Noobs Weekly: Release IV

You have 100 bags of coins each with 100 coins, but only one of these bags has gold coins. The gold coin weighs 1.01 ounce and the other coins weighs 1 ounce. You also have a scale, but can only use it once.

How can you identify the bag of gold coins?

Note by John M.
6 years, 9 months ago

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First label the bags from $N = 0$ through $N = 99$. Next, going through the bags, take $N$ coins from the $N$th bag, gather all these coins together and put them on the scale. The scale will then display $4950.N$, indicating that the bag labelled $N$ has the gold coins.

For example, if the scale reads $4950.13$, then the bag labelled $13$ has the gold coins.

- 6 years, 9 months ago

Ha ha Brian, you're like the Noobs Weekly hero! :))

s

- 6 years, 9 months ago

Wow, that's such a good likeness. :P I'm looking forward to the "Noobs Weekly" that completely baffles me; we might then have to send Mr. Michael Mathopedia a request to work his magic.

- 6 years, 9 months ago

Lol who downvote me comment? Is that you, Brian? Makin me mad!

- 6 years, 9 months ago

No, of course not. I just noticed the downvote myself, so I gave it an upvote, (even though I haven't had time to read your manifesto yet), just to compensate for the injustice of it all.

- 6 years, 9 months ago

Oh thx lol I just spent a really long time typing this and would be dissappointed if you downvoted it. But if it's someone else that's alright; they can't feel teh awesomeness xD

- 6 years, 9 months ago

Oh, and also, my Edmodo post got declined by the teacher [ikr? wtf], so I've made this website and I like its format better than Brilliant's. The text is image fragments off of Edmodo, and I think you'll like it better. And it's easier to memorize:

- 6 years, 9 months ago

Alright, here's something just for you, personally, because I'm sure if I were to post it as a note it wouldn't exactly go viral:

My biology teacher tried to teach the First and Second Laws of Thermodynamics, including entropy and energy transfer. I was annoyed to a great extent by her inability to accurately explain this as far as physics is concerned - hey, as far as Bio is concerned, she was on point. But obviously Biology is just a one big memory game if you don't know physics - so I made this colossal post on "Edmodo" - a tool teachers use to post assignments, quizzes, and other resources online - to teach appropriately.

When you're one day on a hot summer beach or something, take your time to read this - it's an entertaining read, I promise. I also discuss how to destroy and create energy! :DD

s

Here it comes... Word by word, line by line - THE EDMODO POST:

[Note: this is very lengthy, but you only have to read it once, unlike in books when you have to go ten times over the same thing (and still not get it). Consider this, and read on (or not).]

Hello, I'm OverLordGoldDragon from the 12th dimension, and I'd like to explain to you what the Laws of Thermodynamics really mean (in a language you will understand, I promise (if you don't you can slap me (but I'll probably block (but you can keep trying)))).

So, whatever was explained to you today is, as far as your AP Biology class is concerned, is sufficient. But, it can be very misleading as far as the true concepts go.

Reading this nonstop can take about an hour (or two), but you will get the major benefits of almost 2 years of college education about this stuff! (including some Ph. D info!). (and it is max two hours - this is because you wont spend time reading back because most of the info is me reiterating myself for your better understanding. And, the edmodo format makes this look way lengthier than it would be on a word document. And - consider how much I space. If I were to clump it all together, it'd make about 4 word pages (12, single spaced, times new roman)

Here they are:

-The conceptual understanding of laws 1 and 2 of thermodynamics; -What the heck is meant by "SYSTEM"?; -What is "Kinetic Energy"? -What the heck is "ENERGY"? -What does it mean to do "work" (in science)? -What in the world is HEAT?; -DO U FRICTION, BRO?; -Energy transformation explained; -Never feel threatened by words "ENERGY" and "THERMODYNAMICS" ever again! (if you do, call me); -The ball in a park example from Boozeman Biology explained; -BONUS: How you can CREATE and DESTROY energy.

Are you up to it? No? Alright go back to your instagram.

Yes? WELL LET'S DO THIS!!!

Format: [Concept being discussed], explanation.

[SYSTEM]

First of all, let's define the legal termins in a more HUMANE way. We hear the word SYSTEM a lot, so what does it really mean?

