and why?
Difficult form of the puzzle -:
A group of N players, at least 3, are each wearing a hat. The hats are coloured black and white, and there is at least one hat of each colour. Each player can see the colour of every other player's hat, but not that of their own. Without communicating with any other player, some of the players must make a guess as to the colour of their hat. How accurate can the guesses of the players be?
The answer to this question depends on how the players are expected to make their guesses.
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Fork in the Road
A logician vacationing in the Bahamas finds himself on an island inhabited by two proverbial tribes of liars and truth-tellers. Members of one tribe always speak the truth, while other always lie. He stands at the fork of a road (a Tee-junction) and has to ask a bystander which leg he needs to follow to reach the village. He knows not whether the native is a truth-teller or a liar. The logician thinks for a moment and then asks only one question. What does he ask?
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License to Kill Puzzle
Inspector Ixolite of the Yard was investigating a murder at Nottonmye Manor. It was a difficult case, and Ixolite was completely stumped until he noticed a message sent to him by the killer cunningly hidden in a newspaper advertisement selling Car Licence Plates.
Inspector Ixolite thought about it for a while, and when he had solved the puzzle, immediately arrested the guilty man.
Now answer these :
Q1) How did Ixolite know the advert was a clue for him?
Q2) Solve the code and tell me who Ixolite arrested.
Following is the newspaper advert (Car license plates for sale) that Inspector Ixolite saw.
Plates For Sale
[W 05 NWO]
[H 13 HSR ]
[O 05 EBM]
[D 08 UNE]
[U 10 HTY]
[N 04 BRE]
[N 16 TTE]
[I 26 LHC ]
[T 10 AEE]
[I 26 CNA]
[X 22 VDA]
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Inspector Ixolite thought about it for a while, and when he had solved the puzzle, immediately arrested the guilty man.
Now answer these :
Q1) How did Ixolite know the advert was a clue for him?
Q2) Solve the code and tell me who Ixolite arrested.
Following is the newspaper advert (Car license plates for sale) that Inspector Ixolite saw.
Plates For Sale
[W 05 NWO]
[H 13 HSR ]
[O 05 EBM]
[D 08 UNE]
[U 10 HTY]
[N 04 BRE]
[N 16 TTE]
[I 26 LHC ]
[T 10 AEE]
[I 26 CNA]
[X 22 VDA]
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Match and Lemon-aid Puzzle
A man in a restaurant asked a waiter for a juice glass, a dinner plate, water, a match, and a lemon wedge. The man poured enough water onto the plate to cover it.
"If you can get the water on the plate into this glass without touching or moving this plate, I will give you $100," the man said. "You can use the match and lemon to do this."
A few minutes later, the waiter walked away with $100 in his pocket. How did the waiter get the water into the glass?
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"If you can get the water on the plate into this glass without touching or moving this plate, I will give you $100," the man said. "You can use the match and lemon to do this."
A few minutes later, the waiter walked away with $100 in his pocket. How did the waiter get the water into the glass?
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Poisoned Wine Puzzle
You are the owner of a renowned Wine catering services. You have a biggie offer of catering service to a party for the Queen of your place. So they have ordered a thousand bottles of wine (Yes a 1000!!!).
You are obviously so happy about it and worked hard to arrange the complete order. But suddenly tragedy occurred, one of you employee accidentally mixed a poisoned bottle with the wine bottles in the container. Being the same type of bottle you are not able to distinguish it without drinking and the death occurs in 24 hours after drinking.
The ceremony being tomorrow , the queen will order for your execution, if the order is not completed. Now you have to find a solution to it. You cannot have another 1000 bottles and you have to figure out that bottle. The queen takes care of this situation and tells you that you have 1000 prisoners to let them drink the bottles and find out the poisoned bottle.
Find the minimum number of prisoners required to find the poisoned bottle from the 1000 bottles in 24 hours!!
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You are obviously so happy about it and worked hard to arrange the complete order. But suddenly tragedy occurred, one of you employee accidentally mixed a poisoned bottle with the wine bottles in the container. Being the same type of bottle you are not able to distinguish it without drinking and the death occurs in 24 hours after drinking.
The ceremony being tomorrow , the queen will order for your execution, if the order is not completed. Now you have to find a solution to it. You cannot have another 1000 bottles and you have to figure out that bottle. The queen takes care of this situation and tells you that you have 1000 prisoners to let them drink the bottles and find out the poisoned bottle.
Find the minimum number of prisoners required to find the poisoned bottle from the 1000 bottles in 24 hours!!
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