Puzzles

[firewalker99]

You have two identical barrels, one half full of water and the other half full of whisky. You take one teaspoon of water from the water barrel, put it into the whisky barrel and give it a stir. Then you take one teaspoon of this mixture from the whisky barrel and put it into the water barrel. Which of the barrels contains more of its original contents? Ignore physical properties of liquids like density.

This always used to stump me.

I know, my first reaction would be to say the whisky barrel.
But then I look at it this way:

Suppose the number of teaspoons in each barrel = 100
suppose w = a teaspoon of water, y = a teaspoon of whisky

1) We put one teaspoon of water from the water barrel and put it into the whisky barrel.
the water barrel loses 1 teaspoon of water => 99 left

the whisky barrel gains 1 teaspoon of water
100 y + 1 => the concentration of whisky is 100/101

2) We put one teaspoon of the whisky+water barrel and put it back into the water barrel.
We suppose that we stirred it sufficiently so the water is evenly spread over the whisky barrel.
so the concentration of water is 1/101

* the water barrel now has 99 + 1/101 teaspoons of water = 99,0099... (a)
* the whisky barrel now has 100 whisky teaspoons minus what 1 teaspoon that we removed which is 1 teaspoon of the mixture containing 100/101 whisky
100 - (100/101) = 99,0099... whisky teaspoons (b)

(a) = (b)
qed...

I'm sure there's a more beautiful way of proving this counter-intuitive riddle...

 

[firewalker99]

Sms

Ok, here goes another one:

Suppose you can enter a competition by voting by SMS.
Each day of the week except for the weekend there's a competition.
It's not a quiz of some kind, no it's just a competition where you enter by sending an SMS and the computer randomly picks out the winner. Each day a certain number of other participants compete also and all those other people together send exactly the same number of SMS each day.

You may compete no more than 5 times.

The question is, do you send 5 text messages on day 1, or do you send 1 message every day?
Or... do you send them in another way (eg. 2 on day 1, none on day 2, 3 on day 3,... or some other combination)?

What way is the best to maximise your chances on winning?

 

[dick_dastardly]

Something for the weekend

Haven't read the whole thread so don't know if this one's been done already......



I throw a dice.

If it's a one, a two or a three I put a pound in the pot and throw the dice again.

If it's a four I throw the dice again ( nothing goes in the pot ).

If it's a five the game ends and you win the pot.

If it's a six the game ends and you win nothing.



How much would you pay to play this game ?

dd

 

[trendie]

Haven't read the whole thread so don't know if this one's been done already......



I throw a dice.

If it's a one, a two or a three I put a pound in the pot and throw the dice again.

If it's a four I throw the dice again ( nothing goes in the pot ).

If it's a five the game ends and you win the pot.

If it's a six the game ends and you win nothing.



How much would you pay to play this game ?

dd

???
I must not be reading this right, as I think the answer is that you would pay nothing.

 

[dick_dastardly]

???
I must not be reading this right, as I think the answer is that you would pay nothing.

So you wouldn't even pay one penny ?

Perhaps I haven't worded it quite right. How's this ?

Before the game starts the pot = zero

The dice is thrown.

If it's a one, a two or a three I add a pound to the pot and throw the dice again.

If it's a four I add nothing to the pot and throw the dice again.

If it's a five the game ends and you win the pot.

If it's a six the game ends and you win nothing.


How much would you pay to play this game ?


dd

 

[firewalker99]

So you wouldn't even pay one penny ?

Perhaps I haven't worded it quite right. How's this ?

Before the game starts the pot = zero

The dice is thrown.

If it's a one, a two or a three I add a pound to the pot and throw the dice again.

If it's a four I add nothing to the pot and throw the dice again.

If it's a five the game ends and you win the pot.

If it's a six the game ends and you win nothing.


How much would you pay to play this game ?


dd

First you need to calculate the expectancy of this game.

The game only finishes if you throw a 5 or 6. So half of the games (50%) will finish with you winning nothing. If your first throw is a 5, you win the pot but there is nothing in it (1 chance in 6), but the game is also over in all cases where you throw only a '4' before a 5.

These are:
4,5
4,4,5
4,4,4,5
4,4,4,4,5
4,4,4,4,4,5
....5 you get the point...

The chances for throwing a 4 are 1 in 6, the chances for throwing a 5 obviously 1 in 6 too. So chances for throwing 4,5 are 1/6 x 1/6 = 1/36, or the square of 1/6.

4,5 -> 1/6 square
4,4,5 -> (1/6)^3
4,4,4,5 -> (1/6)^4
4,4,4,4,5 -> (1/6)^5
4,4,4,4,4,5 -> (1/6)^6
...
Use a limit function to infinity and the net result is 0.20 or 2 chances in 10.

So we have a 50% chance that the game will finish without winning anything and an additional 20% chance that you will win the game but get an empty pot => there is only a 30% chance that you will gain anything from this game.