Nothing. It doesn't mean anything. At least, nothing defined. The thing is, YOU define your own system. A system is simply a set of elements within some sort of scope or restriction that you define for purposes of analysis. And by analysis I mean it could be anything; observation, calculation, etc.

Consider yourself inside a train. The train is moving at around 60mph; but you are not moving. How so? This is because if you define your system to include just the train and yourself, then you're not moving relative to anything within that system (that is, if you're seated or stand still). But, include the rail track, and now you're moving relative to it as fast as 60mph.

In fact, the Earth is moving at the speed of around 20 miles per second - yup. But we don't sense it (for reasons, that includes that it moves 20mps with respect to the sun, not you).

A system may be as tiny as an atom or as large as the universe. ITS OF YOUR CREATION! MWHAHAH!!

[First Law of Thermodynamics]

Legal definition:

"When heat flows to or from a system, the system gains or loses an amount of energy equal to the amount of heat transferred."

Get it? Great, move on to the next term. No? Read below:

First of all, what the heck is "Kinetic Energy"? No no no, I'm sorry: Zero of all, what in the universe in ENERGY? Well, I can argue that energy is everything. But I won't go that far (if you want me to, buy me lunch).

So, most basically, energy is the ability to do work. It's the ability of one object to do work on another object. What is work? Work is simply Force x Distance. Yup, that's all it is. For example:

If you push a with a force of 50N over a distance of 2 meters, you've done 100 units of work on the crate. On the other hand, if you push a wall with a force of 1,000,000N and it doesn't move, you've done 0 work on the wall. Now it may seem that Work done on an object is independent of the object's mass, but that's not true; the heavier the object, the harder it is to move it over that distance. HOOHOO!

"But I heard that kinetic energy is when the rollercoaster goes down it gets more kinetic energy"

"But I heard that kinetic energy is the energy of motion"

That's true. But consider this: in order for an object to move, work must be done on it.

...

...

Get it? HOOHOOO! No? Okie: Consider a crate. You push it, it moves. Before you pushed it, KE=0. After you pushed it, KE>0. Guess what: in order for the crate to move, work had to be done on it. That's basically it.

Oh, and crates and all that stuff can get confusing. For precision purposes, we'll use billiard balls. Here's why: they closely resemble particles (as far as you're concerned (AFAYC)), and the pool table can be thought of as our "closed system".

...

So, Kinetic Energy is the energy that results when work done on an object causes it to accelerate and gain speed - or, move through space over time. Cool? Alright.

[HEAT]

This one annoys you, doesn't it? Here you think heat is when you feel worm, and there Mrs. Addi is telling you that heat has to do with the universal properties of energy or whatever... Well guess what; she right & u right.

How? BELOW:

What's heat? When you feel hot? yeah. What else?

Heat is motion. That's basically it. It's the motion at subatomic levels that's mostly caused by friction.

IMAGINE THE BILLIARD BALLS ON A POOL TABLE; NOW, IMAGINE YOU HITTING THE WHITE BALL; NOW, IMAGINE THE WHITE BALL SLOWING DOWN AND ALL THE OTHER BALLS GOING CRAZY;

That's heat.

What happens is, when particles of one object interact with particles of another object, they transfer their kinetic energies on subatomic levels to the particles of the other objects. Why? Because they do work on them! When you hit a ball with your hands, what happens to the ball? It moves. Why? Because you've applied force on it and this force caused it to move a certain distance. That's work! And HEAT is simply work done by individual particles on microscopic level, thus transferring their kinetic energies! And this energy mostly gets stored in forms of potential energies, like electric potentials, chemical potentials, etc. This is also called the total energy, or the INTERNAL ENERGY - the sum of all "available" energies of an object (like a particle).

With the ball in the park example, what really happens to the potential energy? No, it doesn't get "RELEASED." And it doesn't become "USELESS." It gets converted to heat energy. How? Consider this:

Imagine the surface of a ball on a particle level. Think of billiard balls. So when the ball rolls down the slide, as it rotates and rubs all over the nasty little slide, its particles, due to friction, transfer their energies of motion to the particles of the slide as the ball rolls down. This causes the ball to decelerate at the bottom and finally come to a stop. k00L?

So energy isn't released, it is transferred, like stated by the First Law of Thermodynamics. But in biology you can think of it as "released" and "useless."

