The Secret Santa Exchange
A group of ten friends decide to exchange gifts as secret Santas. Each person writes his or her name on a piece of paper and puts it in a hat. Then each person randomly draws a name from the hat to determine who has him as his or her secret Santa. The secret Santa then makes a gift for the person whose name he drew.
When it's time to exchange presents, each person walks over to the person he made the gift for and holds his or her left hand in his right hand.
What is the probability that the 10 friends holding hands form a single continuous circle?
When it's time to exchange presents, each person walks over to the person he made the gift for and holds his or her left hand in his right hand.
What is the probability that the 10 friends holding hands form a single continuous circle?
Hint: It's not as difficult as it seems.
It's the number of ways the friends can form a circle divided by the number of ways the names can be drawn out of the hat.
1/10
For a group of n friends, there are n! (n factorial) ways to draw the names out of the hat. Since a circle does not have a beginning and end, choose one person as the beginning and end of the circle. There are now (n-1)! ways to distribute the remaining people around the circle. Thus the probability of forming a single circle is
(n-1)! / n!
Since n! = (n-1)! * n (for n > 1), this can be rewritten as
(n-1)! / (n*(n-1)!)
Factoring out the (n-1)! from the numerator and denominator leaves
1/n
as the probability. Did you answer this riddle correctly?
YES NO
For a group of n friends, there are n! (n factorial) ways to draw the names out of the hat. Since a circle does not have a beginning and end, choose one person as the beginning and end of the circle. There are now (n-1)! ways to distribute the remaining people around the circle. Thus the probability of forming a single circle is
(n-1)! / n!
Since n! = (n-1)! * n (for n > 1), this can be rewritten as
(n-1)! / (n*(n-1)!)
Factoring out the (n-1)! from the numerator and denominator leaves
1/n
as the probability. Did you answer this riddle correctly?
YES NO
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
Little Billy's Calculator
Little Billy has a calculator with 15 buttons. He has 10 keys for 0-9, a key for addition, multiplication, division, and subtraction. Finally, he has an = sign. However, Mark the Meanie messed up the programming on Billy's calculator. Now, whenever Billy presses any of the number keys, it comes up with a random single-digit number. The same goes for the four operations keys (+,-,x, /). So whenever Billy tries to press the + button, the calculator chooses randomly between addition, multiplication, subtraction, and division. The only key left untouched was the = sign.
Now, if Billy were to press one number key, one operation key, then another number key, then the = button, what are the chances the answer comes out to 6?
Now, if Billy were to press one number key, one operation key, then another number key, then the = button, what are the chances the answer comes out to 6?
Hint: Think about how many ways he could possibly get 6.
There is a 4% chance.
There are 16 possible ways to get 6.
0+6
1+5
2+4
3+3
6+0
5+1
4+2
9-3
8-2
7-1
6-0
1x6
2x3
6x1
3x2
6/1
There are 400 possible button combinations.
When Billy presses any number key, there are 10 possibilities; when he presses any operation key, there are 4 possibilities.
10(1st#)x4(Operation)x10(2nd#)=400
16 working combinations/400 possible combinations= .04 or 4% Did you answer this riddle correctly?
YES NO
There are 16 possible ways to get 6.
0+6
1+5
2+4
3+3
6+0
5+1
4+2
9-3
8-2
7-1
6-0
1x6
2x3
6x1
3x2
6/1
There are 400 possible button combinations.
When Billy presses any number key, there are 10 possibilities; when he presses any operation key, there are 4 possibilities.
10(1st#)x4(Operation)x10(2nd#)=400
16 working combinations/400 possible combinations= .04 or 4% Did you answer this riddle correctly?
YES NO
Gun Fighting Riddle
Kangwa, Rafael and Ferdinand plans for gun fighting.
They each get a gun and take turns shooting at each other until only one person is left.
History suggests:
Kangwa hits his shot 1/3 of the time, gets to shoot first.
Rafael, hits his shot 2/3 of the time, gets to shoot next if still living.
Ferdinand having perfect record at shooting(100% accuracy) shoots last , if alive.