Ok this is the first step... next is determining how much that 30% chance will give you (expectancy) and the result of that should be the amount you are willing to bet.

But that's enough thinking for now on a Saturday

 

[kriesau]

HOW TO SAVE THE AIRLINES

Dump the male flight attendants.
No one wanted them in the first place.
Replace all the female flight attendants with good-looking strippers!
What the hell -- they don't even serve food anymore, so what's the loss?

The strippers would at least triple the alcohol sales and get a "party atmosphere" going in the cabin and, of course, every businessman in this country would start flying again, hoping to see naked women.

Because of the tips, female flight attendants wouldn't need a salary, therefore the airlines would be saving even more money.
I suspect tips would be so good that we could charge the women for working the plane and have them kick back 20% of the tips, including lap dances and "special services."

Muslims would be afraid to get on the planes for fear of seeing naked women. Hijackings would come to a screeching halt, and the airline industry would see record revenues.

This is definitely a win-win situation if we handle it right -- a golden opportunity to turn a liability into an asset.

Why didn't Bush think of this?

Why do I still have to think of everything myself?

Bill Clinton

 

[firewalker99]

3 Sisters

You are the most eligible bachelor in the kingdom, and as such the King has invited you to his castle so that you may choose one of his three daughters to marry. The eldest princess is honest and always tells the truth. The youngest princess is dishonest and always lies. The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.

As you will be forever married to one of the princesses, you want to marry the eldest (truth-teller) or the youngest (liar) because at least you know where you stand with them.

The problem is that you cannot tell which sister is which just by their appearance, and the King will only grant you ONE yes or no question which you may only address to ONE of the sisters. What yes or no question can you ask which will ensure you do not marry the middle sister?

 

[peto]

You are the most eligible bachelor in the kingdom, and as such the King has invited you to his castle so that you may choose one of his three daughters to marry. The eldest princess is honest and always tells the truth. The youngest princess is dishonest and always lies. The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.

As you will be forever married to one of the princesses, you want to marry the eldest (truth-teller) or the youngest (liar) because at least you know where you stand with them.

The problem is that you cannot tell which sister is which just by their appearance, and the King will only grant you ONE yes or no question which you may only address to ONE of the sisters. What yes or no question can you ask which will ensure you do not marry the middle sister?

How about "Do you always tell the truth?"

Only the middle sister could reply "no". But then again she might say "yes" , in which case we are no further forward!
Nice one firewalker

 

[frugi]

******* hard problem, nice work FW. It's gonna be something like "Are you older than your other sisters?" Otherwise why mention their ages? But I can't nail down the specific question. Anyway I think I'd like the michievous middle sister best. I'll take it to the pub with me.

 

[WinstonSmith]

******* hard problem, nice work FW. It's gonna be something like "Are you older than your other sisters?" Otherwise why mention their ages? But I can't nail down the specific question. Anyway I think I'd like the michievous middle sister best. I'll take it to the pub with me.

I think its to do with the age too. The helpful thing is you don’t have to identify every one - just avoid the middle one.

So you could ask about the two others, “is that one older than the other one?” (is x older than y?)

Whether the liar or the truthteller answers, the response is the same :-

If the eldest/truthteller answers yes, pick y (x must be the middle one, y the youngest),
If the eldest/truthteller answers no, pick x (y must be the middle one, x the youngest),

If the liar/ youngest answers yes, pick y (x must be the middle one, y the oldest),
If the liar/ youngest answers no, pick x (y must be the middle one, x the oldest),

If the middle one answers, it doesn’t what she says anyway, as you are not picking her.

Hope that’s not too confused!

 

[rols]

You are the most eligible bachelor in the kingdom, and as such the King has invited you to his castle so that you may choose one of his three daughters to marry. The eldest princess is honest and always tells the truth. The youngest princess is dishonest and always lies. The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.

As you will be forever married to one of the princesses, you want to marry the eldest (truth-teller) or the youngest (liar) because at least you know where you stand with them.

The problem is that you cannot tell which sister is which just by their appearance, and the King will only grant you ONE yes or no question which you may only address to ONE of the sisters. What yes or no question can you ask which will ensure you do not marry the middle sister?

"I suppose just a F***s out of the question?"

 

[firewalker99]

"I suppose just a F***s out of the question?"

I guess that's a way to determine somebody's age too

 

[firewalker99]

******* hard problem, nice work FW. It's gonna be something like "Are you older than your other sisters?" Otherwise why mention their ages? But I can't nail down the specific question. Anyway I think I'd like the michievous middle sister best. I'll take it to the pub with me.

close, but not close enough

Winstonsmith explained it very well.

I'll put it together in short:
We ask daughter A "Is daughter B older than daughter C?" If daughter A is the eldest, we marry the one she indicates is younger. On the other hand if daughter A is the youngest, we want to marry the elder of the other two, which means marrying the one she says is younger. If daughter A is the middle one, it doesn't matter which of the other two we choose. So if the answer is yes, we always marry daughter C, and if it's no, we always marry daughter B.

