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
Yahtzee Riddle
The game of Yahtzee is played with five dice. On the first turn, a player rolls all five dice, and then may decide to keep any, all, or none of the dice aside before rolling again. Each player has a maximum of three rolls to try to get a favorable combination of dice "kept" on the side.
If a player rolls two 2s and two 4s on his/her first roll, and keeps all four of these dice aside, what is the probability of getting a full house (three of one value and two of another) in one of his/her next two rolls? (ie what is the probability of getting either a 2 or a 4 in one of the next two rolls?)
If a player rolls two 2s and two 4s on his/her first roll, and keeps all four of these dice aside, what is the probability of getting a full house (three of one value and two of another) in one of his/her next two rolls? (ie what is the probability of getting either a 2 or a 4 in one of the next two rolls?)
Hint: Think of the probability of NOT getting a full house.
5/9
The answer is NOT 2/3 because you cannot add probabilities. On each roll, the probability of getting a 2 or a 4 is 1/3, so therefore, the probability of not getting a 2 or a 4 is 2/3. Since the die is being rolled twice, square 2/3 to get a 4/9 probability of NOT getting a full house in two rolls. The probability of getting a full house is therefore 1 - 4/9, or 5/9. Did you answer this riddle correctly?
YES NO
The answer is NOT 2/3 because you cannot add probabilities. On each roll, the probability of getting a 2 or a 4 is 1/3, so therefore, the probability of not getting a 2 or a 4 is 2/3. Since the die is being rolled twice, square 2/3 to get a 4/9 probability of NOT getting a full house in two rolls. The probability of getting a full house is therefore 1 - 4/9, or 5/9. Did you answer this riddle correctly?
YES NO
The Cheap Mp3 Player
My MP3 player is cheap 'n' nasty and has now broken: it is stuck on 'Shuffle'. In this mode it starts with whatever track you put it on, but then plays tracks in a random order. The only restriction is it never plays a song that's already been played that day.
I purchased my favourite murder mystery book in audio format, and put the first 6 chapters on my MP3 player. (Each chapter is exactly 1 track.) There's nothing else on my player at the moment. What is the probability that I will hear the 6 chapters in order as I listen today, without having to change tracks at all? (Obviously, I will ensure it plays chapter 1 first.)
The next day I empty the player before putting on the next 6 chapters. This time I also transfer a CD of mine with 11 songs on. I don't mind songs coming in between the chapters of my book, as long as the chapters are in order. What's the probability of that happening now?
I purchased my favourite murder mystery book in audio format, and put the first 6 chapters on my MP3 player. (Each chapter is exactly 1 track.) There's nothing else on my player at the moment. What is the probability that I will hear the 6 chapters in order as I listen today, without having to change tracks at all? (Obviously, I will ensure it plays chapter 1 first.)
The next day I empty the player before putting on the next 6 chapters. This time I also transfer a CD of mine with 11 songs on. I don't mind songs coming in between the chapters of my book, as long as the chapters are in order. What's the probability of that happening now?
Hint:
With only 6 tracks on the player:
The first chapter has been set to play first. The probability of the next 5 chapters playing in order is 1/5! = 1/120.
With the music on the player as well:
Seeing as I don't care about when the music plays, it doesn't change anything. The answer is still 1/120. Did you answer this riddle correctly?
YES NO
The first chapter has been set to play first. The probability of the next 5 chapters playing in order is 1/5! = 1/120.
With the music on the player as well:
Seeing as I don't care about when the music plays, it doesn't change anything. The answer is still 1/120. Did you answer this riddle correctly?
YES NO
The End Of Your Arm Riddle
This might be made into a fist
If you are not feeling calm
This is a part of your body
Thats at the end of your arm
What is it?
If you are not feeling calm
This is a part of your body
Thats at the end of your arm
What is it?
Hint:
Egg Drop Riddle
Hint:
Gentle Enough To Soothe Your Skin Riddle
I am gentle enough to soothe your skin light enough to fly in the sky strong enough to crack rocks. What am I?
Hint:
Fish Wish Riddle
Hint:
Invisible At Night Riddle
I fly like a bird of many colors through the sky. I am made with both wood and fire but I do not burn up. You can see me clearly during the day, but I am nearly invisible at night. What am I?
Hint:
Vegetable Necklace
Hint:
Backwards Cheese Riddle
Hint:
A Woman Is Sitting In Her Hotel Room Riddle
A woman is sitting in her hotel room when there is a knock at the door. She opened the door to see a man whom she had never seen before. He said "oh I'm sorry, I have made a mistake, I thought this was my room." He then went down the corridor and in the elevator. The woman went back into her room and phoned security. What made the woman so suspicious of the man?
Hint:
3 Gallon Jug And 5 Gallon Jug
You have a 3-gallon and a 5-gallon jug that you can fill from a fountain of water.
The problem is to fill one of the jugs with exactly 4 gallons of water. How do you do it?
You've got to defuse a bomb by placing exactly 4 gallons (15 L) of water on a sensor. The problem is, you only have a 5 gallon (18.9 L) jug and a 3 gallons (11 L) jug on hand! This classic riddle, made famous in Die Hard 3.
The problem is to fill one of the jugs with exactly 4 gallons of water. How do you do it?
You've got to defuse a bomb by placing exactly 4 gallons (15 L) of water on a sensor. The problem is, you only have a 5 gallon (18.9 L) jug and a 3 gallons (11 L) jug on hand! This classic riddle, made famous in Die Hard 3.
Hint:
Fill the 5-jug up completely. There will be, of course, 5 gallons in the 5-jug. You must fill all the gallons up to the top, otherwise you don't actually know how much you have.
