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        riddles >> easy >> Glass Half Full
        
(Message started by: sov on Nov 3^rd, 2006, 4:22pm)

Title: Glass Half Full
Post by sov on Nov 3^rd, 2006, 4:22pm

The best way to gauge the fullness of the glass is to use your hand to seal the opening of the glass, then turn the glass sideways and lay it on any flat surface, such as the floor. The perfect circle of the cylinder creates a perfect measuring tool.

Title: Re: Glass Half Full
Post by Icarus on Nov 3^rd, 2006, 7:48pm

But your hand is not flat, so it adds a bit of volume on one side of your cylinder. If the water was halfway up with the cylinder on its side like that, you could be sure that in fact the cylinder is more than half full. Where the water level must fall to be exactly half full is still a guess.

There is another approach that is more accurate.

Title: Re: Glass Half Full
Post by danny.paulsen on Nov 8^th, 2006, 10:55pm

the best way to accurately guage the amount of water is to tilt the cylinder glass to the side till the edge of the water is exactly at the open rim's edge. If the water intersects the corner of the bottom of the glass, then you have a glass half full/ if the the water is above the bottom rim, its more than half full, below-less than half full

Title: Re: Glass Half Full
Post by housewifeman on Dec 29^th, 2006, 12:08pm

Excellent. One could also use a piece of clothing such as a shoe string. Place one end at the bottom of the glass. Hold the middle at the level of the water. Then raise the part below water level. If the string reaches the top exactly then the glass is half full. I it goes above it is more than half full and if it doesn't reach the top it is less than half full. It didn't say you are naked!

Title: Re: Glass Half Full
Post by fiziwig on Dec 29^th, 2006, 8:46pm

Measuring the depth won't due i the glass is tapered as most glasses are.

Of course to an engineer, the glass is neither half full nor half empty. It's simply that the glass is twice as big as it needs to be.

Title: Re: Glass Half Full
Post by rmsgrey on Dec 30^th, 2006, 10:42am

on 12/29/06 at 20:46:28, fiziwig wrote:

Of course to an engineer, the glass is neither half full nor half empty. It's simply that the glass is twice as big as it needs to be.

Not necessarily - what level of perturbations are anticipated, and what design tolerances are required?

If a glass is filled to the brim, then it requires an inconvenient degree of care to drink from it without spilling. A factor of two may be overkill, but I'd prefer a moderately oversized glass to having fluid sloshed down my front...

Title: Re: Glass Half Full
Post by ChemEngineer on Jan 26^th, 2007, 9:23am

A quick and dirty way to solve this is to cover the top of the glass, hold your finger outside the glass at the top of the current water level, and then flip upside down (keeping your finger in place). If the new water level is; below your finger then the glass is less than half full, above your finger then the glass is more than half full, and of course at your finger then it is exactly half full.

Title: Re: Glass Half Full
Post by fiziwig on Jan 27^th, 2007, 9:27am

on 01/26/07 at 09:23:35, ChemEngineer wrote:

A quick and dirty way to solve this is to cover the top of the glass, hold your finger outside the glass at the top of the current water level, ....

Good solution. But again, it assumes that the glass is cylindrical rather than tapered. However, a tapered glass could use nearly the same technique:

Cover the top of the glass. Hold the glass on its side with the bottom-to-rim axis horizontal, mark the water level on the two diametrically opposed sides of the glass, and then rotate the glass about the bottom-to-rim axis until the marks have been rotated to the opposite side. If both marks still line up with the water level then the glass is half full.

If both marks are above the water level the glass is less than half full, and if both marks are below water level the glass is more than half full.

This also works with glasses that have irregular vertical cross sections such as the old fashioned soda fountain Coke glass, or even the traditional green glass wasp-waist Coke bottle.

Title: Re: Glass Half Full
Post by towr on Jan 28^th, 2007, 7:15am

on 01/27/07 at 09:27:52, fiziwig wrote:

Good solution. But again, it assumes that the glass is cylindrical rather than tapered.

I don't think it does, I think it works for almost any shape glass, as long as the water has only one level when turned either way (i.e. it isn't caught in other 'pockets')
In that case you will have one dividing plane with a half above it and below it, and a mark where that plane cuts the glass provides adequate proof.

Quote:

However, a tapered glass could use nearly the same technique:

<snip>

It only works for rotationally symmetric glasses though. Which admittedly includes most, but still.

Title: Re: Glass Half Full
Post by fiziwig on Jan 28^th, 2007, 9:07am

on 01/28/07 at 07:15:23, towr wrote:

In that case you will have one dividing plane with a half above it and below it, and a mark where that plane cuts the glass provides adequate proof.

AHA! I see what you mean. I stand corrected.

