Married Problem with solution (plus extra problem)YouTube↗  IA↗(long shot)
Education  185.2K views 3.6K likes 39 dislikes   28 Mar 2016
singingbanana 228K subscribers United Kingdom YouTube↗


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Spanish B. Bel
Dutch Angela Flierman
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hello everyone I've got a problem for
¡Hola a todos!
you today which you may have seen it in my earlier video but let me run through
Hoy os traigo el problema que propuse en mi anterior video
the problem again what I'm going to do
Vamos a revisar el problema
is go through the problem we're going to
Vamos a revisarlo, y hablar de la colución
talk about the answer and also we're going to talk about what we can learn from this problem including how it
Y vamos a ver qué podemos aprender del mismo
applies for natural real-life maths
Incluyendo como podemos aplicarlo a un problema real de matemáticas
problem 2 so the problem was this jack
El problema era éste:
is looking at Anne but Anne is looking
Jack mira a Anne, pero Anne mira a george.
at George Jack is married but George is
Jack está casado, pero George no.
not is a married person looking at an unmarried person there are three options
¿Está una persona casada mirando a una persona soltera?
for this a yes B no or C cannot be
Nos encontramos con tres opciones A) Si B) No C)No podemos determinarlo
determined now the claim was that over eighty percent of people get this wrong
Y se afirmaba que el 80% de la gente se equivocaría.
so if you haven't tried this yet pause the video have a go otherwise I assume
Si no lo habéis intentado aun, pausad el video e intentadlo,
you've got an answer in mine so now I
De lo contrario, asumo que tenéis una respuesta en mente,
can tell you that the correct answer is a yes there is a married person looking
Y ahora os puedo decir que la respuesta correcta es A) Si. Hay una persona casada mirando a una persona soltera.
at an unmarried person now I know some of you are not going to be happy with
Y lo sé, algunos de vosotros no estáis contentos con esa respuesta
that answer why is it a why is it a and not C cannot be determined so let's look
¿Por qué es A), es A) pero no C) No puede determinarse?
at this answer and also what we can learn from this problem I got this
Vamos a ver el por qué de esa respuesta, y qué podemos aprender de ella.
problem from a book called the science
Vi este problema en un libro llamado "The Science of Genius"
of genius by Scientific American and in
del Scientific American.
particular this problem was described in a chapter by Keith Stanovich now let's
en concreto, este problema aparecía en un capítulo de Keith Stanovich
look at the setup for this problem we've got three people we've got Jack and and George now we know that Jack was looking at Anne which I represent by drawing in
Vamos a ver este problema esquemáticamente, tenemos tres personas Jack, Anne, y George, y sabemos Y sabemos que Jack mira a Anne, lo que representaré con una flecha
an arrow like that so we had Jack
Así, Jack mira a Anne
looking at and we had an looking at George which I'll join another arrow for
Y Anne mira a George, dibujaré otra flecha para eso
that now Jack was married and George was
Bien, Jack esta casado, y George soltero
unmarried but we knew nothing about the marital status of Anne now the way this
Pero no sabemos nada acerca de Anne
question is written is I mean it's
La forma en la que se plantea la pregunta es algo ridícula,
ridiculous there's a lot of opportunity to set up your own flirtatious backstory between Jack and Anne and Jordan married
Con un montón de oportunidades para imaginar cualquier cosa, historias entre Anne y Jack, y George
people stealing glances at unmarried
Gente casada echándole miradas a gente soltera,
people but the question itself was used by a computer science lecturer at the
Pero la pregunta original fue propuesta por un lector, un ingeniero Informático de la Universidad de Toronto
University of Toronto and when he tested it out he found that over 80% of people where responding cannot be determined that will see in
Que descubrió que un 80% de la gente respondía que no podía determinarse
our three options now I can think of three reasons why people might say
tras ver las tres opciones. Se me ocurren tres razones por las que la gente pensaría que no puede determinarse
cannot be determined so let's look at
vamos a verlas.