Use the water from the 5-jug to fill up the 3-jug. You're left with 3 gallons in the 3-jug and 2 gallons in the 5-jug.
Pour out the 3-gallon jug. You're left with nothing in the 3-jug and 2 gallons in the 5-jug.
Transfer the water from the 5-jug to the three jug. You're left with 2 gallons in the 3-jug. And nothing in the 5-jug.
Fill up the 5-jug completely. You now have 2 gallons in the 3-jug and 5 in the 5-jug. This means that there is 1 gallon (3.8 L) of space left in the 3-jug.
Use the water from the 5-jug to fill up the 3-jug. Fill up the last gallon of space in the 3-jug with the water from the 5-jug. This leaves you with 3 gallons in the 3-jug, and 4 gallons in the 5-jug.
Fill the 3-jug completely with water. You now have 3 gallons (11.4 L) of water.
Transfer this water into the 5-jug. You now have nothing in the 3-jug, and 3 gallons (11.4 L) in the 5-jug.
Re-fill the 3-jug with water. You now have 3 gallons (11.4 L) in the 3-jug and 3 gallons in the 5-jug.
Fill the 5-jug with water from your 3-jug. You now have 1 gallon (3.8 L) in the 3-jug and 5 gallons (18.9 L) in the 5-jug. This is because, in the last step, you only had 2 gallons (7.6 L) of space left over, so you could only pour 2 gallons.
Pour out the 5-jug and refill it with your 1 gallon. You now have nothing in the 3-jug and 1 gallon in the 5-jug
Fill up the 3-jug. You now have 3 gallons (11.4 L) in the 3-jug and 1 in the 5-jug.
Transfer the 3 gallons (11.4 L) of water into the 5-jug to end up with 4 gallons (15.1 L). Simply pour over your three gallons into the 5-jug, which only had 1 gallon (3.8 L) in it previously. 1+3=4, and a successfully defused bomb. Did you answer this riddle correctly?
YES NO
Use the water from the 5-jug to fill up the 3-jug. You're left with 3 gallons in the 3-jug and 2 gallons in the 5-jug.
Pour out the 3-gallon jug. You're left with nothing in the 3-jug and 2 gallons in the 5-jug.
Transfer the water from the 5-jug to the three jug. You're left with 2 gallons in the 3-jug. And nothing in the 5-jug.
Fill up the 5-jug completely. You now have 2 gallons in the 3-jug and 5 in the 5-jug. This means that there is 1 gallon (3.8 L) of space left in the 3-jug.
Use the water from the 5-jug to fill up the 3-jug. Fill up the last gallon of space in the 3-jug with the water from the 5-jug. This leaves you with 3 gallons in the 3-jug, and 4 gallons in the 5-jug.
Fill the 3-jug completely with water. You now have 3 gallons (11.4 L) of water.
Transfer this water into the 5-jug. You now have nothing in the 3-jug, and 3 gallons (11.4 L) in the 5-jug.
Re-fill the 3-jug with water. You now have 3 gallons (11.4 L) in the 3-jug and 3 gallons in the 5-jug.
Fill the 5-jug with water from your 3-jug. You now have 1 gallon (3.8 L) in the 3-jug and 5 gallons (18.9 L) in the 5-jug. This is because, in the last step, you only had 2 gallons (7.6 L) of space left over, so you could only pour 2 gallons.
Pour out the 5-jug and refill it with your 1 gallon. You now have nothing in the 3-jug and 1 gallon in the 5-jug
Fill up the 3-jug. You now have 3 gallons (11.4 L) in the 3-jug and 1 in the 5-jug.
Transfer the 3 gallons (11.4 L) of water into the 5-jug to end up with 4 gallons (15.1 L). Simply pour over your three gallons into the 5-jug, which only had 1 gallon (3.8 L) in it previously. 1+3=4, and a successfully defused bomb. Did you answer this riddle correctly?
YES NO
The Person Who Built It Sold It Riddle
The man who made it sold it. The man who bought it never used it. The man who used it never saw it. What was it?
Hint:
I Come At The Start Of Rocket Riddle
Hint:
8 College Students Riddle
There was a group of 8 college students who all belonged to the mountain climbing club. One day, during the Winter, they decided to climb the tallest mountain in the area. During the ascent, the weather took a turn for the worse. They ran into trouble and were stranded near the top for two weeks.
Eventually, a rescue team managed to reach them. There were only 7 survivors. They were airlifted to a nearby hospital. After a few days, 6 of them made a full recovery, but the seventh survivor was so traumatized by the experience that he lost his mind and was put in a mental hospital.
The police questioned the remaining 6 about what happened during the two weeks they were stranded on the mountain. They asked what happened to the missing climber.
He just wandered off and never came back, they said. The police questioned each of the 6 survivors and they all told the same story.
Then, they went to the mental hospital to question the 7th survivor, but they couldnt get any sense out of him. When they asked him what happened to the missing climber, he just kept banging his head against the padded walls and repeating over and over, 8.. 8 8...
What does this mean?
Eventually, a rescue team managed to reach them. There were only 7 survivors. They were airlifted to a nearby hospital. After a few days, 6 of them made a full recovery, but the seventh survivor was so traumatized by the experience that he lost his mind and was put in a mental hospital.
The police questioned the remaining 6 about what happened during the two weeks they were stranded on the mountain. They asked what happened to the missing climber.
He just wandered off and never came back, they said. The police questioned each of the 6 survivors and they all told the same story.
Then, they went to the mental hospital to question the 7th survivor, but they couldnt get any sense out of him. When they asked him what happened to the missing climber, he just kept banging his head against the padded walls and repeating over and over, 8.. 8 8...
What does this mean?
Hint:
Add Your Riddle Here
Have some tricky riddles of your own? Leave them below for our users to try and solve.