The cycle repeats. If you are Kangwa, where should you shoot first for the highest chance of survival?
They each get a gun and take turns shooting at each other until only one person is left.
History suggests:
Kangwa hits his shot 1/3 of the time, gets to shoot first.
Rafael, hits his shot 2/3 of the time, gets to shoot next if still living.
Ferdinand having perfect record at shooting(100% accuracy) shoots last , if alive.
The cycle repeats. If you are Kangwa, where should you shoot first for the highest chance of survival?
Hint:
He should shoot at the ground.
If Kangwa shoots the ground, it is Rafael's turn. Rafael would rather shoot at Ferdinand than Kangwa, because he is better.
If Rafael kills Ferdinand, it is just Kangwa and Rafael left, giving Kangwa a fair chance of winning.
If Rafael does not kill Ferdinand, it is Ferdinand's turn. He would rather shoot at Rafael and will definitely kill him. Even though it is now Kangwa against Ferdinand, Kangwa has a better chance of winning than before. Did you answer this riddle correctly?
YES NO
If Kangwa shoots the ground, it is Rafael's turn. Rafael would rather shoot at Ferdinand than Kangwa, because he is better.
If Rafael kills Ferdinand, it is just Kangwa and Rafael left, giving Kangwa a fair chance of winning.
If Rafael does not kill Ferdinand, it is Ferdinand's turn. He would rather shoot at Rafael and will definitely kill him. Even though it is now Kangwa against Ferdinand, Kangwa has a better chance of winning than before. Did you answer this riddle correctly?
YES NO
Two In A Row Riddle
A certain mathematician, his wife, and their teenage son all play a fair game of chess. One day when the son asked his father for 10 dollars for a Saturday night date, his father puffed his pipe for a moment and replied, "Let's do it this way. Today is Wednesday. You will play a game of chess tonight, tomorrow, and a third on Friday. If you win two games in a row, you get the money."
"Whom do I play first, you or mom?"
"You may have your choice," said the mathematician, his eyes twinkling.
The son knew that his father played a stronger game than his mother. To maximize his chance of winning two games in succession, should he play father-mother-father or mother-father-mother?
"Whom do I play first, you or mom?"
"You may have your choice," said the mathematician, his eyes twinkling.
The son knew that his father played a stronger game than his mother. To maximize his chance of winning two games in succession, should he play father-mother-father or mother-father-mother?
Hint: Who does he need to beat to win?
Father-mother-father
To beat two games in a row, it is necessary to win the second game. This means that it would be to his advantage to play the second game against the weaker player. Though he plays his father twice, he has a higher chance of winning by playing his mother second. Did you answer this riddle correctly?
YES NO
To beat two games in a row, it is necessary to win the second game. This means that it would be to his advantage to play the second game against the weaker player. Though he plays his father twice, he has a higher chance of winning by playing his mother second. Did you answer this riddle correctly?
YES NO
The Emperor's Proposition Riddle
You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls. He then says, "Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die."
How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?
How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?
Hint: The answer does not guarantee 100% you will chose a white marble, but you have a much better chance.
Place 1 white marble in one bowl, and place the rest of the marbles in the other bowl (49 whites, and 50 blacks).
This way you begin with a 50/50 chance of choosing the bowl with just one white marble, therefore life! BUT even if you choose the other bowl, you still have ALMOST a 50/50 chance at picking one of the 49 white marbles. Did you answer this riddle correctly?
YES NO
This way you begin with a 50/50 chance of choosing the bowl with just one white marble, therefore life! BUT even if you choose the other bowl, you still have ALMOST a 50/50 chance at picking one of the 49 white marbles. Did you answer this riddle correctly?
YES NO
Coconut Toll Booth Riddle
There is a beautiful garden surrounded with water on three sides and only one road leading to it. This garden has thousands of coconut trees. Anyone can visit to pick coconuts.