those one reason might be that the question doesn't say anything about where these people are standing and I
Una de las razones es que no se aclara dónde están estas personas
can see that might be a problem for people who are less experienced at these
y eso puede ser un problema para gente menos experimentada
kind of puzzles because they're trying
con este tipo de cuestiones
to apply it to the physical world so
Ya que tratan de aplicarlo en el mundo físico
they're thinking are these people standing in a line are they standing in a triangle can they look at two people at the same time but people have more
Pueden imaginar a la gente en linea,dispuestos triangularmente, viendo dos personas simultáneamente,
experience with these kind of puzzles we'll know that when it says something like an is looking at George and that is
Pero la gente con mas experiencia saben que cuando se dicen cosas como Anne mira a George,
simply a relation between two objects
se trata simplemente de un tipo de relación entre dos objetos
the other problem might be that the question doesn't say anything about where George is looking now again people
El segundo problema puede ser no se dice hacia donde mira George
who are more experienced with puzzles might think well if that information is not included in the question that I probably don't need it to determine the
de nuevo, la gente mas experimentada sabrá que si no dan esa informacion, entonces no es relevante para dar con la respuesta.
answer and the other point is the question says is a married person looking at an unmarried person and here
la pregunta es, ¿Está una persona casada mirando a una soltera?.
George is unmarried so it's actually irrelevant where he's looking he could
George está soltero, es irrelevante a donde mira
be staring off into space for as far as I'm concerned the third problem is that the question doesn't say anything about Ann's marital status
podría estar mirando al espacio, por lo que a nosotros respecta. El tercer problema, es que no nos dicen nada acerca del estado marital de Anne
you see married or see not married now this is the crux of the problem because
¿Está casada, o está soltera?
at first glance it does appear that the question is not giving you enough
Y aquí esta la clave, ya que asi parece que no te estan dando información suficiente
information and so you think that it cannot be determined but if we take our
y puedes pensar que no se puede determinar, pero,
thinking just one step further it turns
si podemos ir un poco mas allá
out that we actually can come up with an
podremos dar con una respuesta
answer if you think about it there are only two possibilities here either Ann is married or Ann is not married
Si lo piensas, solo tenemos dos posibilidades, Anne esta casada, o no lo está.
those are the only two possibilities so
Son las únicas posibilidades
let's consider each one so let's say Ann is married if Ann was married this would be the picture that we have and in this
Vamos a considerar cada una. Digamos que Anne está casada Si Anne está casada, no encontramos con esto
case the answer to the question would be
y en este caso, la respuesta sería A) Si
yes so a married person is looking at an unmarried person in
Una persona casada está mirando a una persona soltera
this case we have an looking as George
tenemos a Anne mirando a George
on the other hand if Ann was unmarried
por otra parte, si Anne estuviera soltera,
then the answer to the question would still be yes it still yes because in
la respuesta a la pregunta seguiría siendo A) Si
this case we have Jack looking at Ann
porque tenemos a Jack mirando a Anne
which means we have Ann married person looking at an unmarried person in this
lo que quiere decir que tenemos a una persona casada mirando a una soltera
case it's Anne who is the unmarried
ya que en este caco es Anne la persona soltera
person either way the conclusion is the
de cualquier forma, la conclusión es la misma
same even though we don't know anything about Anne's marital status we are still
incluso sin saber nada acerca del estado marital de Anne
able to deduce that there is one married person looking at one unmarried person
Somos capaces de concluir que siempre habrá una persona casada mirando a una persona soltera.
in the book I got this from Keith
En el libro en el que leí este problema
Stanovich explains that this sort of
Keith Stanovich explicaba que este tipo de razonamiento se llama
reasoning is called fully disjunctive
"fully disjunctive reasoning" (Razonamiento totalmente disyuntivo)
reasoning that's reasoning that considers all the possibilities now this
el razonamiento que considera todas las posibilidades.
question does suggest that there isn't enough information and so people take
Este planteamiento sugiere que no hay bastante información, así que la gente toma el camino corto
the easiest inference which is cannot be
que es decir que no puede determinarse.
determined without considering the full range of possibilities but people can do fully disjunctive reasoning if they know
Sin llegar a considerar todo el rango de posibilidades. pero la gente podría usar el "razonamiento totalmente disyuntivo"
it's necessary for example if we didn't
si supieran que es necesario.
give you the option of it cannot be
Por ejemplo, si no diera la opción de no poder ser determinado.
determined now this problem did remind me of another problem from mathematics
Este problema me recuerda a otro problema de matemáticas
where the same sort of reasoning applies
en el que se aplica el mismo razonamiento.
let's look at that so this second
vamos a verlo.
