A Mexican fisherman and philosopher(philosophical tale 5)

At the edge of the water in a small Mexican coastal village. A boat returns to port, with several tuna. A North American complimented the Mexican fisherman on the quality of his fish and asked how long it took him to catch them.
Not very long, says the Mexican. But then, why did not you stay out longer and catch more? asked the American. The Mexican replied that small catch was sufficient to provide for his family.
 The American then asked, "But what do you do the rest of the time"? "I sleep late, fish a little, play with my children, take a siesta with my wife. In the evening I go to the village to see my friends. We drink wine and play the guitar. I have a full life, "replied the Mexican.
 The American interrupts: I have an MBA from Harvard and I can aider.Vous should start by fishing longer. With the extra revenue, you could buy a bigger boat. With the money you bring in this boat, you could buy a second one and so on until you have an entire fleet of trawlers. Instead of selling your fish to a middleman, you could negotiate directly with the factory, and even open your own plant. You could then leave this little village to Mexico City, Los Angeles and New York may be, from where you direct your business.
 The Mexican then asks: "How long would that take?" -15 To 20 years, says the banker. And after ? - Then that's where it gets interesting, answers the American, riant.Quand the time comes, you can introduce your company stocks and make millions. - Millions ?
 But after ?
 - Then you can retire, live in a small coastal village, to sleep late, play with your children, catch a few fish, take a siesta with your wife and spend your evenings to drink and play guitar with your friends...
 ooH Yep, that promises the System, in recognition of our submission is to offer us, perhaps, in the best case at the end of our life, what we had available to us at birth, for free and of course, before his domination.
 A beautiful bad bargain !!!

Correct answers ...(philosophical tale 4)

 

One morning , the Buddha was in the company of his disciples when a man approached .
 - Does God exist? he asked .

 - There answered the Buddha. After lunch , another man approached .

 - Does God exist? he asked .

 - No, it does not exist, said the Buddha. At the end of the afternoon , a third man asked the same question .

 - Does God exist?

 - It is up to you , replied the Buddha. When the man was gone, a disciple exclaimed , revolted :

 - Master, it is absurd ! Why do you give different answers to the same question?

 - Because they are different people, each will reach God by his own way.

 The first believe me. The second will do everything he can to prove me wrong. The third only believe what he chooses himself.

The frog in the well bottom.(philosophical tale 3)

There was once a frog that lived in a well. She was born and brought up there . It was a tiny frog. One day , another frog who had lived at the seaside came to fall into this pit . The inhabitant of the well asked the newcomer .

 - " Where are you from ? "

 - "I come from the sea," replied the other .

 - " The sea ? Is she tall ? "

 - "Oh ! Yes I do. She is very tall. "Said the visitor.

 - " Would it therefore as big as my well? "

 - " How can you , my dear, compare the sea with your own well ? "

 - " No. There can be nothing greater than my well .

    " This sprightly then ment and must be expelled from here. "
 The same is true of all men in the narrow minds : Sitting at the bottom of their small wells , they imagine that the world can not be greater than them !

The farmer and his donkey(philosophical tale 2)

One day a farmer's donkey fell into a well. The animal groaned for hours, and the farmer wondered what he was going to do. Finally he concluded that the animal was old, and that in any case the well no longer useless. It was not profitable to try to save the donkey, so he decided to fill the well. At first the donkey realized what was happening screamed miserably. Then finally he stopped. So the farmer looked at the well bottom and was very surprised. Each shoveled falling on him the ass ... it reacted immediately to remove the earth shook her back and then stomp the ground with his hooves. Gradually the donkey still climbing higher, and soon the farmer was surprised to see him out of the well and happily trotted.
 _____________________________

Everyday life brings its share of worries, hardships and worries, which, if we let them accumulate, eventually engulf us. The trick to get by, grow and rise is to shake constantly and resolve problems as and when they arise without ever procrastinate. Generally each of us is never tested beyond what he can overcome in the moment ... but the accumulation of unresolved hassle, laziness, negligence or cowardice eventually weigh as heavy a mountain and create cataclysmic events .... then come weeping and gnashing of teeth.

Meditation pebbles (philosophical tale 1)

   One day an old professor was hired to provide training in "effective planning of his time."
The old teacher said, "we will conduct an experiment."
He took a large pot, put it gently in front of him. And he took twelve stones and put it in the big pot. When the jar was filled to the brim, he asked: "Is the jar full? " They all said "yes." " really ? ".
Then he took a container filled with gravel. and poured the gravel on the big stones and then stirred the pot. Gravel infiltrated between the big rocks to the pot bottom. The old teacher asked again, "Is the jar full? ". One student replied: "probably not! " "Well," said the old teacher. He then took a sandbox he poured into the pot.
The sand went and filled the spaces between the big rocks and gravel. Again he asked, "Is the jar full? "
 This time, without hesitation, the students answered "No! ". " Good ! "Said the old teacher. He then took a pitcher of water and filled the pot to the brim. The old teacher finally asked: "What great truth shows us that experience? "
 One of the students, thinking about the course, said, "this shows that even when we believe that our agenda is completely full, if we really want, we can add more appointments, more thing to do" .
 'No,' said the old teacher, not that! the great truth that shows us that experience is the following: if we do not put the big stones first in the pot, you can never make them fit all. " "What are the big rocks in your life? : It's up to you! "
 What to remember is the importance of putting these large stones first in his life, otherwise we may not succeed ... his life. If we give priority to peccadilloes, we will fill peccadilloes of his life and we will not have enough precious time to devote to what is important. So be sure to ask yourself the question: what are the big stones in my life?
 Then put them first in the pot. "