But why isn't it useless, just to justify?

Well, think of it like this: if you take a hot tire after a long day of driving and place it inside a big water bowl, does the water inside the bowl not get heated? Look - we just made the useless energy do something useful! Well, when I say AFAYC (as far as you're concerned), I'm right. AFAYC, the heat dissipated to the ground when the ball rolls is pretty much useless. You can't just take that energy out of the ground and make light out of it.

But precisely, it is not; remember, that heat gets stored in one of the forms of potential or energies, either chemical, electric, or some other form. When the conditions are right, this energy is converted back to a useful form of energy ( a kinetic energy ) and we're good to go.

[But what is FRICTION?]

When you fall and slide on a football field, does your skin peel off sometimes (or does it just feel really nasty)? Well, that's friction. Basically, friction caused by the degree of distortion of objects' surfaces. That's because on quantum levels, nothing is perfectly straight. Think of a polished ice skating rink; very low friction. That's because the surface is very, very smooth. But it's not perfectly smooth, either.

BACK TO BILLIARD BALLS:

Imagine your hand. Imagine the table. Now, imagine the billiard balls of your hand coming in contact with the billiard balls of the table. Why do you constantly have to struggle to move your hand across the table? Now think of two grassfields; think one grass field being rubbed against another grass field. Now imagine instead of grass there are particles. As particles from your hand move against the particles of the table, they fact obstacles, namely the particles of the table, that are firmly glued to the table, bound by the electric bonds. They don't want to move, but you want to move anyway. So you apply force to get your hand to move a distance; in other words, you apply work. Or, in other words, you use up energy. And guess what; when you apply work to the particle tables, what happens? Your original mechanical (which is basically kinetic for big, clumsy objects) energy gets dissipated as what? HEAT!!!! THAT'S RIGHT!!!

WEN TIRE ROLLZ AND STOPZ, Y IT STOPZ?

HEAT!!!

WEN U HIT TEH GROUND FROM THE TENTH FLOOR Y U STOPZ?

HEAT!!!

YEAH!!!!

And notice the energy conservation at work: when you hit the cue ball, does it just stay stiff and not move? Well, it could, if it's glued to the table. And what does it mean if something is glued? It means that there's an electric attraction between that object and the object it's clued to. So, when you hit a glued object, the work your particles (or the particles of whatever you're hitting the object with) expend work on the object, but that work, instead of transforming into the kinetic energy of the ball, dissipates as heat (or, is transformed into the kinetic energy of the individual particles.) Maybe you have a question: but why doesn't the energy always get transferred to the particles when you hit an object that's not necessarily glued? Magic glue?

No! The truth is, the energy transferred ALWAYS involves heat dissipation! In fact, this is the Second Law of Thermodynamics! (which we'll get to later). But it's just on different levels. Like, for the glued ball, you need to apply much more work to actually move it because you need to invest some work in breaking that electric bond between the glued object and itself, and then additional work to move the entire ball. But if the ball is free to go, much less work, and thus much less transfer of energy is required to move the ball.

Anyway, back to the energy conservation at work (two paragraphs above): so now the case when the ball does move. So, if we can define a closed system of billiard balls and the pool table, then what happens? Why do the balls stop all of a sudden? Well, this should be easy for you: BALLZ RUB ALL OVER THE POOL TABLE'S HAIRY FACE AND THEIR ENERGYZ DISSIPATEZ AZZ HEATZ :DDD

So basically, energy always transforms to one form or another. And most of the times objects stop moving because their energy is dissipated as heat (their particles do work on surroundings and therefore transfer their kinetic energies on particle levels to those energies).

Goot? Groot.

Just briefly, why do we feed hot or cold?

Well, our surroundings have particles in motion. Think of a hot pan: why is the pan hot? Because it's been heated, probably on a gas, by the fire that did work on the plate's particles over an extensive periods of time. So when the pan touches you, it does work on your cells, which send neurological signals to your brain, alerting it of the presence of the pan. If there's too much heat, cells send a more painful message, alerting you to remove your hand. Well, that's more neurology, but you get the point.

What about cold? Well, if cold, that means heat flows from you to the pan, and cells are wasting ATP (oh look, Biology for once!) on the pan instead of doing work on your skin tissues to regulate bloodflow, nutrients, etc.

