Maths- Gym for Brainiacs

Kamina wrote:

Lord Hades wrote:

Kamina wrote:Next question, goallegacy troll edition

Once upon the time, GL had 200 members to start off with. Among them were trolls and non trolls. Trolls, if asked whether they are one, they never said the truth Non trolls, of course, always stated the truth. Seeing each other posting everyday, all the 200 knew among themselves who is a troll and who isn't
Redoranje tried to find out how many trolls were present in those days. He made a survey:

1.) He asked, "how many trolls are in GL?", the first one answered " there's at least one troll in GL", the second one said " there're at least 2 trolls in GL" and so on, the last one said " there're at least 200 trolls in GL"...
How many trolls did Redoranje find with his survey?
(junior high level)


2). Redoranje wasn't satisfied with his first survey. He started a new one with the question " how many trolls are exactly present in GL?"
Again, the first one answered " there's exactly one troll in GL", the second " there're exactly 2 trolls in GL" and so on, the 200th said " there're exactly 200 trolls in GL"
What were Redoranje's results from his improved survey?
( logic question, everyone who could count up to 200 is able to answer theoretically)



Lord Hades, if you know the answer, PM me

if trolls were asked that were they trolls they would lie right? but redoranje just asked them how many troll are there . so they would also speak the truth right? so the last one said there at least 200 trolls in gl .. assuming that he is speaking the truth 200 is the right answer since ther arent more than 200 members? for the first question?

No To which question do you refer, to the first or second one? Your assumption should be, there's at least one troll and one non troll. This way, you can't get 200 trolls even if you wanted to

was referring to the first question..

Lord Hades wrote:

was referring to the first question..

You no solve anything? The answer is really easy, you don't need complex statistical data, just common sense

Kamina wrote:

halamadrid2 wrote:wow i just found this thread and i love maths

However, This is friggin statistics i hate that... give me pure maths and ill do it

ill guess for the first one you gonna have to use 0.5 somewhere since there are only two outcomes troll and non-trolls and the maximum number of posters are 200... i think this will help you solve it

For you,
F(t)=36*e^t /(1+e^t) is a function which describes the bread area mildew covers in time t (t in days).
When does the mildew spread the fastest?
(senior high level)

Post answer and why

fastest means t(time) has to be infinity

so if t is infinity e^t has to be 1

so 36(1)/1+(1)=18

F(t)=18

halamadrid2 wrote:

Kamina wrote:

halamadrid2 wrote:wow i just found this thread and i love maths

However, This is friggin statistics i hate that... give me pure maths and ill do it

ill guess for the first one you gonna have to use 0.5 somewhere since there are only two outcomes troll and non-trolls and the maximum number of posters are 200... i think this will help you solve it

For you,
F(t)=36*e^t /(1+e^t) is a function which describes the bread area mildew covers in time t (t in days).
When does the mildew spread the fastest?
(senior high level)

Post answer and why

fastest means t(time) has to be infinity

so if t is infinity e^t has to be 1

so 36(1)/1+(1)=18

F(t)=18

Right approach and right answer but I didn't ask for that The question was WHEN does the mildew spread the fastest and not how much of bread area it will cover?
You're very close to the answer

Kamina wrote:

halamadrid2 wrote:

Kamina wrote:

halamadrid2 wrote:wow i just found this thread and i love maths

However, This is friggin statistics i hate that... give me pure maths and ill do it

ill guess for the first one you gonna have to use 0.5 somewhere since there are only two outcomes troll and non-trolls and the maximum number of posters are 200... i think this will help you solve it

For you,
F(t)=36*e^t /(1+e^t) is a function which describes the bread area mildew covers in time t (t in days).
When does the mildew spread the fastest?
(senior high level)

Post answer and why

fastest means t(time) has to be infinity

so if t is infinity e^t has to be 1

so 36(1)/1+(1)=18

F(t)=18

Right approach and right answer but I didn't ask for that The question was WHEN does the mildew spread the fastest and not how much of bread area it will cover?
You're very close to the answer

after 15 seconds?

edit: right at the start, 0 seconds it has the fastest spread rate then it decelerates.

Kamina wrote:Next question:

Franchise , alexjanosik and friends from Farca section meet RM section in a goallegacy brawl
Franchise says to Jack Daniels: Come over to us and we'll overwelm them with doubled number of posters.
Jack Daniles answers to Franchise: Come over to our side, this way each side will have equal number of posters. The discussion will be active and balanced=> what the forum needs

The question, how many posters participate in the GL brawl from Farca and Real Madrid section?

P.S. junior high level

Again, answer and justify why

Dani;s group = 7.