The Condorcet paradox

Since we are in an intense election period , it is essential to me today to talk about the Condorcet paradox. This is a finding in the eighteenth century by Nicolas - mathematician -philosopher Marquis de Condorcet , who observed that in some situations, regardless of the voting method one chooses , it is impossible to appoint a indisputable winner. This may seem surprising , but as we shall see, the Condorcet paradox is far from a theoretical situation . However you will see, it does not mean completely unable to imagine a fair democratic election .

An example of the paradox Imagine that an election will have three candidates : Alain Beatrice and Claude . Suppose that about 40 % of the population prefers to Alain Beatrice, Beatrice but prefers to Claude . For these 40 % of the population , so we Alain > Beatrice > Claude .
 

Now assume that 35% of people we have Beatrice > Claude > Alain , and 20% for the remaining Claude > Alain > Beatrice. We will note it like this :

 Group 1 (40 %): A> B > C 
 Group 2 (35 %): B > C > A 
 Group 3 ( 25%): C > A> B

Where is the paradox? It is that regardless of the voting method used to determine the winner , there will always be a majority of the population that will be ready to change it for another . No winner is indisputable ! Imagine that the winner is Beatrice. Then the groups 1 and 3 ( which weigh 65 % of the population between them ) would agree to replace Béatrice Alain , since both of them prefer A to B. And you see that all cases are similar : if Alain who is elected , then the groups 2 and 3 (60% of the population) prefer to have Claude in its place. In short, it is inextricable : there can be no undisputed winner. And you see that it in no way depends on the electoral system , just the respective preferences of each other .

The Condorcet winner 
 Fortunately, all situations are paradoxical! There are cases where one escapes the paradox. This happens when a candidate would win a duel against any of the others. So if he is elected, there is no possibility for a majority of the population wants to replace it with another. There is therefore an indisputable winner was then called the Condorcet winner. Let's make a small retrospective. In the 2007 presidential election in France, there was clearly a Condorcet winner: François Bayrou. Indeed according to the time of polls, it would beat Nicolas Sarkozy in the second round, but Ségolène Royal! When there is a Condorcet winner, we should be thankful because it means that escapes the paradox. And yet you see it on the example of 2007, a Condorcet winner is not necessarily the winner in a classic election! It is also very rarely the case with the typical modes of ballots in force. A voting system that allows fail to elect the Condorcet winner (if any) is called Condorcet method. Here is one very simple: organize duels between all possible candidates. If someone wins all his duels, he is the Condorcet winner, and if no one wins all his duels, it is in the case "paradoxical" (and wrong!). Obviously if you have 15 candidates, we must organize a hundred duels, I doubt that people accept this type of election where you have to give 100 times its opinion, such as "Do you prefer Philippe Poutou and Nathalie Arthaud? ". Good fast way to do this is to ask everyone to classify the 10 candidates in order of preference. That would be perfectly playable.

The Fermi paradox and the invisible extraterrestrials

In the early 1950s, the physicist and Nobel laureate Enrico Fermi launched the discussion on the following apparent paradox: while about two hundred billion stars in our galaxy exist, and most likely, as we know fairly precisely today ' hui, hundreds of billions of planets also orbit around them, how can it be that we have not yet been visited by (many) of extraterrestrial civilizations?
 Indeed, hypothesize that life emerges on one very small fraction of those billions of planets in our galaxy dimensions (a few tens of thousands of light years) give hope for a civilization like ours close enough the ability to explore an appreciable fraction of the speed of light surrounding systems, an exploration of a large part of the galaxy in a time less than 1 million years. But this time is only about the ten thousandth of the age of our galaxy, the Milky Way, aged about 13 billion years, or the Universe, who is 14 billion years. It would therefore have been highly likely that Earth has been visited by hundreds of different species of aliens, who are notably absent this day.

Just a matter of time ? 
One point , however, seems to have little discussed by Fermi : the time we have before exhausting the resources at our disposal, whether the scale of our planet Earth, or even on the scale of the observable Universe ( say within a radius of 10 billion light-years , or about 100 billion billion kilometers ) . Under the seemingly reasonable assumption of a growth rate of consumption and the use of resources by 2% a year, the stripping length of the Earth's resources is a few hundred years , with a wide margin uncertainty. For the observable entire universe , curiously, the estimate is more accurate : between 5000 and 6000 years, very little about ...

