[Guest]

My apologies if this is a repeat, but I couldn't find it anywhere.

You are given a cup and a water source, nothing else. The cup is perfectly cylindrical, and has no markings. Fill the cup exactly halfway.

Assume no

meniscus.

[Guest]

Well, I would think that you'd

fill the cup and tilt it until the top edges of the water in the cup are at the top "left" tip and the lower "right" tip of the cylinder. This will fill the cup exactly halfway.

Edited December 14, 2010 by Akariass

[Guest]

Fill the glass with water (more than half), then slowly tilt the glass allowing water to pour out. Keep tilting the glass till the bottom end of the water level reaches the edge of the base of the glass--- and your glass is now half full (or half empty)... Imagine the glass being a rectangle and the water level, a diagonal

[Guest]

Since everyone would be arriving at the most common answer which goes like:

tilt the glass 45 degrees and fill it until an overflow OR fill the glass and tilt it until you can see the edge of the bottom

let's try some different solutions...

how about?

freezing the water and cutting in half? or something even more whacky...

[Guest]

I liked your obvious solutions more than mine because they're simpler and more accurate, but I'd like to show you what my twisted mine thought about in his first trial to solve this.

The idea requires that the glass from the inside can reflect like a mirror. So when you adjust your eye to the line created by the two stars, Start pouring the water until you see the reflected surface reaching the top of the glass. Check the diagram attached.

[Guest]

Since everyone would be arriving at the most common answer which goes like:

tilt the glass 45 degrees and fill it until an overflow OR fill the glass and tilt it until you can see the edge of the bottom

let's try some different solutions...

how about?

freezing the water and cutting in half? or something even more whacky...

Different solution 2 --

fill the glass up and see how long it takes to evaporate to nothing. Then fill the glass again and wait half as long so that half the liquid has evaporated.

Different solution 3 --

time how long it takes to fill the glass with water at a constant speed. Then pour water in for half that time.

Different solution 4 --

using a particle accelerator, count the number of molecules ...

[Guest]

Well done everyone. Keep the original solutions coming, they're fun!

Elegir, your solutions 2 and 3 assume constant evaporation speed and constant filling speed. My initial question specified a water source, nothing else; this could be just a lake, or a puddle from melted snow during an unseasonal heat wave in late February.

Can anyone come up with a solution that guarantees that you don't have to pour out any water? Again, let's get some fun solutions.

Edited December 14, 2010 by j.green

[Guest]

What about my solution?

It guarantees you don't have to pour out any water.

[Guest]

...can pour water into the glass until the respective frequency of the half-full glass is reached

[plainglazed]

fill the glass half full by eye, make a mark as to the height when level, cap with some flat surface and invert until again level, compare mark and add/remove as needed, repeat until half is achieved

[Guest]

My apologies if this is a repeat, but I couldn't find it anywhere.

You are given a cup and a water source, nothing else. The cup is perfectly cylindrical, and has no markings. Fill the cup exactly halfway.

Assume no

meniscus.

ok since the cylinder is perfect and there are no resstrictions we can do this:

1) find the middle of the (botom) circle and draw a line. this line will have legth 2R

2)turn the cylinder horizontially

3) we put the whole cylinder incide a water source.

4) when the water level is excactly at the line(the line is also horizontially or else there is no mean to do this)

5)finally we carefully put the cylinder out and since is a perfect one we will have him fill by half.

I HOPE YOU UNDERSTOOD IT

[Guest]

ok since the cylinder is perfect and there are no resstrictions we can do this:

1) find the middle of the (botom) circle and draw a line. this line will have legth 2R

2)turn the cylinder horizontially

3) we put the whole cylinder incide a water source.

4) when the water level is excactly at the line(the line is also horizontially or else there is no mean to do this)

5)finally we carefully put the cylinder out and since is a perfect one we will have him fill by half.

I HOPE YOU UNDERSTOOD IT

1) You don't have a pencil, just a cup and a water source.

2) When you lift it out of the water the water will spill out.

[Guest]

Fill the glass approx half then put your hand on top of glass then invert it, it should be at same level when it was not inverted (add remove water if needed till you get a single point with and without inverted). You can use your finger or nail to get hold of the mark while inverting. It will give you half glass of water.

Edited December 20, 2010 by Panwar

[Guest]

What about my solution?

It guarantees you don't have to pour out any water.

Your solution requires the measurement of 2L to make a 45º angle, with no measuring devices provided (it is not accurate enough to use the glass as a measuring tool, among other reasons because there is no guarantee of colinearity); also, I didn't say anything about a reflective surface.

Edited December 21, 2010 by j.green

[Guest]

Fill the glass approx half then put your hand on top of glass then invert it, it should be at same level when it was not inverted (add remove water if needed till you get a single point with and without inverted). You can use your finger or nail to get hold of the mark while inverting. It will give you half glass of water.

1) Your hand is not perfectly flat

2) I didn't specify the size of the glass (it could be much larger than your hand), so your solution doesn't solve the general problem

[Guest]

Can anyone come up with a way to solve for a general frustum-shaped glass? (I haven't... I'm not sure it's possible)

Edited December 21, 2010 by j.green