100 Blank Cards Riddle
Someone offers you the following deal:
There is a deck of 100 initially blank cards. The dealer is allowed to write ANY positive integer, one per card, leaving none blank. You are then asked to turn over as many cards as you wish. If the last card you turn over is the highest in the deck, you win; otherwise, you lose.
Winning grants you $50, and losing costs you only the $10 you paid to play.
Would you accept this challenge?
There is a deck of 100 initially blank cards. The dealer is allowed to write ANY positive integer, one per card, leaving none blank. You are then asked to turn over as many cards as you wish. If the last card you turn over is the highest in the deck, you win; otherwise, you lose.
Winning grants you $50, and losing costs you only the $10 you paid to play.
Would you accept this challenge?
Hint: Perhaps thinking in terms of one deck is the wrong approach.
Yes!
A sample strategy:
Divide the deck in half and turn over all lower 50 cards, setting aside the highest number you find. Then turn over the other 50 cards, one by one, until you reach a number that is higher than the card you set aside: this is your chosen "high card."
Now, there is a 50% chance that the highest card is contained in the top 50 cards (it is or it isn't), and a 50% chance that the second-highest card is contained in the lower 50. Combining the probabilities, you have a 25% chance of constructing the above situation (in which you win every time).
This means that you'll lose three out of four games, but for every four games played, you pay $40 while you win one game and $50. Your net profit every four games is $10.
Obviously, you have to have at least $40 to start in order to apply this strategy effectively. Did you answer this riddle correctly?
YES NO
A sample strategy:
Divide the deck in half and turn over all lower 50 cards, setting aside the highest number you find. Then turn over the other 50 cards, one by one, until you reach a number that is higher than the card you set aside: this is your chosen "high card."
Now, there is a 50% chance that the highest card is contained in the top 50 cards (it is or it isn't), and a 50% chance that the second-highest card is contained in the lower 50. Combining the probabilities, you have a 25% chance of constructing the above situation (in which you win every time).
This means that you'll lose three out of four games, but for every four games played, you pay $40 while you win one game and $50. Your net profit every four games is $10.
Obviously, you have to have at least $40 to start in order to apply this strategy effectively. Did you answer this riddle correctly?
YES NO
Blue Eyes Riddle
Both of my parents have brown eyes, as do I. My brother and my wife have blue eyes. Using the simple brown-blue model (two genes; a brown gene dominates blue gene), what are the chances of my first child having blue eyes?
Hint: Given my brother's blue eyes, what are the odds on my pair of eye-color genes?
1 in 3.
Since my brother has blue eyes (bb), both of my parents carry one brown and one blue gene (Bb). The three possibilities for my genotype, equally likely, are BB, Bb, and bB. Thus, there is a 2/3 chance that I carry a blue gene.
If I carry a blue gene, there is a 50% chance I will pass it on to my first child (and, obviously, 0% if I carry two brown genes).
Since my child will certainly get a blue gene from my wife, my gene will determine the eye color.
Multiplying the probabilities of those two independent events, there is a chance of 1/2 x 2/3 = 1/3 of my passing on a blue gene. Did you answer this riddle correctly?
YES NO
Since my brother has blue eyes (bb), both of my parents carry one brown and one blue gene (Bb). The three possibilities for my genotype, equally likely, are BB, Bb, and bB. Thus, there is a 2/3 chance that I carry a blue gene.
If I carry a blue gene, there is a 50% chance I will pass it on to my first child (and, obviously, 0% if I carry two brown genes).
Since my child will certainly get a blue gene from my wife, my gene will determine the eye color.
Multiplying the probabilities of those two independent events, there is a chance of 1/2 x 2/3 = 1/3 of my passing on a blue gene. Did you answer this riddle correctly?
YES NO
Russian Roulette Riddle
You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?
Hint:
Russian Roulette
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Puzzle ID: #17681
Fun: *** (2.59)
Difficulty: ** (2.07)
Category: Probability
Submitted By: JMCLEOD****
Corrected By: cnmne
You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?
Answer
Label the chambers 1 through 6. Chambers 1 through 3 have bullets and chambers 4 through 6 are empty. After you spin the cylinder there are six possible outcomes:
1. Chamber 1 is fired first: Player 1 loses
2. Chamber 2 is fired first: Player 1 loses
3. Chamber 3 is fired first: Player 1 loses
4. Chamber 4 is fired first: Player 2 loses (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)
5. Chamber 5 is fired first: Player 1 loses (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)
6. Chamber 6 is fired first: Player 2 loses (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)
Therefore player 2 has an 4/6 or 2/3 chance of winning. Did you answer this riddle correctly?
YES NO
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Puzzle ID: #17681
Fun: *** (2.59)
Difficulty: ** (2.07)
Category: Probability
Submitted By: JMCLEOD****
Corrected By: cnmne
You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?