Life , instability accelerator

We therefore wish here what I think is the best answer to the Fermi paradox : life
is a kind of accelerator, which causes extreme instability. Thus, without an extremely precise and rigorous strategy, it is highly probable that such ants living on a pile of saltpeter , we grillions the day we discover the matches , even before being able to develop interstellar travel . For if we analyze our history and repeated violence , quasi- permanent , if we look lucidly our greed to use shamelessly natural resources, many of which are even now being depleted , with a few lower horizon decades , the high instability brought by life seems the most likely explanation for the Fermi paradox .

The Monty Hall Paradox

The Monty Hall problem is a famous game of probabilities named after a television program . It calls the paradox , because the right strategy we often seems against - intuitive. Experiments also show that even repeating several times the game , humans really hard to understand the trick , as the pigeon , he 's doing very well. From there to conclude that intellectual superiority volatile , it is only one step !





The game principle :
 The Monty Hall paradox originates in the game show Let's Make a Deal , aired in the US from 1963. The host Monty Hall are offered the following choice . A candidate is presented face 3 doors : Behind one of these doors is a gift , whereas behind each of the other two doors is an object without interest (typically a goat ) . The candidate chooses one of those three doors, but without opening ; The host ( who knows where the gift is) opens one of the two remaining doors , taking care (if necessary) to avoid the door that contains the gift ( the door opened by the host always so reveals a goat ) ; The candidate can then choose between keeping the original door, or to change to take the other remaining door. What should the candidate? Keep or change? So think 5 minutes ...



One chance in two (or three) :


By doing a quick reasoning, we can say we have a choice between two doors, and each door initially just as likely as the other to contain the gift. While the changing or that one keeps his door, we win with an even chance. In fact this argument is misleading and the real result is that the probability of winning if we change is 2/3 against 1/3 only if one retains its original door: so we always interest in changing! One can spend hours trying to convince himself of this result. Here is the most simple argument: if you stay, you win if you had originally made the right choice (which occurs in one third of cases), if you change, you win if you made the wrong choice from (which occurs 2 times 3). So you change saves in 2/3 of cases. For skeptics, the most definitive method is to count all cases, even to a numerical simulation (it is said that the mathematician Erdos had to do this simulation to be convinced of the result). For skeptics who do not like the physicist methods, the solution with Bayesian probabilities.

French version

Calculer une racine sans calculette

Pour calculer la racine d'un nombre quelconque , dès maintenant c'est facile :D !

On pose tout d'abord :

1²=1                         
2²=4
3²=9
4²=16
5²=25
6²=36
7²=49
8²=64
9² =81

Supposons qu'on veut calculer la racine de 576 :
 Premièrement on prend le nombre à droite (6) , on regarde les carrés qui se termine par le nombre 6

C'est ( 4 ou 6 ) ! Comment choisir entre les deux , on prend le nombre à gauche (5) on cherche un nombre tel que son carré est inférieur à 5 , ça saute au yeux (2) , ce 2 est le nombre du dizaine de la réponse , il nous reste l'autre nombre ,pour le trouver on multiple le 2 par le nombre qui le suit (2x3=6) et ensuite on compare 6 avec le 5 , si il est supérieur on va choisir le plus petit nombre entre ( 4 et 6 ) sinon on prend le plus grand
et donc la racine du nombre 576 égale 24 :D

English version

Calculate a root without a calculator

To calculate the root of any number , now it's easy : D! We first asked:
1² = 1
2² = 4
3² = 9
4² = 16
25 = 5²
6² = 36
7² = 49
8² = 64
9² = 81
Suppose we want to calculate the root of 576 : First we take the number to the right (6) , we look at the square which finishes with the number 6 Is ( 4 or 6) ! How to choose between the two , we take the number to the left (5) we look for a number such that its square is less than 5 , it jumps to the eye (2), this 2 is the number of ten the answer , we have the other number , to find the multiple is 2 by the number following the ( 2x3 = 6) and then compared with the 6 5, if it is greater than one will choose the smaller of ( 4 and 6) if the largest one takes and thus the root of the number 576 equals 24: D

The wisdom of prisoners

A young American 19-year-old was jailed on charges of terrorism was able to enter the US intelligence building and steal a lot of secrets and was nicknamed Fox, for cunning.
His father, an old man living alone desired to sow potatoes inside his farm, but he can not because his age he sent to his son jailed message telling him where:
My beloved Son, I wished to be with me now and help me in plowing the farm in order to sow potatoes I have no help me ..!
After a while, the father received a letter from his son telling him imprisoned in which:
I beg my father Aziz Never plowed farm where I hid something important when they get out of prison I'll tell you what it is!
I did not spend an hour on the letter And as men of intelligence and army besieging the farm and dig the ground Shubra Shubra not Ajdo Xia Gadro farm.
The letter arrived to the Father of his son the next day he says he has had:
Abe Aziz I hope that the land has been plowed well this is what I could do and I help you if you need Shi told me last

Filling the curves (or how to make a one-time coloring with pencil)

My daughter does not like when the colored pencils are cut too thin . Yeah what, after it takes longer to color ! I'm explaining that thanks to Filling curves , one can always just coloring even with an infinitely thin pencil, I feel that the argument does not pass. And yet, we'll see in this post that we can actually find curves that completely fill a surface through all points . And even if it goes against intuition !