Oh, and why, if you hit a pan repetitively, it won't get hot? Well, hit it hard enough, trust me it will. But why doesn't it, usually? Well, that's because when the hot gas does work on the pan's surface it is more effective on the micro level: imagine tiny particles hitting the pan at rates of trillions each second. Can your hand do that? HEAL no! Ok if u wanna kno more buy me lunch.

Oh, and a P.S.: notice that you can't have your entire arm melting if you put it under a matchstick for two seconds. Why? Because you get only as much energy as is transferred to you. And remember, energy is work in action. If you push an object with a moderate force, it can't just go fling into space at the speed of light. You'd need a colossal amount of energy for that! To move an object over a distance, you apply a force. To move the same object over the same surface (- don't forget heat!) over twice the distance, you apply twice the force. And the total amount of energy between the interactions remains the same, always. Oh, and you can call it a system. It doesn't really matter. If you want to have a system of my headphones, you bat, and a ball, go ahead; but if you hit the ball with the bat, it doesn't affect my headphones (because no work was done on it). :)

So, back to FLT:

[First Law of Thermodynamics]

Legal definition:

"When heat flows to or from a system, the system gains or loses an amount of energy equal to the amount of heat transferred."

:)

...

:|

...

:(

...

;-<

...

DO U GET IT O NO? IF NO, STOP READING AND DO 9,001 PUSHUPS!!!

Lol but seriously, this should make sense now. What it is pretty much saying, is

Heat added to a system = increase in internal energy + external work done by the system.

That's all it is. And I'm not even making this equation up; it's legal! I just wrote it out in words instead of the weirdo math symbols and all that. But if you don't get it, well, I'll thank you for reading all the way through (unless you skipped and stopped to look at my smiley faces >:-() Okay, let's wrap this giganto up with the Second Law of Thermodynamics:

[The Second Law of Thermodynamics]

There are three parts to the Second Law of Thermodynamics:

"Heat of itself never flows from a cold object to a hot object."

"When work is done by a heat engine operating between two temperatures, Thot and Tcold, only some of the input heat at Thot can be converted to work, and the rest is expelled at Tcold."

"In natural processes, high-quality energy tends to transform into lower-quality energy - order tends toward disorder."

So, let's tackle part 1:

"Heat of itself never flows from a cold object to a hot object."

Why? Well, considering our definition of energy, work needs to be done to heat an object. But cold objects don't just heat hot objects; think of it as billiard balls. If on one side you have billiard balls that are moving, and on the other the ones that are still, if you had a boundary between those two areas and you release it, do the balls that are still just start to do work on moving balls and make them go faster (increase their energy)? No! Lol. But notice that this is not always what it seems; how to air conditioners regulate heat and make heat flow from outside (cold) to inside (hot)? Well, notice the phrase "Heat of ITSELF." The key word is ITSELF; this means that the heat of the object doing the work never goes from cold to hot. But this says nothing about the heat of EXTERNAL objects! Consider this:

Heat can be made to flow the other way, but only by doing work on the system or by adding energy from another source - as occurs with heat pumps and air conditioners, both of which cause heat to flow from cooler to warmer places. What is this "another source"? Mostly electricity.

Another example:

The huge amount of internal (total) energy in the ocean cannot be used to light a single flashlight bulb without external effort. Energy will not of itself flow from the lower-temperature ocean to the higher-temperature bulb filament. Without external effort, the direction of heat flow is FROM hot TO cold. (so, for example, we could install the turbines to spin when water flows onto them, and thus generate electric energy (how this works is another topic) which can then light the bulb).

Cool? Cool.

Part 2:

"When work is done by a heat engine operating between two temperatures, Thot and Tcold, only some of the input heat at Thot can be converted to work, and the rest is expelled at Tcold."

Wow wow whoa - heat engine? Don't let this scare you; we're not studying THAT engine.

A heat engine is any device that changes internal energy into mechanical work. Remember what internal energy is? Just the grand sum of all of its kinetic and potential energies. So, when this potential energy is, well, RELEASED, in a sense, or, more precisely, converted into kinetic energy on subatomic levels by some sort of a trigger (like when potential energy is converted into kinetic (macro scale) when you push the ball and it rolls down the hill), then this big-scale interaction is just dubbed "mechanical work". Mechanical because human-made mechanisms aren't atom-sized, as you may probably know.