Answer
Label the chambers 1 through 6. Chambers 1 through 3 have bullets and chambers 4 through 6 are empty. After you spin the cylinder there are six possible outcomes:
1. Chamber 1 is fired first: Player 1 loses
2. Chamber 2 is fired first: Player 1 loses
3. Chamber 3 is fired first: Player 1 loses
4. Chamber 4 is fired first: Player 2 loses (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)
5. Chamber 5 is fired first: Player 1 loses (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)
6. Chamber 6 is fired first: Player 2 loses (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)
Therefore player 2 has an 4/6 or 2/3 chance of winning. Did you answer this riddle correctly?
YES NO
The Prime Number Riddle
Two hundred people in an auditorium are asked to think of a single digit number from 1 to 9 inclusive and write it down. All those who wrote down a prime number are now asked to leave. Ninety people remain behind in the hall. How many of these are expected to have written down an odd number?
Hint: Remember that 1 is not a prime number.
Those that remain behind must have written {1,4,6,8,9} and from this only {1,9} are odd. The probability of an odd number is thus 2/5.
Expected number of odds is 2/5 * 90 = 36 Did you answer this riddle correctly?
YES NO
Expected number of odds is 2/5 * 90 = 36 Did you answer this riddle correctly?
YES NO
How Old Could He Be?
In 1940, a correspondent proposed the following question:
A man's age at death was one twenty-ninth of the year of his birth. How old was he in 1900?
A man's age at death was one twenty-ninth of the year of his birth. How old was he in 1900?
Hint:
He was 44 years old.
From the question you know the man died between 1900 and 1940. We also know his age at death (x) is one twenty-ninth of the year of his birth (29x). If you add his age at death to the year he was born you get the year he died (30x). Only one year between 1900 and 1940 is divisible by 30, 1920 (the year he died). The year he was born can now be found: 1920 * (29/30) = 1856. So in 1900 he was (1900 - 1856) = 44 years old. Did you answer this riddle correctly?
YES NO
From the question you know the man died between 1900 and 1940. We also know his age at death (x) is one twenty-ninth of the year of his birth (29x). If you add his age at death to the year he was born you get the year he died (30x). Only one year between 1900 and 1940 is divisible by 30, 1920 (the year he died). The year he was born can now be found: 1920 * (29/30) = 1856. So in 1900 he was (1900 - 1856) = 44 years old. Did you answer this riddle correctly?
YES NO
I Supply The Facts
I supply the facts, but you supply the thoughts. I am also used to describe realistic droughts. My inhabitants are abstract as their places, And I provide details of their words & faces. I hold details in a very complex form, I may cause your mind to conjure up a storm. I hold many different views from different eyes, My facts can be hard to find; as if in disguise. I may tell of facts, but it may be theories I contain, I can inform, persuade, and can even entertain. I tell of a little girl, and of men chasing a whale, and only through me can you find the answer to this tale. What am I?
Hint: I am educational.
The Red Hat
Once upon a time there lived a king who wished to find the wisest man in the realm to be his assistant. He summons the 3 known wisest men to his court and he administers the following test.
He sits them in a circle, facing each other and he says Im going to put either a red hat or a white hat on each of your heads. He proceeds to place a red hat on each of their heads. Obviously they can see each other but there are no mirrors in the room so they cant see whats on their heads. He says If you can see a red hat, raise your hand. They all raise their hands. Then he says If you can tell what color hat you have on, stand up.
Time goes on, one guy looks at another guy, he looks at the other guy. The other guy looks at him. Finally one guy stands up. The question is how did he know he was wearing a red hat?
He sits them in a circle, facing each other and he says Im going to put either a red hat or a white hat on each of your heads. He proceeds to place a red hat on each of their heads. Obviously they can see each other but there are no mirrors in the room so they cant see whats on their heads. He says If you can see a red hat, raise your hand. They all raise their hands. Then he says If you can tell what color hat you have on, stand up.
Time goes on, one guy looks at another guy, he looks at the other guy. The other guy looks at him. Finally one guy stands up. The question is how did he know he was wearing a red hat?
Hint: For a moment or two, nobody moved. Nobody knew for certain what color his hat was, and thats what told the wisest guy that all of the hats were red.
Step 1:
Wiseguy #1 knows he can see two red hats.
Step 2:
Wiseguy #1 thinks, "Hey, if I were wearing a white hat, Wiseguy #2 would see one red hat and one white."
Step 3:
Wiseguy #1 then thinks, "If I were wearing a white hat, and Wiseguy #2 saw one red hat and one white (and if he were wearing a white hat himself), then Wiseguy #3 would have seen two white hats. So, Wiseguy #3 wouldnt have raised his hand to the first question.
Wiseguy #1 thinks, "If that were true, Wiseguy #2 would be sure that he had a red hat. But since Wiseguy #2 was actually unsure about his hat color, it can only mean one thing, my hat is red." Did you answer this riddle correctly?