 

[bluetipex]

You have two identical barrels, one half full of water and the other half full of whisky. You take one teaspoon of water from the water barrel, put it into the whisky barrel and give it a stir. Then you take one teaspoon of this mixture from the whisky barrel and put it into the water barrel. Which of the barrels contains more of its original contents? Ignore physical properties of liquids like density.

This always used to stump me.

This one surely is the easiest of all posted so far!

The whisky barrel gains PURE water.

The water barrel gains a MIXTURE of WATER and WHISKY.

Therefore, the WATER barrel contains more of its original contents.

Easy, peasy, lemon, squeezy.

 

[firewalker99]

This one surely is the easiest of all posted so far!

The whisky barrel gains PURE water.

The water barrel gains a MIXTURE of WATER and WHISKY.

Therefore, the WATER barrel contains more of its original contents.

Easy, peasy, lemon, squeezy.

Sounds easy, but unfortunately it's wrong

Both have the same amount of liquids. In your thought process you forget to mention that both barrels gain something, but also lose something. See also my previous post on that puzzle.

 

[firewalker99]

I found this thread to be fun, but it's been dormant for a while now.

Don't know if this might help, but in an effort to revive it I'd like to ask some questions to see what people might come up with as an answer. These aren't "puzzles" in the real sense of the word, but they should challenge creative thinking Anyone can find answers on the internet, but let's not cheat shall we!

First one:
Why are manholes round? (I know, it's a classic...)

Second:
How would you measure your own volume? (highschool material)

Third:
Which way do doors open? (think about the doors of your car, driver's seat and passenger's seat)

Good luck!

 

[blackcab]

I found this thread to be fun, but it's been dormant for a while now.

Don't know if this might help, but in an effort to revive it I'd like to ask some questions to see what people might come up with as an answer. These aren't "puzzles" in the real sense of the word, but they should challenge creative thinking Anyone can find answers on the internet, but let's not cheat shall we!

First one:
Why are manholes round? (I know, it's a classic...)

Second:
How would you measure your own volume? (highschool material)

Third:
Which way do doors open? (think about the doors of your car, driver's seat and passenger's seat)

Good luck!

Good idea to reactivate this thread

Manholes - it's something to do with the symmetry meaning they'll always fit.

Volume - get into a bath and measure the displacement

Doors - umm?

 

[PKFFW]

I found this thread to be fun, but it's been dormant for a while now.

Don't know if this might help, but in an effort to revive it I'd like to ask some questions to see what people might come up with as an answer. These aren't "puzzles" in the real sense of the word, but they should challenge creative thinking Anyone can find answers on the internet, but let's not cheat shall we!

First one:
Why are manholes round? (I know, it's a classic...)

Second:
How would you measure your own volume? (highschool material)

Third:
Which way do doors open? (think about the doors of your car, driver's seat and passenger's seat)

Good luck!

1: A circle is the only shape where the manhole lid will never be able to fall into the manhole.

2: The bath idea is a good one.

3: Not sure I understand the question. It will depend on the door. My car doors open outwards. ie: away from you if you are in the car and towards you if you are outside the car. However the door to enter my home(and every other place of "residence" I can think of) opens inwards. The exact opposite of my car doors. The reason car doors open outwards should be obvious and is twofold. 1: Not enough room in the car to make it practical to have them open inwards. 2: In the event of a crash it is easier to rip a car door off and get to the injured occupant if the door opens outwards.
Why a "residence" door opens inwards would be purely psychological I would think. It is more "inviting" to have the door open inwards.

Cheers,
PKFFW

 

[firewalker99]

Good idea to reactivate this thread

Manholes - it's something to do with the symmetry meaning they'll always fit.

Volume - get into a bath and measure the displacement

Doors - umm?

Manholes, what exactly do you mean they'll always fit? I think you are close to the answer. Or one of the possible answers.

Ok, the bath one was too easy

1: A circle is the only shape where the manhole lid will never be able to fall into the manhole.

2: The bath idea is a good one.

3: Not sure I understand the question. It will depend on the door. My car doors open outwards. ie: away from you if you are in the car and towards you if you are outside the car. However the door to enter my home(and every other place of "residence" I can think of) opens inwards. The exact opposite of my car doors. The reason car doors open outwards should be obvious and is twofold. 1: Not enough room in the car to make it practical to have them open inwards. 2: In the event of a crash it is easier to rip a car door off and get to the injured occupant if the door opens outwards.
Why a "residence" door opens inwards would be purely psychological I would think. It is more "inviting" to have the door open inwards.

Cheers,
PKFFW

1. Ok, so why is the inside of a manhole (or the sewer that it leads to for instance) also round?

2. Yip.

3. Good answer about the car. Next thing you should try is - if your call still has a oldfashion key - check which way to turn the lock to open it on the driver-side and on the passenger side. Both normally turn in opposite directions. Why is that?

Interesting suggestion about the doors of a "residence". So do all the doors of the rooms of your house open inwards?