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
Knights Of The Round Table Riddle
King Arthur, Merlin, Sir Lancelot, Sir Gawain, and Guinevere decide to go to their favorite restaurant to share some mead and grilled meats. They sit down at a round table for five, and as soon as they do, Lancelot notes, "We sat down around the table in age order! What are the odds of that?"
Merlin smiles broadly. "This is easily solved without any magic." He then shared the answer. What did he say the odds were?
Merlin smiles broadly. "This is easily solved without any magic." He then shared the answer. What did he say the odds were?
Hint: Does it matter if they are sitting clockwise or counterclockwise? Or where the oldest sits?
The odds are 11:1. (The probability is 1/12.)
Imagine they sat down in age order, with each person randomly picking a seat. The first person is guaranteed to pick a seat that "works". The second oldest can sit to his right or left, since these five can sit either clockwise or counterclockwise. The probability of picking a seat that works is thus 2/4, or 1/2. The third oldest now has three chairs to choose from, one of which continues the progression in the order determined by the second person, for a probability of 1/3. This leaves two seats for the fourth oldest, or a 1/2 chance. The youngest would thus be guaranteed to sit in the right seat, since there is only one seat left. This gives 1 * 1/2 * 1/3 * 1/2 * 1 = 1/12, or 11:1 odds against. Did you answer this riddle correctly?
YES NO
Imagine they sat down in age order, with each person randomly picking a seat. The first person is guaranteed to pick a seat that "works". The second oldest can sit to his right or left, since these five can sit either clockwise or counterclockwise. The probability of picking a seat that works is thus 2/4, or 1/2. The third oldest now has three chairs to choose from, one of which continues the progression in the order determined by the second person, for a probability of 1/3. This leaves two seats for the fourth oldest, or a 1/2 chance. The youngest would thus be guaranteed to sit in the right seat, since there is only one seat left. This gives 1 * 1/2 * 1/3 * 1/2 * 1 = 1/12, or 11:1 odds against. Did you answer this riddle correctly?
YES NO
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 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
Around The Yard Riddle
Hint:
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:
Almond Joy And Mounds
This is brown and fuzzy on the outside
And has a weight of two or three pounds
Its inside is white and has some water
And is used in Almond Joy and Mounds
What could this be?
And has a weight of two or three pounds
Its inside is white and has some water
And is used in Almond Joy and Mounds
What could this be?
Hint:
White And Soft
A little pool with two layers of wall around it, one white and soft and the other dark. What could I be?
Hint:
Making Sound Without Lips
I am black and white, I have strings I have keys I make sound without my lips, I make dough with no flour what am I?
Hint:
Hung Around Peoples Necks
It can look like a T
It can look like an X
They can be found on chains
Hung around peoples necks
What is it?
It can look like an X
They can be found on chains
Hung around peoples necks
What is it?
Hint:
The Walls Of Jericho
When tasked with what seemed impossible
He didnt just refuse and frown
He marched the people round Jericho
And the walls came tumbling down
He is?
He didnt just refuse and frown
He marched the people round Jericho
And the walls came tumbling down
He is?
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:
Be Careful At Night
If you see one flying around
Youd better be careful at night
As some turn into vampires
And will give your neck a big bite
What are they?
Youd better be careful at night
As some turn into vampires
And will give your neck a big bite
What are they?
Hint:
Winged Creatures Riddle
These winged creatures often scare people
If you touch one you are brave
Theyre often found just hanging out
Upside down inside a cave
What are these creatures?
If you touch one you are brave
Theyre often found just hanging out
Upside down inside a cave
What are these creatures?
Hint:
Electrically Charged Particles Riddle
Hint:
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