JD's group = 5.

x+1 = 2(y-1)
x-1 = y+1

Solve the two equations.

Kamina wrote:Next question, goallegacy troll edition

Once upon the time, GL had 200 members to start off with. Among them were trolls and non trolls. Trolls, if asked whether they are one, they never said the truth Non trolls, of course, always stated the truth. Seeing each other posting everyday, all the 200 knew among themselves who is a troll and who isn't
Redoranje tried to find out how many trolls were present in those days. He made a survey:

1.) He asked, "how many trolls are in GL?", the first one answered " there's at least one troll in GL", the second one said " there're at least 2 trolls in GL" and so on, the last one said " there're at least 200 trolls in GL"...
How many trolls did Redoranje find with his survey?
(junior high level)


2). Redoranje wasn't satisfied with his first survey. He started a new one with the question " how many trolls are exactly present in GL?"
Again, the first one answered " there's exactly one troll in GL", the second " there're exactly 2 trolls in GL" and so on, the 200th said " there're exactly 200 trolls in GL"
What were Redoranje's results from his improved survey?
( logic question, everyone who could count up to 200 is able to answer theoretically)



Lord Hades, if you know the answer, PM me

Is the first survey 100 trolls and the second survey 199 trolls?

kiranr wrote:

Kamina wrote:Next question, goallegacy troll edition

Once upon the time, GL had 200 members to start off with. Among them were trolls and non trolls. Trolls, if asked whether they are one, they never said the truth Non trolls, of course, always stated the truth. Seeing each other posting everyday, all the 200 knew among themselves who is a troll and who isn't
Redoranje tried to find out how many trolls were present in those days. He made a survey:

1.) He asked, "how many trolls are in GL?", the first one answered " there's at least one troll in GL", the second one said " there're at least 2 trolls in GL" and so on, the last one said " there're at least 200 trolls in GL"...
How many trolls did Redoranje find with his survey?
(junior high level)


2). Redoranje wasn't satisfied with his first survey. He started a new one with the question " how many trolls are exactly present in GL?"
Again, the first one answered " there's exactly one troll in GL", the second " there're exactly 2 trolls in GL" and so on, the 200th said " there're exactly 200 trolls in GL"
What were Redoranje's results from his improved survey?
( logic question, everyone who could count up to 200 is able to answer theoretically)



Lord Hades, if you know the answer, PM me

Is the first survey 100 trolls and the second survey 199 trolls?

Right on but you didn't explain the solution so the answer is incomplete

spanky489 wrote:

Kamina wrote:

halamadrid2 wrote:

Kamina wrote:

halamadrid2 wrote:wow i just found this thread and i love maths

However, This is friggin statistics i hate that... give me pure maths and ill do it

ill guess for the first one you gonna have to use 0.5 somewhere since there are only two outcomes troll and non-trolls and the maximum number of posters are 200... i think this will help you solve it

For you,
F(t)=36*e^t /(1+e^t) is a function which describes the bread area mildew covers in time t (t in days).
When does the mildew spread the fastest?
(senior high level)

Post answer and why

fastest means t(time) has to be infinity

so if t is infinity e^t has to be 1

so 36(1)/1+(1)=18

F(t)=18

Right approach and right answer but I didn't ask for that The question was WHEN does the mildew spread the fastest and not how much of bread area it will cover?
You're very close to the answer

after 15 seconds?

edit: right at the start, 0 seconds it has the fastest spread rate then it decelerates.

Right answer but where is the solution?

Unsolved mystery:

What's between mountain and valley?

requirements: none

Kamina wrote:

halamadrid2 wrote:wow i just found this thread and i love maths

However, This is friggin statistics i hate that... give me pure maths and ill do it

ill guess for the first one you gonna have to use 0.5 somewhere since there are only two outcomes troll and non-trolls and the maximum number of posters are 200... i think this will help you solve it

For you,
F(t)=36*e^t /(1+e^t) is a function which describes the bread area mildew covers in time t (t in days).
When does the mildew spread the fastest?
(senior high level)

Post answer and why


Question for everybody except LH and Halamadrid2:

What's between mountain and valley?

requirements: none

When the first derivative of the function = 0. That is when the mildew will spread the fastest.

Kamina wrote:
Right on but you didn't explain the solution so the answer is incomplete

Wanted to make sure i had the answer right first

Should be solved by induction.

In the first survey, take 2 posters.

There is alteast 1 troll and 1 non troll. Trolls will always lie and non trolls will never lie.

By those conditions, the second poster is lying and hence is a troll, which makes the first one a non troll.

