-
A bat and ball cost $1.10.
The bat costs one dollar more than the ball.
How much does the ball cost?
I want to say 0.05 dollars.... please don't let there be a 'bat and ball paradox' wiki page
-
Both correct, but you clearly spent too much time thinking about it, you're meant to answer intuitively and say 10 cents. LFGSS, 2smart4me.
-
i like this thread, but this needs some damn order! One puzzle to be solved at a time. Then perhaps the champ gets to post the next?
And ignoring my own suggestion, in reference to this:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
I know it's in your advantage to switch, but i don't know the logic why. It's something i've been meaning to look up - so although i'm a geek, I'm not enough of a geek to have actually bothered to do that yet.
-
• #33
i like this thread, but this needs some damn order! One puzzle to be solved at a time. Then perhaps the champ gets to post the next?
And ignoring my own suggestion, in reference to this:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
I know it's in your advantage to switch, but i don't know the logic why. It's something i've been meaning to look up - so although i'm a geek, I'm not enough of a geek to have actually bothered to do that yet.
The odds of your first choice are 1/3. When one of the three is removed, the odds change to 1/2 - but only for the door you haven't chosen. That is, the door you're on remains 1/3 as it was so when you chose it, and it was not taken into consideration when the other door was removed.
So you can move from a 1/3 chance to a 1/2 chance by switching.
(It's called the Monty Hall Problem if you do want to read up on it).
-
More commonly known as Russell's paradox, but applicable to anything.
-
a cowboy rides into town on Wednesday, stays two nights in a Premier inn, and leaves un satisfied
how?
The horse was called Lenny Henry
-
A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.
On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.
The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:
"I can see someone who has blue eyes."
Who leaves the island, and on what night?
There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."
And lastly, the answer is not "no one leaves."
-
This is more a reading exercise that a test of logic, I think.
Given the ferry arrives daily, it could be any night anyone leaves. If it arrived alternate days and the Guru spoke on Wednesday, then the next to leave, regardless of eye colour, would do so on Friday. But the premise doesn't contain any information that helps in this way, so either I'm plain wrong or the suggestion of a day in the answer is the clue to it being a diversion.
-
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Don't think I've got the right answer for this but here goes... When you pick door 1, the chances of getting a goat is 2 in 3, the chances of getting the car are 1 in 3. Once one of the known goat-doors is opened (door 3) then you still had a 1 in 3 chance of getting the right door if you stick with door 1, because it was picked before door 3 was opened.
If you decide to swap you'll be picking a door with a 1 in 2 chance of getting the car, because one of the goat doors has been removed.
So yes you could argue you should swap....Although, if you don't swap you are still choosing to pick door 1 with a known 1 in 2 chance of being it being a car...
-
This is more a reading exercise that a test of logic, I think.
Given the ferry arrives daily, it could be any night anyone leaves. If it arrived alternate days and the guru spoke on Wednesday, then the next to leave, regardless of eye colour, would do so on Friday. But the premise doesn't contain any information that helps in this way, so either I'm plain wrong or the suggestion of a day in the answer is the clue to it being a diversion.
They can't get on the ferry till they've worked out their eye colour. The guru is asking them to know for sure whether they have blue, brown (or another colour) from that one statement.
-
A group of people with assorted eye colors live on an island.
I remember this one, it's something like, they all hang around for X number of days then they all leave at once. But I can't remember why.
Something like, they're all thinking "well, if no-one's left yet then there must be more people with blue eyes". And they all know that everyone's thinking that, as they're all perfect at logic.
But then it gets to D-day and they all leave together.
-
-
...Although, if you don't swap you are still choosing to pick door 1 with a known 1 in 2 chance of being it being a car...
no - if you don't swap you're sticking with a door with a 1/3 chance of a car, if you swap you're changing to a door with a 1/2 change of a car :)
Try shunting the number of doors up to 1,000,000. You pick one, you've got a 1/1000000 chance of getting the right door.
Intuitively, if someone then opened 999,998 of them, would you still stick with the one you originally chose (almost no chance of being correct)? Or would you think that the other door, from the population of doors you didn't open, had a 999,998/999,999 chance of containing the car?
-
• #47
Bonus question: Does the door maintain its odds if a new person walks up and has to choose between the two (1/3 and 1/2 or 1/1000000 and 1/2)?
-
The odds of your first choice are 1/3. When one of the three is removed, the odds change to 1/2 - but only for the door you haven't chosen. That is, the door you're on remains 1/3 as it was so when you chose it, and it was not taken into consideration when the other door was removed.
So you can move from a 1/3 chance to a 1/2 chance by switching.
(It's called the Monty Hall Problem if you do want to read up on it).
The thing I don't understand here is:
Why doesn't the chance for your door change to 1/2? After all, you have chosen the door at 1/3 chance, but as one door is eliminated, your door should automatically become 1/2 as there is only two doors left?
Or is this a statistics "rule" saying that my chance doesn't change when I dont change my guess?headache.
Edit:
And what if i choose again, but happen to choose the same door again?
such confuse. -
Bonus question: Does the door maintain its odds if a new person walks up and has to choose between the two (1/3 and 1/2 or 1/1000000 and 1/2)?
Is the new person told the story of the door opening, and which was chosen / which one was left unopened by the host? I imagine if they know nothing then it's a straight 50/50 choice for them.
christianSpaceman
Drakien
umop3pisdn
greeno
EB
Trunkie
BeauNidle
TheorySwine
Murphy's_Law-
Post a reply
About
Logic Puzzles
Posted by
@Arducius
A lighthouse keeper needs a new carpet. His room is ring shaped as the lighthouse has a central column. The only measurement that he can make is the length of the chord from the outer wall to the other side touching the central column.
His carpet fitter can't work out how to calculate the square footage of carpet he needs to generate a quote for the lighthouse keeper, so consults an old mate who's a famous mathematician.
After a couple of days the mathematician calls back and says "I've worked out the formula that calculates the area of carpet from just the chord measurement! The formula is" at which point the carpet fitter stops him and says "don't worry, from what you've said I know what the area is!"
Let's say, hypothetically, that the length of the chord was 20 feet, how many square feet of carpet did the carpet fitter quote for?