The coconuts can be taken in boxes only. Each box can carry 20 coconuts.You can take as many boxes as you like for free but there are ten toll barriers on the road. Each toll booth collects tax in the form of you guessed it: coconuts. The number of coconuts taken is equal to the number of boxes. For example if you are carrying 50 boxes of coconut you have to pay 50 coconuts at each barrier.
If you took 10 boxes filled with coconuts from garden, tell me how many coconuts would you have remaining after crossing all ten toll booths?
The coconuts can be taken in boxes only. Each box can carry 20 coconuts.You can take as many boxes as you like for free but there are ten toll barriers on the road. Each toll booth collects tax in the form of you guessed it: coconuts. The number of coconuts taken is equal to the number of boxes. For example if you are carrying 50 boxes of coconut you have to pay 50 coconuts at each barrier.
If you took 10 boxes filled with coconuts from garden, tell me how many coconuts would you have remaining after crossing all ten toll booths?
Hint:
Dropping Coconuts Riddle
You have two coconuts and you want to find out how high they can be dropped from a 100 story building before they break. But you only have $1.40 and the elevator costs a dime each time you ride it up (it's free for rides down).
How can you drop the coconuts to guarantee you will find the lowest floor they will break at, while starting and ending at floor 1?
How can you drop the coconuts to guarantee you will find the lowest floor they will break at, while starting and ending at floor 1?
Hint: They break when dropped from the same height and they don't weaken from getting dropped.
You could drop it at floor 1 first (because you start at floor 1). Then you would go to the floors: 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, and 100. Whatever floor your first coconut breaks at, go to the floor above the last floor the coconut survived and drop the second coconut from this floor. Then go up by one floor until the second coconut breaks and that is the lowest floor it will break at. Did you answer this riddle correctly?
YES NO
YES NO
Brown Shell On The Outside
Ive a brown shell on the outside
And my shape is an oval
However, I am not an egg
From a palm trees where I fall
I am?
And my shape is an oval
However, I am not an egg
From a palm trees where I fall
I am?
Hint:
Found In A Cave Riddle
Im black but Im not a marker pen
Im a mammal but Im not a whale
I can fly but Im not a plane
I go before man to make a superhero but Im not a spider
I might be found in a cave but Im not a stalagmite
I'm a?
Im a mammal but Im not a whale
I can fly but Im not a plane
I go before man to make a superhero but Im not a spider
I might be found in a cave but Im not a stalagmite
I'm a?
Hint:
The 1000km Layer
Hint:
Born In Mourning
I have a name, but it isn't my name. My face shows signs of age. I always mean the same thing, no matter what I say. I'm born in mourning, and I last 'til the end of days. Men plant me, but I never grow. They run from me, but I never move. They look at me and see their future, rotting in the fields where I bloom. What am I?
Hint:
Dying Of Thirst
You are dying of thirst walking through me. You starve to death over night. You find nothing in my path. Ambiguous and furious in my sight. Kill and threatened by my people. I am?
Hint:
Sand
Desert is the answer to this riddle. Kill and threatened by my people are talking about animals that live in the desert. Did you answer this riddle correctly?
YES NO
Desert is the answer to this riddle. Kill and threatened by my people are talking about animals that live in the desert. Did you answer this riddle correctly?
YES NO
Found Beneath A Chimney
I can keep you warm but Im not a scarf
Im often made of brick or stone but Im not a wall
I sometimes have a poker but I dont have a deck of cards
I contain logs but Im not a forest
Im found beneath a chimney but Im not Santa
What could I be?
Im often made of brick or stone but Im not a wall
I sometimes have a poker but I dont have a deck of cards
I contain logs but Im not a forest
Im found beneath a chimney but Im not Santa
What could I be?
Hint:
I Can Fly Riddle
Im colorful but Im not a rainbow
Im sometimes found on a shoulder but Im not a bag strap
I have two legs but Im not an ostrich
I can talk but Im not a person
I can fly but Im not an airplane
I'm a...
Im sometimes found on a shoulder but Im not a bag strap
I have two legs but Im not an ostrich
I can talk but Im not a person
I can fly but Im not an airplane
I'm a...
Hint:
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