Why this seems impossible courbe ?
Alors square and let's go , let's take up the challenge : finding a curve that completely crayon square. It sounds difficult , because everyone knows that in mathematics , the lines are not thick. Under these conditions , we have a mind to think that the surface covered by a curve is always zero . It is not ready to come to cover an entire square. Moreover, a curve is a dimension object 1, while a square is size 2. We see that it can not work ! Another way to tell is to count the number of points on a segment and a square . While the segment , there is an infinity . But in the square , we feel that there is an infinity of times more points in a segment ! And yet…

The Peano fractal curves 
 The construction exhibited by Cantor definitely shows that a square is not "bigger" than a segment. Yet as such, this does not constitute proof of the fact that you can color a square with a curve. What he lacks is continuity! Indeed the correspondence established by Cantor is not continuous as would a true curve. With the application of Cantor, two points in very close segment will be sent on very different square areas. Cantor's correspondence can not therefore draw without lifting your hand!
 However, since Cantor brought down the main psychological obstacle to the discovery of a curve filling the square, the solution will come a few years later in the writings of the Italian Peano. The latter indeed proposes to construct a curve which fills a square, and in stages. The drawing below shows the first three steps of the process

By continuing the process "to infinity", a curve that goes through all the square of dots is obtained! This is called a filling curve. Some of you may be here will recognize the principle of fractals: one starts with a pattern, then repeat on the lower level, then again and so on. (For those that this way of constructing curves bothers, I will return to my "To go further ...") Following the discovery of the Peano curve, many other mathematicians propose Filling curves based on the principle of fractals. Hilbert curve is one of the best known and the Lebesgue curve shown above-cons, whose principle is to construct a fractal from a pattern Z. Ah small detail for those who like math, these curves are of a species entirely made exotic; they are continuous everywhere but differentiable nowhere! Basically any point of the curve is an amazing way ... right? In short, if you want to color a square with an infinitely thin pencil possible: choose the path of one of
these curves Filling. Once again you find in mathematics, it does not always have to rely on intuition, especially when it comes to infinity! However Filling the curves are not just entertainment for amateur mathematicians of paradoxes, it is also a useful tool in areas such as data reduction. With the trajectory of a filling curve, you can actually browse effectively a multidimensional space.

How to prevent the Simpson 's paradox ?

  I guess you easily see the potential for manipulation behind this paradox :

one can make you believe in something (unemployment decreased, such treatment works best, such an individual is better, etc.) so that looking the figures in detail, the effects may disappear or be reversed! So what? First, we must remember: This effect occurs when there is a hidden influential variable, and that the sample on which it is based is not homogeneous. In science, this is why we generally prefer the "randomized" experiences, which ensure an even distribution: for example if you have kidney stones and that you are participating in an experiment to compare treatments, you are assigned randomly treatment A or B, without the size calculations affect the decision. So one gum inhomogeneity distribution, and the paradox disappears: A treatment is seen as the best. When you are presented with numbers, so you have to have a critical eye, and be especially wary when those figures come from data analyzed a posteriori, rather than a test sample that has built itself a priori (randomizing ). (Think about the following: conclude that "The bed is the most dangerous place in the world, this is where most people die" is wrong because you are using non-randomized data).

Finally remember, this paradox occurs when there is a hidden highly influential variable. This means that the raw numbers have little meaning, and must be criticized by a domain expert may point the existence of such a factor. At a time when fashion flourishes of "fact-checking" was a tendency to make us believe that the figures would be the "naked" truth. No, the naked truth does not exist, and will always need people aware to correctly interpret the figures, be they scientific, economic and medical.

Simpson's paradox

No, the Simpson 's paradox is not named for Homer , but to Edward Simpson , the statistician who described for the first time in 1951. It is one of those paradoxes that mathematics can we make knots to the head, but which unfortunately is more than just a curiosity to understand this paradox may be essential to make the right decisions! So if you do not know this statistical phenomenon very against -intuitive , read on , and the arms should you fall!
 Kidney stones: which treatment to choose?

