Logic Puzzles

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.

So if I forgot the story the host told me, my chances are 1/2 because I don't know that they once were 1/3?

Riddle me that

They are both girls?

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.

Yeah, that's right. It's only because we know that the host has opened a load of doors because the host knew that they weren't winners that we have more information about the remaining choices.

So if I forgot the story the host told me, my chances are 1/2 because I don't know that they once were 1/3?

if you were presented with two doors, without all the previous knowledge and the door opening nonsense that's gone on before then yeah - I think so :)

Try running this ten times or so, first keeping then changing your choices and see what your figures come out at:
http://math.ucsd.edu/~crypto/Monty/monty.html

So if I forgot the story the host told me, my chances are 1/2 because I don't know that they once were 1/3?
That's what I was getting at with the quote below.

...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...
If you don't change doors then you are still picking door 1 *when there is a known 1 in 2 chance of it being right. *Because you are now simply picking between 2 doors....

No, wait. The host is always going to open an incorrect door. This changes things. I think. Ok, I think I just got it when trying to justify myself.

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).

Can of worms. Cheers though. I'm content just knowing I can put a name to it.

(http://xkcd.com/246/)

Okay, maybe I am getting it now.
You choose 1 out of three. So your chance that your choice is right is 1/3.
Now someone comes and opens one wrong door, leaving you with two closed doors and one wrong one. The 1/3 chance of your pick stays the same though, because... your pick is not taking the new situation into account. The fact that you know, that 1/3 is definitely wrong does not change the number of doors.
Only when you choose again, from two doors your chances rise.
Crazy.
Not 100% sure yet.

I like this one, maybe because I got the answer!

A man is stranded on an island covered in forest.

One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the man survive the fire? (There are no buckets or any other means to put out the fire)

Assuming he can't climb down the cliffs and to the water then. And making a wee circle round himself won't suffice as an answer....

Is chopping the trees down to make a break in the vegetation realistic? Or digging a shelter somehow.

Wind blowing from the west means it is blowing easterly?

Start another fire

He sets a fire to his East.

^Although this saves his life it leaves his previously verdant Eden scorched and barren. After months of starvation he is reduced to wandering the blackened wasteland and dies when, half-mad with hunger, he stumbles off a cliff and plummets to the rocks below.

Bear Grylls turns up from his 4* hotel to rescue him.

And then drinks his piss.

Start another fire
Is the right answer.

He sets a fire to his East.
Yes, and then can shelter on the now cool earth where there is nothing left to burn.

^Although this saves his life it leave his previously verdant Eden scorched and barren. After months of starvation he is reduced to wandering the blackened wasteland and dies when, half-mad with hunger, he stumbles off a cliff and plummets to the rocks below.
I particularly like this ending.

Wind blowing from the west means it is blowing easterly?
No that's a Wetserly wind. Wind is names from the direction it comes from, not the direction it's going.

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?

No takers then? In the example the carpet would be 314.1592 square feet....

I assume it has something to do with figuring out the radius of each circle? Not sure how to get there though.

Working out the formula is straight forward enough, but why would the carpet fitter suddenly be able to work this out from the mathematician's statement?

I assume it has something to do with figuring out the radius of each circle? Not sure how to get there though.

It's deduction. Because the formula exists it must exist for all diameters of room and central column. Therefore you could have a circular room with a 0 diameter column, at which point the chord length is the diameter of a circular carpet,

Yeah, it's something to do with the fact that the area required is pi(R^2 - r^2), where R is the radius of the tower and r is the radius of the column. The area appears to end up being multiples of pi, and the factor is (chord length/2)^2 (from the answer SimonAh gave)

Haven't quite worked out why.

In your cellar there are three light switches in the off position. Each switch controls 1 of 3 light bulbs on the floor above. You may move any of the switches but you may only go upstairs to inspect the bulbs one time. How can you determine the switch for each bulb with one inspection?

don't get the moving switches bit - just take them upstairs then no?