Title: Re: Glass Half Full
Post by UNKNOWN on Feb 6^th, 2007, 5:45pm

Easy:Pour the water out... then its less than half full/empty. :D

Title: Re: Glass Half Full
Post by Greg on Mar 1^st, 2007, 1:39am

Suppose the water in the glass was chilled, and that the floor of the room is flat.

The glass of the cup that was surrounding the water will form a layer of condensation, so place the cup on the level ground to form a nice, even condensated surface area (you can smear away any formed condesation in the process of placing if you really wanna be pickey, but I don't think you can for the next step, unfortunately). Using centrifugal force, spin the glass upside down without spilling any water and place the cup open-side down on the ground. It will then be much more clear whether the glass is more or less than half full by the difference between the new water level and the line formed from the condensated surface area and non-condensated surface area of the glass.

Note that the ground doesnt actually have to be perfectly perpendicular to the force of gravity. One must simply rotate the glass after placing it upside down on the ground so that the distance between the condensation line and new water level is about equal at all points around either line (the new water level or the condensation line).

Title: Re: Glass Half Full
Post by chad1 on Apr 6^th, 2007, 8:00pm

this is simple. you walk out of the room. Then you mark the top and the bottom of the glass with something outside of the room. Then you measure the glass with a ruler found outside the room. It never says you cannot walk outside the room.

Title: Re: Glass Half Full
Post by Pyotr on Apr 18^th, 2007, 12:32pm

The glass is a cylinder. Just tilt it until the water reaches the lip.

If the level at the base is above the bottom rim, it is more than half full, and vise versa.

Edit: just read WW's request for thinking patterns and not just answers.

In my mind's eye, I just thought of a glass half full and tried to pour it out. When it began to pour, the water level was touching both the lip and the base as it was a right cylinder.

The rest follows.

Very much enjoy your site. The easy level is hard enough for me, although I had a great time with the Sangaku problems at the medium level. I have some overseas Japanese students here in Russia and they find it fascinating to discover that their country had its own mathematical evolution while being cut off from the outside.

Of course, this is not the whole story, but at least it draws them in to the arena of problem solving.

All the best!

Title: Re: Glass Half Full
Post by tedwindsor on Apr 29^th, 2007, 11:19am

Assuming the walls in this empty room are well constructed... being flat, and at a 90 degree angle to eachother and the earth...

Take the glass to the corner of the room, place it open side up against one wall and the side against the adjacent wall... if the water level is above where the glass meets the wall, it's more than half full, below and it's less...

Title: Re: Glass Half Full
Post by Zatanna on Aug 11^th, 2007, 5:37pm

Here's the answer to a related qusetion:
"Is the glass half-empty, or half-full?"
It depends on whether you're FILLING the glass or EMPTYING it. ;D

Title: Re: Glass Half Full
Post by cowboy1 on Sep 6^th, 2007, 5:15pm

SUMMARY: Tilt the glass!

EXPLANATION:
Simplify the problem to two dimensional geometry. Think of the glass as a rectangle and the water as a shape inside of the rectangle.

We know that if we draw a line from one corner of the rectangle to the opposite corner, the rectangle will be split into two equal-sized triangles.

The two triangles are the point, where the glass is exactly half full. If one of the triangle shapes were larger or smaller, we'd know which of the other conditions apply.

Conveniently, such a dividing line can be drawn by tilting the glass to line up the water surface with the top of the glass and bottom of the glass.

If the water surface touches both corners at the same time, it is half full. If water is spilled attempting to tilt the glass enough, it is more then half full. If the water falls short to touch both 'corners', it is less then half full.

Note: The approach would not work, if the glass wasn't symmetric and had right angles.

Title: Re: Glass Half Full
Post by Goomba_5 on Nov 6^th, 2007, 1:35am

on 12/29/06 at 12:08:54, housewifeman wrote:

It didn't say you are naked!

True. But the shoes I'm wearing don't have shoelaces...

Title: Re: Glass Half Full
Post by Dan on Nov 19^th, 2007, 12:01am

Ok so here it goes.

Don't think about what kind of stuff to measure the water with, tilting it or flipping it upside down or against the wall or using a shoe lace or going "outside of the room" or how to find the half way mark.

Try to think about how much water you have and how much water the glass can hold and go from there, meaning find the volume of the glass and the water in it.

So lets see what we have to use, an empty room, a clear right cylinder glass, no measuring or writing utensils, so obviously we can't measure it in any conventional way or in any way at all except for making estimates.

Also, you could think like a child and simply give an answer that way. And the riddle is only looking for the most accurate way to figure out if its half full or more or less.

And so the most accurate way would be to measure it to see if its more than half full, less than half full, or half full. So you don't actually half to measure it to figure it out, you only have to know how to figure it out.

Title: Re: Glass Half Full
Post by Csimbi on Apr 8^th, 2012, 9:19pm

The answer is easy: the glass is full.
Some water, some air, but definitely full.