Under The Cup Riddle
You decide to play a game with your friend where your friend places a coin under one of three cups. Your friend would then switch the positions of two of the cups several times so that the coin under one of the cups moves with the cup it is under. You would then select the cup that you think the coin is under. If you won, you would receive the coin, but if you lost, you would have to pay.
As the game starts, you realise that you are really tired, and you don't focus very well on the moving of the cups. When your friend stops moving the cups and asks you where the coin is, you only remember a few things:
He put the coin in the rightmost cup at the start.
He switched two of the cups 3 times.
The first time he switched two of the cups, the rightmost one was switched with another.
The second time he switched two of the cups, the rightmost one was not touched.
The third and last time he switched two of the cups, the rightmost one was switched with another.
You don't want to end up paying your friend, so, using your head, you try to work out which cup is most likely to hold the coin, using the information you remember.
Which cup is most likely to hold the coin?
As the game starts, you realise that you are really tired, and you don't focus very well on the moving of the cups. When your friend stops moving the cups and asks you where the coin is, you only remember a few things:
He put the coin in the rightmost cup at the start.
He switched two of the cups 3 times.
The first time he switched two of the cups, the rightmost one was switched with another.
The second time he switched two of the cups, the rightmost one was not touched.
The third and last time he switched two of the cups, the rightmost one was switched with another.
You don't want to end up paying your friend, so, using your head, you try to work out which cup is most likely to hold the coin, using the information you remember.
Which cup is most likely to hold the coin?
Hint: Write down the possibilities. Remember that there are only three cups, so if the rightmost cup wasn't touched...
The rightmost cup.
The rightmost cup has a half chance of holding the coin, and the other cups have a quarter chance.
Pretend that Os represent cups, and Q represents the cup with the coin.
The game starts like this:
OOQ
Then your friend switches the rightmost cup with another, giving two possibilities, with equal chance:
OQO
QOO
Your friend then moves the cups again, but doesn't touch the rightmost cup. The only switch possible is with the leftmost cup and the middle cup. This gives two possibilities with equal chance:
QOO
OQO
Lastly, your friend switches the rightmost cup with another cup. If the first possibility shown above was true, there would be two possibilities, with equal chance:
OOQ
QOO
If the second possibility shown above (In the second switch) was true, there would be two possibilities with equal chance:
OOQ
OQO
This means there are four possibilities altogether, with equal chance:
OOQ
QOO
OOQ
OQO
This means each possibility equals to a quarter chance, and because there are two possibilities with the rightmost cup having the coin, there is a half chance that the coin is there. Did you answer this riddle correctly?
YES NO
The rightmost cup has a half chance of holding the coin, and the other cups have a quarter chance.
Pretend that Os represent cups, and Q represents the cup with the coin.
The game starts like this:
OOQ
Then your friend switches the rightmost cup with another, giving two possibilities, with equal chance:
OQO
QOO
Your friend then moves the cups again, but doesn't touch the rightmost cup. The only switch possible is with the leftmost cup and the middle cup. This gives two possibilities with equal chance:
QOO
OQO
Lastly, your friend switches the rightmost cup with another cup. If the first possibility shown above was true, there would be two possibilities, with equal chance:
OOQ
QOO
If the second possibility shown above (In the second switch) was true, there would be two possibilities with equal chance:
OOQ
OQO
This means there are four possibilities altogether, with equal chance:
OOQ
QOO
OOQ
OQO
This means each possibility equals to a quarter chance, and because there are two possibilities with the rightmost cup having the coin, there is a half chance that the coin is there. Did you answer this riddle correctly?
YES NO
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
Taking You To School
This vehicle makes frequent stops
So getting to places can be slow
In London theyre usually red
The ones you take to school are yellow
So getting to places can be slow
In London theyre usually red
The ones you take to school are yellow
Hint:
Dog Breakfast Riddle
Hint:
Running Around The Field
Hint:
Blue Christmas Riddle
Hint:
A Little Helper
It is thanks to beings like me
Your Christmas toys dont come from stores
Because I am a little helper
Who makes your gifts from Santa Claus
Who are we?
Your Christmas toys dont come from stores
Because I am a little helper
Who makes your gifts from Santa Claus
Who are we?
Hint:
A Cruise Between Mexico And The USA Riddle
A man sails off on a cruise between Mexico and the USA. He does not stop at any ports and does not even come out of the cabin, yet he makes $300,000 from his trip. How?
Hint:
When I Am Filled I Can Point The Way Riddle
When I am filled I can point the way. When I am empty, nothing moves me. I have two skins; One without and one within. What am I?
Hint:
What 8 Letter Word Riddle
Hint:
Two Ships Riddle
Two ships leave the port of San Diego, both sailing for the distant shores of Japan. Each ship plans to travel the same route, spending a two-week stopover in Tokyo before returning to California. The first ship churns through the sea at 35 miles per hour throughout the entire journey. The second ship moves slower, at just 30 mph. After two weeks in Tokyo, the captain of the second ship decides to run at a faster pace, moving at 40 mph for the entire return trip. Which ship arrives in San Diego first?
Hint:
The first ship!
First ship = d/35 + d/35 = 2d/35 = 0.0571d
Second ship = d/30 = d/40 = 70d/1200 = 0.058 Did you answer this riddle correctly?
YES NO
First ship = d/35 + d/35 = 2d/35 = 0.0571d
Second ship = d/30 = d/40 = 70d/1200 = 0.058 Did you answer this riddle correctly?
YES NO
Two Ships Riddle
Two ships leave the port of San Diego, both sailing for the distant shores of Japan. Each ship plans to travel the same route, spending a two-week stopover in Tokyo before returning to California. The first ship churns through the sea at 35 miles per hour throughout the entire journey. The second ship moves slower, at just 30 mph. After two weeks in Tokyo, the captain of the second ship decides to run at a faster pace, moving at 40 mph for the entire return trip. Which ship arrives in San Diego first?
Hint:
The first ship!
First ship = d/35 + d/35 = 2d/35 = 0.0571d
Second ship = d/30 = d/40 = 70d/1200 = 0.058 Did you answer this riddle correctly?
YES NO
First ship = d/35 + d/35 = 2d/35 = 0.0571d
Second ship = d/30 = d/40 = 70d/1200 = 0.058 Did you answer this riddle correctly?
YES NO
A Feeling That Cannot Be Touched
I am a feeling that cannot be touched,
But I'm more valuable than gold or clutch.
I'm a force that's strong, yet soft as a dove,
And I'm the reason behind every love.
You can't see me, but you feel me so true,
I'm what makes me say "I love you".
What am I?
But I'm more valuable than gold or clutch.
I'm a force that's strong, yet soft as a dove,
And I'm the reason behind every love.
You can't see me, but you feel me so true,
I'm what makes me say "I love you".
What am I?
Hint: Heart
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