Light one end of the one of the ropes. Light both ends of the second rope. When the second rope has burned completely, 30 minutes has passed as half of 60 minutes obviously equals 30. Seeing as 30 minutes has passed, now light the second end of the first rope. Seeing as 30 minutes has passed, when the first rope burns completely 15 minutes would have passed. And now you have measured 45 minutes... with ropes. Maybe try a watch in the future.

Oh. Four pages. And the first one already has an answer. Well it's no fun figuring out a riddle (okay, I heard it before... :P) and finding out it's already been solved! :(

If it takes 60 minutes for a fire to spread from one side of a block of flats to the other, and you have 2 blocks of flats.........

to steal figles' idea - using lorentz contraction - put the building on a space ship, advance to close to the speed of light. Observe the speed which the building is travelling at when the building and (stationary) barometer has the same lenght. (now please help me with the error analysis... :P

.. How many people will die to time 45minutes

live game anyone?

does it depend on how fast the building is falling and what fraction of the speed of light it was travelling at when you dropped it and set it on fire?

orathaic +1 - [second] best answer ever! :)

Measuring the height of the building with the barometer:

Use perspective, putting the barometer 1 meter from a camera such that it only just obstructs the whole building from view, then do the geometry.

A hand for anyone (GHOST!) trying to do the error analysis for Orathaic:
Let B = height of building, b height of barometer, then
B = b / root(1-[u/c]^2)
for building in intertial frame moving at speed u with respect to observer and barometer, c speed of light.

Similar triangles are waay too simple. Anyway Ghost, the buildings on fire (obviously), so the heat-haze will distort your vision!

Shout at the ground and work out how long the echo took. (I would love to see someone trying this - to everyone else they'd just be shouting hysterically from the top of a block of flats.

ok

let b=1m for a nice barometer

100=1/root(1-(u/c)^2)
gives a velocity damn near to c
We could measure it quite accurately using the red shift involved, so lets give that a 0.1% accuracy.

meanwhile b we could easily measure to 0.1%

gives us 0.3%

However, you're being fairly unfair because your measurement of the velocity of the building is using far better equipment than assumed in the other measurement.

Not to mention you've good an amazing rocket.

Shoot somebody fat 100 meters away from the building and use the depth of penetration to get the velocity of the bullet, know the nozzle speed and hence the height of the building.

Hmm,true on Lorentz issue. Bad news though Ghost: red shift isnt easy in relativity either.

Shooting: Bit harsh but works. Apparently, if they have 1.5m of fat it wont penetrate their organs...

Remove foundations apart from along one wall, and rest other side on bulb of our incredibly strong barometer. then, Fly a plane horizonally into top of block. Read off barometer & calculate height through moments

there is another hard bit in my lorentz measurement, i've got a building traveling at very near c, and a stationary barometer, they are the same lenght but to measure them i have to get the building to fly past the barometer. Getting the building to go at the right speed to match the barometer is not trivial. (asusming you don't know how big it is)

"Not to mention you've good an amazing rocket."

I think i'll be better off using a light powered sail, or perhaps a big spring... to get the building oscillating past (with maximum velocity at) the barometer...

"a big spring" - VERY big spring!
But yes I was thinking that, although I think you could estimate that a building is about 100m tall, work off that, then correct based on your first test?
Big spring and a speaker at the resonant frequency of the system. In theory!

Who on earth is tightening the spring?

it is just completely elastic, with the building in the middle. So as it oscillates the building moves left to right. The idea is that very little energy gets turned into heat when you expand and then contract a spring... so you aren't losing energy from the system and you can build up (using a speaker in figles version, and a laser in mine) the energy in the spring-building system (which is then just an oscillator)

Ah, resonance, nice.

Unfortunately, I suspect that the Newtonian mechanics you are using will be invalid at the speeds you are thinking of.

I'm amazed that no-one else has commented on this.
How would it work with a Lazer?

Lock an infinte number of monkeys on typewriters in a room for an infinite amount of time, then when you come back one of them will have typed out the specifications for the building.

lasers can impart momentum as a sound wave would, in fact they usually operate on a optical cavity - which is similar enough to a resonator with a standing wave (to build up the amplitude) i suppose you could put the building-spring-oscillator inside the optical cavity.... hmm.

If you have an infinte number of monkeys on typewriters then you don't need to lock them in for an infinite time - they'll probably die before infinite time has passed anyway; but so long as you have infinite monkeys you'll get the answer, with the only difficulty being finding out which piece of information is correct - and considering you're talking about finding a finite piece of information in an infinite set that is a non-trivial task.

Yeah, i suspect that chemical bonds (which hold my spring together) will no longer function in exactly the same way at the speeds (and accelerations) i'm talking about - however I also think the fricion (which is usually assumed to be negilable would no longer be... maybe we can do without the spring and create a purely optical oscillator... hmm.

There are certainly difficulties involved.

I'm thinking that perhaps the best way is to use the gravitational force of some star or galaxy to accelerate it?

But how does that use the barometer? Perhaps we could trade it (like that guy with the website who went from a paperclip to a house overall) until we have this super oscillator.

excellent!

The oscillator is there to get the building up to the speed where it is the same size as the barometer. You then measure the speed to work out the stationary size of the building

We need to reinforce the building, for which we need to know the size of the building. I suspect a loop forming....

Oh yeh, I'd forgotten about that!
We own the barometer, but not the flats. However, using the same logic as modern banks, we could float the flats on the stock market, sell it a couple of times, then spend the money to buy ourselves nice cars. Then, when the residents find out we've mucked up their homes we can work out how many there are and so how tall it is.

"Lock an infinte number of monkeys on typewriters in a room for an infinite amount of time, then when you come back one of them will have typed out the specifications for the building. "

But then, you'd have a monkey that wrote the right specs, and another that wrote the exact same specs but changed the height by 5 meters, how do you know wich monkey is right?

@xapi: well done, you said it far more concisely than i did...

Xapi: worse, not if, but *when*