No luck, we just discovered your calculations to the kidney. Fortunately treatments exist, and at the hospital the doctor presents in two. The first (call "Treatment A") is in an open surgery, while the second ("Treatment B") is a surgery that is done through small holes drilled through the skin. The doctor asks you what treatment you prefer. As desired above all to heal, you ask the successful practitioner statistics of these two treatments.
"Oh it's very simple, you answered the doctor, both treatments were tested every 350 patients, and here are the numbers: A treatment has worked in 273 cases and treatment B 289".
 The case seems understood, treatment B market with 83% success, against 79% only for treatment A. So you choose the treatment B. But just leaving the hospital, you cross another doctor who you ask his opinion about treatment. "Oh it's very simple, you he answers: both treatments were tested 350 times on each patient, the latter can be achieved either 'small' calculations, or 'big' calculations, and here are the figures" :

 

As you can see, if you have large stones, treatment A works best , and if you have small stones , treatment A is also the most effective. That is in complete contradiction to what you said the first doctor. And yet you have good counting and recounting , the "Total" line , it is indeed the same figures as those presented by the first doctor ...  
How is it possible that treatment B is better to global, but it is lower than both treatment A small than large stones? And it is not a joke , these numbers are from a real study [1 ] ! There are no statistics entourloupe or no manipulation , what you read there, that's the reality of the figures . You have a fine example of Simpson 's paradox.

The barber

A young student went one day to his barber. He entered into conversation and asked him if he had many competitors in her pretty city. Seemingly innocent way, the barber replied, "I have no competition because of all the men of the city, I obviously do not shave those who shave themselves, but I am fortunate to shave. all those who do not shave themselves. "


What, then, such a statement so simple can it default to the logic of our young student so smart?
The answer is in fact innocent, until one decides to apply to the case of the barber.
If he shaves himself, or not ? 

Suppose he shaves himself, he falls into the category of those who shave themselves, which the barber said he did not shave the course. So he does not shave himself.
Very good ! Suppose when he does not shave himself, he enters in the category of those who do not shave themselves, which the barber said he shaved them all. So he shaves himself.
Fianalement this unlucky barber is in a strange position: if he shaves himself, he does not shave himself, and if he does not shave himself, he shaves. 
 This logic is self-destructive, contradictory stupidly, rationally irrational.

Personally I would answer that the barber has a
very long beard and therefore does not need to be shaved
but then
he does not shave himself, and is destroyed by ...

someone blew me it's a woman or
He lives outside the boundaries of the city and
is not concerned with his statement. tional.

  

alarm clock

You are the subject of an experiment in which the protocol is as follows. On Sunday evening, we were asleep and you start a coin not rigged. If the coin falls on FACE, the next day (Monday) we wake up and we have an interview with you. If so BATTERY, it wakes you up, there was an interview with you, and you sleep again submitting to a treatment that causes total amnesia of the day Monday, Tuesday, and finally, it wakes you up again and we have an interview with you. In interviews, they ask you "what you assign probabilities and FACE PILE for the coin toss Sunday (which remained in place hidden under a box)? ". Two arguments seem possible.  
First argument: "I am sure that the room is normal. I have no information in addition to that I had on Sunday night before falling asleep. Before falling asleep, the probability is 1/2 for each event or FACE PILE. So when I woke up during the experiment, I have to assign probability 1/2 to each contingency. "
Second argument: "Suppose we do the experiment 100 times by operating 100 weeks on. In about half weeks (50), I awake on Monday after a FACE draw. Other weeks (about 50) BATTERY has been shot and I awake on Monday and Tuesday (so there will be about 100 clocks). In total, during the 100 weeks, I awake about 150 times and of these 150 clocks, FACE will be 50 times the right answer and the right answer will BATTERY 100 times. Whenever I woke up, the probability that the piece is launched on Sunday fell on FACE is 1/3, and 2/3 is BATTERY. My answer is: FACE 1/3 and 2/3 BATTERY! "

Answers : 

This paradox (called "paradox of Sleeping Beauty") seems to have found a permanent solution and supporters of both options exchange their arguments today but failed to agree (look for "sleeping beauty paradox" on Internet). However, my preference is clearly to the second solution because of the following argument. While the second argument seems in any acceptable point, the first argument could be defective and therefore not sufficient to conclude 1/2 to 1/2 Battery for Face. Indeed, to assess a probability or, more generally, to know the numerical value of a parameter that is measured, it must take into account the changes or distortions of the greatness that is measured. If, for example, you measure the size of a postage stamp with a double decimeter placed above a magnifying glass covering the stamp, the value you will find exaggerated compared with reality; we speak of "magnifying effect". You will find 2 cm while the stamp actually measures 1 cm. Another example of deformation, if you want to measure "the proportion of fish that are smaller than 50 cm" in a lake, fishing a 100 fish sample with a net with a mesh size of 20 cm, you will find a value well below the reality because your net lets all fish less than 20 cm. There is talk of a "filter effect". Here, when you submit the experimental protocol, you measure the likelihood of battery and Face by examining the room on Sunday before it is launched and you find half for Battery, 1/2 to Face. It is then the property of the room (with regard to the draw on Sunday evening) is subjected to a kind of double-magnifying effect that your Piles of observations (since when battery is pulled, you watch Monday and Tuesday), whereas this is not the case when the face is drawn. As in the case of the magnifying glass - that is to say, for those who observe the stamp through a magnifying glass - the observed probability and measured by you is 2/3 and 1/3 Battery for Face, although actually - for those who do not look through the magnifying glass, that is to say, for one who is not caught in the experimental protocol - the probability is 1/2 to 1/2 for battery and Face. In conclusion: if you accept my way of thinking, when you wake up you have to answer for Face 2/3, 1/3 for battery because you are in the protocol and therefore subject to a magnifying glass effect. But this does not, of course, if they were subjected to a test piece, the piece would give 50% of cells and 50% Faces. The second argument is good while the first confuses what is measured "on the magnifying glass" with the object under the microscope.

smart

Here is a very simple problem (tomatoes)
Especially do Read Later, after the Have Solved !