So we pretty much know everything this is saying from all the above jumbo you've (hopefully) read. Work always flows from hot to cold (unless external work is done), and the rest is dissipated as heat ("expelled at Tcold" - or, basically, if it's not "converted into work", it dissipates to, well, guess what: Tcold. Why? Cause - hot to cold. Cmon man! (or girl ;)))

Part 3:

"In natural processes, high-quality energy tends to transform into lower-quality energy - order tends toward disorder."

So this is where Mrs. Addi's "useful (high-quality)" and "useless (lower-quality)" definitions kick in. The first law of thermodynamics states that energy can neither be created nor destroyed. It speaks of the QUANTITY of energy. The second law qualifies this by adding that the form energy takes in transformations "deteriorates" o less useful forms. It speaks of the QUALITY of energy, as energy becomes more diffuse and ultimately degenerates into waste (as it is much harder to get back the heat off of tires that went into the ground than to just find another heat source, for example). Another way to say this is that organized energy (concentrated, and therefore usable, high-quality energy) degenerates into disorganized energy (nonusable, low-quality energy). Once water flows over a waterfall, it loses its potential for useful work. Similarly for gasoline, where organized energy degrades as it burns in a car engine. Useful energy degenerates to nonuseful forms and is unavailable for doing the same work again, such as driving another car engine. Heat, diffused into the environment as thermal energy, is the graveyard of useful energy.

The quality of energy is lowered with each transformation, as energy of an organized form tends to degrade into disorganized forms. With this broader perspective, the second law can be stated another way:

"In natural processes, high-quality energy tends to transform into lower-quality energy - order tends toward disorder."

Consider a system consisting of a stack of pennies on a table, all heads up. Somebody walks by and accidentally bumps the table and the pennies topple to the floor, certainly not landing all heads up. Order becomes disorder.

Molecules of gas all moving in harmony make up an orderly state - and also an unlikely a broad range of speeds make up a disorderly, chaotic (and more likely) state. If you remove the lid of a perfume bottle, molecules escape into the room and make up a more disorderly state. Relative order becomes disorder. You would not expect the reverse to happen by itself; that is, you would not expect the perfume molecules to spontaneously order themselves back into the bottle and thereby return to the more ordered containment.

Processes in which disorder returns to order without any external help don't occur in nature. Time's arrow always points from order to disorder.

Disordered energy can be changed to ordered energy only with organizational effort or work input. For example, water in a refrigerator freezes and becomes more ordered because work is put into the refrigeration cycle; gas can be ordered into a small region if a compressor supplied with outside energy does work. Processes in which the net effect is an increase in order always require an external input of energy. But, for such processes, THERE IS ALWAYS AN INCREASE OF DISORDER SOMEWHERE ELSE TO MORE THAN OFFSET THE INCREASE OF ORDER.

The idea of lowering the "quality" of energy is embodied in the idea of ENTROPY, a measure of the AMOUNT OF DISORDER in a system. More entropy means more degradation of energy. Since energy tends to degrade and to disperse with time, the total amount of energy in any system tends to increase with time. Whenever a physical system is allowed to distribute its energy freely, it always does so in a manner such that entropy increases while the energy of the system remaining available for doing work decreases.

The net entropy in the universe is continually increasing (continually running "downhill"). We say NET because there are some regions in which energy is actually being organized and concentrated. This occurs in living organisms, which survive by concentrating and organizing energy from food sources. All living organisms, from bacteria to trees to human beings, extract energy from their surroundings and use it to increase their own organization. In living organisms, entropy decreases. .But the order in life forms is maintained by increasing entropy elsewhere; resulting in a net increase in entropy. Energy must be transformed into the living system to support life. When it isn't, the organism soon dies and tends toward disorder.

The second law is a probabilistic statement. Given enough time, even the most improbable states may occur; entropy may sometimes decrease. For example, the haphazard motions of air molecules could momentarily become harmonious in a corner of the room, just as a barrelful of pennies spilled on the floor could all come up heads. These situations are possible, but they are not probable. The second law tells us the most probable course of events, not the only possible one.