problem is far more mathematical in
Este problema es de naturaleza mucho mas matemática
nature so mileage might vary here I know
en principio es muy distinto,
some of my viewers are hardcore maths
se que muchos de mis seguidores son fervientes entusiastas de las matemáticas
enthusiast so for them this is going to go down a storm
para ellos va a ser como una tormenta, estoy seguro
I'm sure it's about irrational numbers
Es acerca de los números irracionales
irrational numbers are those that cannot
que son aquellos que no pueden escribirse como fracciones
be written as fractions so their decimals go on forever like pi pi is an
y los decimales siguen por siempre, como pi, pi es un número irracional
irrational number and the question is
La pregunta es esta
this can an irrational number to the power of an irrational number be rational now this is quite a hard
¿puede un número irracional elevado a otro número irracional ser un número racional?
question to answer particularly if you
se trata de una pregunta difícil de responder
try and construct an answer if you took an irrational number and raise it to the power of an irrational number you get something that is hard to deter
ya que si coges un número irracional, y lo elevas a otro irracional, la respuesta es muy difícil de determinar
if it's rational or not but if you want
si es racional o no
to answer this question can an irrational number to the power of an irrational number be rational we're going to use the same
Pero si quieres responder a la pregunta ¿puede un número irracional elevado a otro número irracional ser racional?
sort of reasoning that we used in the married problem and the proof is kind of
Vamos a usar el mismo razonamiento que usamos en el problema anterior. y la demostración es genial también
nice as well first start we're going to take an irrational number to the power
primero vamos a tomar un número irracional
of an irrational number in this case
elevado a otro número irracional
we're going to take the square root of 2 to the power the square root of 2 the
En este caso, la raíz de dos elevada a raíz de dos
square root of 2 is known to be irrational now I don't know what the
Raíz de dos es un número irracional Ahora, no se cual es la respuesta a esto,
answer to this might be let's call it X
la llamaré X
now I'm going to take the result here X and I'm going to raise that to an
Ahora voy a tomar este resultado X y lo voy a elevar a un número irracional
irrational number I'm going to take X and I'm going to raise it to the square root of 2 again so what I'm getting here
y voy a tomar x y lo voy a elevar por la raíz de dos
is a square root of 2 to the power of the square root of 2 to the power of the square root of 2 again now if you are
e igualándolo tenemos raiz de dos elevado a raíz de dos, elevado a raíz de dos nuevamente.
happy with powers and how they work what this means is we've got the square root
si estas familiarizado con las propiedades de las potencias, sabrás
of 2 squared which is actually 2 right
La raiz de dos al cuadrado es dos.
just the number 2 now how does this help
el número dos, simplemente
well X here is an intermediate step now
¿Y cómo nos ayuda esto? la x de aquí es un paso intermedio
the question is can an irrational number to the power of an irrational number be
La pregunta es, ¿Puede un número irracional elevado a un irracional ser raccional?
rational well if X was rational then the answer to the question is yes by the first line
Bueno, si x es racional, la respuesta a la pregunta es si.
here if X was irrational then the answer
por la primera línea, aquí si x es irracional
to the question is still yes by the
La respuesta sigue siendo si
second line here now I don't know if X is rational or not but it turns out it's
por la segunda línea, aquí. No tengo idea de si X es racional o no,
irrelevant because the conclusion is the
pero es irrelevante, ya que la conclusión sería la misma
same it's a lovely proof yes we don't have to construct X we don't have to know if it's rational or not for
es una prueba encantadora, no tenemos que darle valor a x, no tenemos por qué saber si es irracional o no
completeness I can tell you that X the square root of 2 to the power square root of 2 is irrational but again for
Puedo deciros que raíz de dos elevado a raíz de dos se trata de un número irracional
what we're trying to do is actually
pero para lo que estamos tratando de demostrar es irrelevante.
irrelevant it was just our intermediate step by considering all the possibilities we can deduce the correct answer to the
solo es un paso intermedio , y considerando todas las posibilidades damos con la solución.
problem I teamed up with Alex bellows and he ran the marriage problem on the
Me he unido a Alex Bellos para recoger el problema en el blog de The guardian
Guardium blog which included a survey
incluyendo una encuesta,
where people could record what they thought it will be interesting to see
para que la gente puediera dejar constancia de lo que piensa,
how well people do the original claim
y ver que tal lo han hecho, el problema original decía
with the problem was that over 80% of
que el 80% de la gente se equivocaría
people get this wrong so I'm going to include a link in the description to the results of the survey and it'd be
Así que he incluido un link en la descripción a los resultados de esa encuesta,
interesting to see so you should check
y es interesante de ver, echad un vistazo
that out but for me if you have been thanks for watching
Y, si lo has estado haciendo, gracias por ver el video.
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