A hypermarket manager buys 125 crates of 12 kg tomatoes to 1.35 euro per kilo.
He sold the tomatoes to 2.16 euros a kilo and made ​​a profit of 988.2 euros.
Question : How many kilos of tomatoes were not sold ?

A.
125 crates of 12 kg give 1500kg Euro profit in kg:
2.16 to 1.35 0.81 Total profit : 988.2 euros.
Number of kg for profit : 988.2 0.81 = 1220
Unsold quantity in kg: 1500 - 1220 = 280

B.

Price: profit + purchase price
Euro Price:
988.2 + 1.35 x ( 125 x 12) = 3013.2
Amount sold in kg:
3013.2 : 1395 = 2.16

Unsold quantity in kg:
1500 - 1395 = 105

And you what did you find ? 

A. Profit based on the purchased kilos 125 crates of 12 kg give 1500kg Euro profit in kg: 2.16 to 1.35 0.81 Total profit : 988.2 euros. Number of kg for profit : 988.2 0.81 = 1220 Unsold quantity in kg: 1500 - 1220 = 280
Interpretation: Here unsold tomatoes retain their potential sales value (they were not included in earnings ), and they do not cause any loss. 

B. Profit on actual sales. Price: profit + purchase price Euro Price: 988.2 + 1.35 x ( 125 x 12) = 3013.2 Amount sold in kg: 3013.2 : 1395 = 2.16 Unsold quantity in kg: 1500 - 1395 = 105 

Interpretation: Here we consider that unsold tomatoes no longer have any value. They are already counted in the account of profits.

C. A final solution : Earnings per kg of tomatoes (in euros) 2.16 to 1.35 0.81 Purchase price of all tomatoes (in euros) 125 x 12 x 1.35 = 2025 Selling price of all tomatoes (in euros) 125 x 12 x 2.16 = 3240 Benefit obtained by selling all tomatoes (in euros) 3240 - 2025 = 1215 But it received only 988.2 euros The difference is the absence of profit on the unsold tomatoes , in euros : 1215 to 988.2 = 226.8 Interpretation 1: Unsold tomatoes retain their potential sale value and cause no loss or gain. Number of unsold kg of tomatoes 226.8 0.81 = 280 . Interpretation 2: Unsold tomatoes no longer have any value. The loss is the sale price for each kg not sold. Number of unsold kg of tomatoes 226.8 : 2,16 = 105 .

Finally, it is not easy to get into other people's thinking. Here this problem so simple ... can actually produce two solutions each with their degree of validity . The text does not specify what happens to the unsold tomatoes and especially what is meant by profit.

The paradox Hangman

A judge declares a death row inmate that will be hung during a morning of the following week, but the day of the execution will be a total surprise to the poor man. It will know the day of his hanging that morning or the executioner will come knocking at his door, the only certainty being that the hangings are not held on the weekend. Back in his cell, the prisoner thinks about his award: he begins by saying that the "surprise hanging" will take place on Friday, because if he survives every day of the week until Thursday evening, it remain only on Friday for execution. And in this case, it will not be a surprise. He then said that the hanging will not take place on Thursday, either, because if it is still alive Wednesday night, Friday being eliminated automatically, it will only leave on Thursday. And therefore the execution will still not be a surprise. Following this same logic, the prisoner also eliminates Wednesday, Tuesday and Monday. Reassured, he deduced that the sentence will never be executed. The following week, the executioner comes knocking at the door of the condemned on Wednesday morning, which, despite all the reflections of the latter, actually remains a complete surprise. The judge was right. This paradox, seemingly simple, has divided schools of thought. He still has no clearly established solution.

The girl and the cruel king 

A cruel king was put in jail a girl who refused to marry her. After a year without the girl reverse its decision , the king brought in the castle courtyard and offers him a deal . I'll pick up two stones , one black and one white, he said, and keep them hidden in each hand. Then you will choose freely either of the two . If you pull the white stone you will be free ; if you pull the black , you'll marry me . The girl accepts this market with great fear . But his fear turns into panic when she sees that the king is looking to pick up two black pebbles surreptitiously !

What can she do to not marry the king so cruel ? 

Answers : 

This problem cited by E. de Bono ' Lateral thinking illustrates an erroneous construction of the research universe that makes the statement does indeed apparently no good solution. In reality, the constraint "I'll pick up a white stone and a black " constraint is not respected by the king, beautifully turned against him. The girl chooses a rock in one hand and the fact voluntarily immediately fall to the ground among the other in the courtyard. We see no more.