The laws of thermodynamics are often stated this way: You can't win (because you can't get any more energy out of a system than you put into it), you can't break even (because you can't get as much useful energy out as you put in), and you can't get out of the game (entropy in the universe is always increasing).

Just some closing words on the concept of ENTROPY:

Consider this: If a pool table had ZERO FRICTION, that is, the motion of the balls did not give off any heat to the pool table (or air, in this case - yes it gives it off to air in real life, but let's just speculate a pool table in vacuum - and, assume if balls collide they don't transfer energy to one another - because if we think of particles as the billiard balls, then there isn't that "heat dissipation to the particles", because the billiard balls in this case are the particles), then if we were to hit the cue ball and have the other balls go off, what would happen? Well, the balls would bounce off of each other on and on forever. But what if we were to, now, do the same thing on an infinitely long (and wide) pool table? What would happen? You've guessed it: the balls would all split onto their own paths, never crossing ways again.

Well, the universe is just like that pool table, and particles in it just like those billiard balls; we have our extremely vast, maybe perhaps infinite space, and we have particles. As particles interact, some of them simply go off on their own ways, never returning back. And it doesn't have to be particles: planets, stars, galaxies - they all move away from each other as the universe expands - and eventually, energy interactions decrease and as matter becomes more spaced out in time, we achieve MAXIMUM ENTROPY.

It is predicted by the experts of thermodynamics, that the iminent, 100% death of the universe, also dubbed the "Heat Death of the Universe", will happen in 10^100 years, when matter is so spaced out, that motion ceases to exist and the overall energy of matter in the universe is ZERO.

"But wait, what about conservation of energy?"

Well, this is complicated. Our primitive definitions above don't give the full picture; in fact, matter is energy. But this is very high-level stuff I don't want to pollute your minds with. OK screw it. So you know photons? The particles of light, as they'll tell you in high-school? They're a type of energy particles. Electrons, when converting energies, emit electrons. The energy given off as photons can never be used again if they go into the void of space; we can't catch up to them and they won't change direction unless reflected. So, as matter moves less and less and interacts less and less after so many years, there's less and less stuff for photons to reflect off of, and they just fly into the infinite void of space, never returning. So, with the energy particles gone, all motion ceases existence, and the universe is dead - PERMANENTLY.

But this is not so true! INTELLIGENCE can change all this (- how, I don't want to digress).

Here's the moment you've all been waiting for... The grand finale... The brama-bul... The Big Papa...

this...

is...

[HOW TO CREATE OR DESTROY ENERGY]

So, if you skipped just till the end, lemme warn you: get yo tail off my turf!

Alright, awesome and sexy readers, THIS IS IT!!! HERE YOU SHALL LEARN WHAT QUANTUM PHYSICS PH.Ds LEARN IN THEIR FOURTH YEAR AT COLLEGE (or just nerds googling or wikiing)!

How to DESTROY ENERGY!

Well, since my Edmodo post about destroying energy has been deleted (does the same fate await this post? D:), I'll have to reiterate myself.

So, how to destroy matter:

There are three known ways of doing this.

Way 1: Through a black hole.

All matter that falls through a black hole ceases existence in this space-time dimensional universe. The matter is converted into pure entropy and treated as pure information near the point of singularity. At the point of singularity, the matter seeks no return on the way back. As that matter contained some energy, its energy was destroyed alongside matter. There - you've destroyed energy.

Way 2: Albert Einstein's Mass-Energy Equivalence bursts.

As stated earlier about the Heat Death of the universe, as time goes on and matter expands, more and more matter gets converted to radiant energy. Matter converted to energy - WHAT?? Well, this is RADIANT ENERGY, which is most commonly released during matter-anti matter interactions, but also, very fractionally, during nuclear explosions, where subatomic particles break down to very fundamental levels (hence, "splitting atoms"). This energy, released into the void, can never be harnessed again. And we can prove this - Einstein's Relativity states that nothing travels faster than light through space. In complicated physics, photons have "infinite timewarp", meaning, one second in their reference frame is infinity seconds in our reference frame. Or, in other words, THEY GONE! FOREVER! (exceptions apply, AFAYC).