YES NO
Wiseguy #1 knows he can see two red hats.
Step 2:
Wiseguy #1 thinks, "Hey, if I were wearing a white hat, Wiseguy #2 would see one red hat and one white."
Step 3:
Wiseguy #1 then thinks, "If I were wearing a white hat, and Wiseguy #2 saw one red hat and one white (and if he were wearing a white hat himself), then Wiseguy #3 would have seen two white hats. So, Wiseguy #3 wouldnt have raised his hand to the first question.
Wiseguy #1 thinks, "If that were true, Wiseguy #2 would be sure that he had a red hat. But since Wiseguy #2 was actually unsure about his hat color, it can only mean one thing, my hat is red." Did you answer this riddle correctly?
YES NO
The Savage Sister Riddle
A woman has incontrovertible proof in court that her husband was murdered by her sister. The judge declares, "This is the strangest case I've ever seen. Though it's a cut-and-dried case, this woman cannot be punished."
Hint:
Floor Math Riddle
Hint:
Dangerous Chemicals Riddle
There is a chemical that is very dangerous. If this chemical is inhaled, it may be fatal. Under certain conditions, contact with the skin can cause a burn. However, once a person's body becomes dependent on this chemical, prolonged separation from this chemical can cause death. However, even though many people know of this chemical, and it is found in nearly every drinking source, nothing is being done to try to get rid of it. Why is nothing being done about this chemical?
Hint: This is a real chemical. Think about everything that is being said.
No one does anything about it because the chemical is water. Did you answer this riddle correctly?
YES NO
YES NO
A Goat, A Wolf, And A Head Of Cabbage
A man has a goat, a wolf, and a head of cabbage. He comes to a river that has no bridge, but a small boat to cross the river. The boat can hold only one of the three things he has. If he takes over the wolf first, the goat will eat the cabbage. If he take over the cabbage first, the wolf will eat the goat.
How does he solve the problem?
How does he solve the problem?
Hint:
First, he takes over the goat. Then, he takes over the cabbage, but takes the goat back. Then, he takes over the wolf. Finally, he takes over the goat again. Did you answer this riddle correctly?
YES NO
YES NO
Twin Witches Riddle
Hint:
Snow Boots Riddle
Hint:
Often A Mountain Riddle
I produce ash but Im not a bonfire
I can throw rocks great distances but Im not a slingshot
Im often a mountain but Im not in the Himalayas
I have a crater but Im not the moon
I erupt but Im not someone with a bad temper
I can throw rocks great distances but Im not a slingshot
Im often a mountain but Im not in the Himalayas
I have a crater but Im not the moon
I erupt but Im not someone with a bad temper
Hint:
The 100 Seat Airplane
People are waiting in line to board a 100-seat airplane. Steve is the first person in the line. He gets on the plane but suddenly can't remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it's available, otherwise they will choose an open seat at random to sit in.
The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?
The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?
Hint: You don't need to use complex math to solve this riddle. Consider these two questions:
What happens if somebody sits in your seat?
What happens if somebody sits in Steve's assigned seat?
The correct answer is 1/2.
The chase that the first person in line takes your seat is equal to the chance that he takes his own seat. If he takes his own seat initially then you have a 100% chance of sitting in your seat, if he takes your seat you have a 0 percent chance. Now after the first person has picked a seat, the second person will enter the plan and, if the first person has sat in his seat, he will pick randomly, and again, the chance that he picks your seat is equal to the chance he picks someone your seat. The motion will continue until someone sits in the first persons seat, at this point the remaining people standing in line which each be able to sit in their own seats. Well how does that probability look in equation form? (2/100) * 50% + (98/100) * ( (2/98) * 50% + (96/98) * ( (2/96) * (50%) +... (2/2) * (50%) ) ) This expansion reduces to 1/2.
An easy way to see this is trying the problem with a 3 or 4 person scenario (pretend its a car). Both scenarios have probabilities of 1/2. Did you answer this riddle correctly?
YES NO
The chase that the first person in line takes your seat is equal to the chance that he takes his own seat. If he takes his own seat initially then you have a 100% chance of sitting in your seat, if he takes your seat you have a 0 percent chance. Now after the first person has picked a seat, the second person will enter the plan and, if the first person has sat in his seat, he will pick randomly, and again, the chance that he picks your seat is equal to the chance he picks someone your seat. The motion will continue until someone sits in the first persons seat, at this point the remaining people standing in line which each be able to sit in their own seats. Well how does that probability look in equation form? (2/100) * 50% + (98/100) * ( (2/98) * 50% + (96/98) * ( (2/96) * (50%) +... (2/2) * (50%) ) ) This expansion reduces to 1/2.
An easy way to see this is trying the problem with a 3 or 4 person scenario (pretend its a car). Both scenarios have probabilities of 1/2. Did you answer this riddle correctly?
YES NO
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