" FORGIVENESS she said , but the color of it remains , as well decide my fate , giving in contrast color the fallen ."
The other is black, of course, and the girl is FREE as it is supposed to have chosen a white fell to the ground !
 

One equal two

Consider two numbers A and B equal:

    A = B
    so
    A² = B²
    A² - B² = A² - B²
    (A + B) (A - B) = A² - B²
    therefore as A = B
    (A + B) (A - B) = A2 - AB
    (A + B) (A - B) = A ( A - B)
    Is simplified by (A - B)
    and there is obtained
    (A + B ) = A
    and as A = B
    A + A = A
    2 A = A

    A by simplifying found

        2 = 1

False , of course! To you to prove it ...


Answers : 

It is the simplification (AB) is illegal.
    What for ? because A = B then A - B = 0 .
    It has no right to simplify by 0 .
    Naughty course, but let's look at the following equation :
    2 x 0 0 x = 5
    If simplified by 0, we have 2 = 5
    or ... anything else since the product of any number by zero is zero !

The unmasked one is pink confusion !

The surprise tiger

* Always the unexpected happens ... 

The Princess and Louis loved each other tenderly . But the king did not approve . So he launched a challenge to Louis :

    'You 'll have to kill the tiger which is hidden in locked rooms 5 by 5 grids. But it will be a surprise for you can no tiger guess where is the tiger.

Then Louis watched the gates 5 and said: -if the first four gates open four empty rooms , I know that the tiger is behind the fifth . But as the king has said that I can not guess where is the tiger, it can not be behind the grill No. 5 . -the # 5 thus eliminated , tiger must be in one of four parts. What happens if I open three empty rooms ? The tiger will surely find the room No. 4, but it will not be a surprise since it can be either in the room 's eliminate No. 5. So the grid No. 4. By the same reasoning, Louis concluded that the tiger may be behind other grids. It is reassured and he exults : no tiger is behind the bars , in fact if there was one it would not be unexpected. Also here are the 5 grids below , open each one by clicking on it with Louis .

Hopefully the tiger was averted in time! ; o)

Surprising as it may seem, there is indeed a tiger behind a grille . The king was right , you were surprised whatever the grid behind which was the tiger ! If you arrived before the fifth door, you thought there was no tiger since it would necessarily be in that cage and thus the king was mistaken . But the tiger was there and suddenly you have been very surprised !

 

This paradox exists in other forms : 

hanging surprise that a prison director would be visited one of his prisoners ... 

or surprise inspection : a teacher told his students that there will be a surprise inspection in the week : Monday to Friday. Students argue thus : if the teacher chooses to do surprise check on Friday , so Thursday night students will know that the inspection will take place the next day and it will not be a surprise. So control will not take place on Friday . And so on ... as in the problem of the tiger , students conclude that the teacher can give surprise control. Yet if the teacher chooses Wednesday , for example, how could we know that monitoring will take place that day ?

Logicians are puzzled by this paradox 

If the king knows that he can keep his word , Louis know, so it has no reason to consider as valid a deduction found no tiger behind the bars including the last . In the issue of control , if the teacher chooses Wednesday , how will they know the students they will have a interro that day? Ian Stewart lost in paradoxes and Found For Science in August 2000 think the paradox is based on the ambiguous use of the word "surprise" . If every moment we expect a surprise, the surprise is no longer a ... Even if students say the control date is not a surprise they will have to work and revise every night to control! And conclude that this paradox is a paradox lost.

 

The girl and the magnets

The girl long hair ribbon is left alone in an empty room with two identical steel bars , except that one is magnetized and the other not. To be finally free, it must determine which one is magnetized . The bars are heavy, solid , UNBREAKABLE and no hardware is available. 

 

How will it take them ?

 

 

 

 

 

 

Answers : 

 

 

In this problem we are capable of any immediate reference. The resolution is of type ' all or nothing ' . But it may well insconscient after an inside job. The solution exists and it is simple . We must break symmetry . But here the solution must be purely physical and manipulable objects are the only two bars , and ... the tape . The magnetic attraction is completely symmetric with respect to two bars, it does not mean that attracts and is attracted ... except precisely one point: the one corresponding to the middle of the bar magnet , which by symmetry it can be magnetized . Therefore determined the middle of one of the bar B. For this, ' take ' the length thereof with the tape. Is folded into two the part of the ribbon which corresponds to the length of the bar to determine the environment. So we present another A perpendicular to the middle of the bar B.

Si rien ne se passe, alors la barre A n'est pas aimantée, puisqu'elle n'attire pas le milieu de B. C'est donc la barre B qui est aimantée.

Si, il y a attraction , c'est la barre A qui est aimantée et attire la barre B non aimantée.

Alec

Julien

Alec gives a coffee spoon Julien 

Julien

Alec

Julien gives a spoonful of its mixture Alec .

Finally Alec as much milk as Julien coffee.

Of course this can be generalized without difficulty, and the result is always true. 