Way 3: Virtual Particles

In complicated physics, it is known that matter-anti matter interactions take place during time periods so small, they're "unrecorded" in this space-time dimension. This has to do with complicated properties of the universal gravitational constant, space properties, and all that jaz. But basically what it is, is particles "pop in" and "pop out" of existence from time to time. This is so rare that we don't notice such things happen in the real world (imagine trying to take attendance of quadrillions of students that all look identical and have the same name - electron ?). Sometimes, those particles never return, and thus - carry their small fraction of energy- but STILL SOME FRACTION - and thus this energy is destroyed.

Now, how to create energy? Well, as far as human knowledge is concerned, this can only be done in two ways:

1. Wormhole to another dimension

2. White holes

Wormholes are confirmed, white holes are theoretical. But however, alternate universes (the multiverse) is theoretical, so even though we can access higher dimensions with wormholes, it would only be within the scope of our own universe (we'd be accessing higher dimensions of our own universe).

So yeah, they're both theoretical, but they're both possible, nonetheless. In yo face, Republicans!

BAM!!!

Well, I hope it was worth your time (if you've read all this), and that now you're a, if not an expert, a confident knower of concepts of energy and thermodynamics. And maths? Ah, who needs that. maths only helps us compute things very precisely - which is of course the whole point of learning all this, but not essential as far as understanding goes. (and well, to attain full understanding, you MUST understand the maths behind it, but you still get the >50% chunk of knowledge of the concepts, and I say that's good).

So, now that you know all this.................................................................

Why is the sky blue?

:DDDD

- 6 years, 9 months ago

man! I did the same way, but I thought that the scale is not digital, like this

I wonder if this case can be solved!

- 6 years, 9 months ago

I think we can solve it using a variation of the above method. Remove the coins from the $N$ bags as before, but this time place the coins from bags $0$ through $67$ inclusive along with those from bags $98$ and $99$ on one side of the scale, and the coins from all the other bags on the other side of the scale. If all the coins in all the bags were just $1$ ounce then the scales would balance with $2475$ ounces of coins on both sides, so if the gold coins are in bag $N$ then the side that includes the coins from that bag will then be $0.N$ ounces heavier than the other side.

- 6 years, 9 months ago

Yes I got it...

but the problem is that how can we know that a side is heavier than the other side by a certain known number!

this scale has no numerical indications, just tells us: a side is heavier than the other.

Thanks!

- 6 years, 9 months ago

Oh, if there are no numerical indications then I don't think we could do this in one measurement. I think then we would have to rely on the "divide and conquer" approach. First divide the bags into $3$ groups of $33, 33$ and $34$ bags, respectively. Now compare the two groups with $33$ bags; if they weigh the same then then group with $34$ bags has gold coin bag, but if they don't weigh the same then the heavier side has the gold coin bag. If it's one of the $33$ bag groups, then divide into $3$ groups of $11$, and if it is the $34$ bag group then divide into groups of $11, 11$ and $12$, respectively. Then in either case compare two groups of $11$ bags; this will tell us which group has the gold coin bag in the same way as in the previous step. The next step would involve groups of either $3, 4, 4$ bags or $4, 4, 4$ bags. Compare two $4$ bag groups and then determine as before which group has the gold. Then if a $4$ bag group has the gold, we would need to make two more measurements to isolate the bag with the gold coins. Thus we would require a minimum of $5$ measurements to be certain of which bag has the gold coins.

- 6 years, 9 months ago

Y'know, that is very interesting. And I didn't exactly solve this problem, but I solved this: It's a German barrel problem during during some war so basically heres' teh problemL: you got 10 barrels each has balls and one's balls are twice as heavy

so I was like get one ball from first barrel, two from second, three from third, ... ten from tenth. And so if all were 1 ounce the weight would be 55. If barrel one had 2 ounce balls, then, the total weight would be 56. If third, 57. And so on. So basically, in your $N$ notation, the barrel would be denoted by

$W-55=Barrel$.

Weight - 55 = barrel.

is this how u did it? sorry no really time to interpret and all taht, but Im curiours.

thxa

- 6 years, 9 months ago

Yup, that's essentially the same method. :)

In the coin problem when I saw that a gold coin was $1.01$ ounces I knew what the game was. If there had been more than $100$ bags then we would be out of luck; we would probably have to start cutting coins in half or something to be able to do it in one measurement.

- 6 years, 9 months ago