The latte

Alec Julien and sit in a Parisian cafe. Alec takes a cup of coffee and Julien takes one cup of milk. I give you a coffee spoon in your milk Alec said . OK , Julien meets and now I 'll give you a spoonful of coffee in my milk in your coffee .   

So Alec said: "I think I have less milk in my coffee that you have coffee in your milk , for I have given you a spoon full of coffee and you gave me a coffee spoon pudding ! "

 

 

And you what do you think ?

Answers :

In reality , there is much coffee in milk than milk in coffee. Initially it does not seem obvious because Alec gives a pure coffee spoon while Julien does not give a spoon full of milk. But the cup is no longer Alec completely full, so it does not need a spoon full of milk. Furthermore each finds himself right in the end with the same amount of liquid that initially .

 Let's take an example :

 

Alec

Julien

 

Consider that a spoon is a tape. Each band is 5 tiles wide and 1 high.

(Following in another Articles)

Sharing dromedaries

Feeling his end was near , an old sheik indicated his will to his wise counselor . He wanted to share his livestock as well : half for his eldest son, the third in the second and finally the ninth cadet. Unfortunately his death , his flock consisted of 17 camels ... Then the wise counselor to the neighbor borrowed a camel .. So he had 18 cattle , and he shared : half or 9 senior, third or 6 for the second and finally the ninth or 2 for the cadet. And as 9 + 6 + 2 = 17 ... he gave the 18th animal to its owner. And each of the heirs had the satisfaction of receiving more than his father had given them . The first animal received 1/2 (9 instead of 8.5 ), the second 1/3 of dromedary more and more in the last 1/9

Paradoxical ? But the old counselor was very wise ,
he did not commit injustice ! To you to prove it ...

Solutions : 

Of course the old counselor did not give half to the eldest of the herd or third in the second , nor the third to ninth . This curious result paradoxical at first, can be explained if we notice the sum of the fractions 1/2 , 1/3 and 1/9 of 17/18 is not the unit 18/18 . As a result , following to the letter the instructions of the father and assuming we have been able to share , it would have remained a part of the estate, that is to say 1/18 of this succession without owner. But he respected the proportions between the three heirs. The numbers obtained are proportional to 1/2, 1/3 and finally 1/9 : indeed 6 represents 2/3 of 9 (which is the ratio of 1/3 and 1/2) ; 2 represents 2/9 of 9 (which is the ratio of 1/9 and 1/2) . The sharing is fair .

The currency of the room ...

Three young people take a dish on a sunny terrace in the month of June They have to pay 30 euros and give each a room of 10 euros. The owner, charming , makes them a discount of 5 euros. The server then takes 5 1 coins , unable to share the three he decided to slip surreptitiously 2 euros in his pocket and generously gives 1 coin to each of the three young men .

 

 
Finally each paid ( 10 - 1 ) euros, so 9 euros. By adding 2 euros of Sir, we obtain ( (9 x 3) + 2) euros or 29 euros. BUT we had 30 euros. What happened to the last euro?
 

 

 

Solutions : 

 

 

 

This is good scam , but it is in the text : it makes no sense to calculate 27 + 2 .
Either one calculates from 27 :
9 x 3 = 27 ( 27 euros disbursed , 25 flat and 2 in the indelicate pocket )
and then calculates 27-2 to find the 25 euros due;
Either one calculates from 30 :
30 = 25 + 2 + 3 ( flat more money : 2 euros in the pocket and made ​​3 euros )
or 30 = 27 + 3 (27 euros and 3 euros paid actually rendered .

I await you commentaire :D ! (Enjoy)

 

The second paradoxe :

All in paradise

A man who has just died comes into a room where two doors are located.
One leads to heaven , the other to hell. In front of each door is a guard who can not say yes or no. The man knows that one of the two guards always lying and that the other always tells the truth .
But he does not know which ment which neither speaks the truth.
He is entitled to a single question. 

What should he ask for one of the two guards to find the door of paradise?

Solutions :

A sensible question is:

 "Let me answer the other guard if I ask him if he is at the door of paradise?" 

There is always exactly a lie in the response also:
If the answer is NO, paradise is the door the other guard (the one that is not questioned);

If the answer is YES, paradise is in front of the goalkeeper who was questioned.

Another Question proposed by Olivier a user is:

 "Is the liar Before Paradise?"

 If the answer is NO, Paradise is the gate behind the guard to whom the question was asked. 

 If the answer is YES, Paradise is the other door. 

Réponse Proposed by Bruno that we would a math teacher  English 

"If I had asked you which door to take five minutes earlier, which would you have told me?" The obvious benefit of this response is to implicitly speak twice on the same person. Thus two consecutive lies will cancel and two right answers will give a good answer.

 -The Liar lied and gave the wrong door. The second time, he clearly says the opposite of what he had said and finally show the correct door.

 -Celui Who is right, gives the right place every time. 

In both cases, we obtain directly the door of paradise. However, this interesting response was not acceptable because the two guards would know that answer YES or NO!