Then take 3 posters. The 3rd poster is lying which makes him a troll. Hence the first poster is speaking the truth and is a non troll. The second one says there are atleast 2 trolls. We already know first is not a troll and the third is a troll which means the second one is either counting himself or the first one. We already know the first one is not a troll and the second one if a troll will never say he is a troll. Hence his statement is also a lie and has to be a troll. Hence there are two trolls and 1 non troll.

If you then take 4 posters, the last one is a troll which makes the first one a non troll. Then you take the third poster who says there are atleast 3 trolls which means he is counting himself too as we already know the first is not a troll. But as per the condition, this is not possible, hence he is lying and is a troll. This makes the second one a non troll.

Follow this logic for 200 and you get 100.

The second survey is more complicated. The last one is always lying anyway, so he is troll. By induction, if you take 3 posters, the first one might be saying the truth, which makes the second one's statement false and hence a troll which inturn makes the first one's statement false and a troll. So as the first one and the third one are trolls, the second one is a non troll.

If you take four posters, then the fourth will always be a troll. If the first one is saying the truth, then second one and the third must be lying which makes the first one's statement false and hence is a troll. If the second one is stating the truth, the third one must be lying and hence a troll which inturn makes the second poster's statement a lie and hence a troll. That leaves the third poster's statement to be the truth.

Follow this logic to 200 and you get 199.

Kamina wrote:

spanky489 wrote:
after 15 seconds?

edit: right at the start, 0 seconds it has the fastest spread rate then it decelerates.

Right answer but where is the solution?

Spanky is right. When the first derivative = 1 and not 0, the mildew spread will be the fastest. Scratch my earlier answer.

Well done with the first two questions We have our very own indian


Question for everybody:

What's between mountain and valley?

requirements: none

A little bit geometry

You're given a square. One side is divided into 3 even pieces and the other in 4 ( see in the pic, viva MS Paint ). If you connect two ends like in the pic, you'll get a plane angle. The question, what angle is it?

requirements: junior high school

Kamina wrote:A little bit geometry

You're given a square. One side is divided into 3 even pieces and the other in 4 ( see in the pic, viva MS Paint ). If you connect two ends like in the pic, you'll get a plane angle. The question, what angle is it?

requirements: junior high school

Great drawing

Kamina wrote:Well done with the first two questions We have our very own indian


Question for everybody:

What's between mountain and valley?

requirements: none

What is the answer/solution for the question you asked Hala?

kiranr wrote:

Kamina wrote:Well done with the first two questions We have our very own indian


Question for everybody:

What's between mountain and valley?

requirements: none

What is the answer/solution for the question you asked Hala?

Complete answer? You have to find the first derivative and equal it to zero:
F(t)=36*e^t /(1+e^t)

f(t)= (36*e^t*(1+e^t)-36*e^t*e^t)/(1+e^t)²=36e^t*(1+e^t-e^t)/(1+e^t)²=36e^t/(1+e^t)²
As you see the first derivative can't possibly be zero at any point given. You have to prove that the derivative is steadily decreasing by looking at limis t-> infinity. You'll get 0 which means in return that the starting point was the time when the mildew spread the fastest, t=0

Kamina wrote:

halamadrid2 wrote:

Kamina wrote:

halamadrid2 wrote:wow i just found this thread and i love maths

However, This is friggin statistics i hate that... give me pure maths and ill do it

ill guess for the first one you gonna have to use 0.5 somewhere since there are only two outcomes troll and non-trolls and the maximum number of posters are 200... i think this will help you solve it

For you,
F(t)=36*e^t /(1+e^t) is a function which describes the bread area mildew covers in time t (t in days).
When does the mildew spread the fastest?
(senior high level)

Post answer and why

fastest means t(time) has to be infinity

so if t is infinity e^t has to be 1

so 36(1)/1+(1)=18

F(t)=18

Right approach and right answer but I didn't ask for that The question was WHEN does the mildew spread the fastest and not how much of bread area it will cover?
You're very close to the answer

ohh ok, understood it wrong blasphemy...anyways spanky solved it before me

in that next one does it mean what angle as in 90, 180, 360 etc???

Kamina wrote:A little bit geometry

You're given a square. One side is divided into 3 even pieces and the other in 4 ( see in the pic, viva MS Paint ). If you connect two ends like in the pic, you'll get a plane angle. The question, what angle is it?

requirements: junior high school

ok i am not very good with this...

that top triangle has two equal division... i.e. its a right angle therefore the top corner is 90 degrees

the bottom one is a right angle as well so it has 90 degrees angle on the bottom hand corner

since the top triangle is double the size of the bottom triangle the the angle on the left side of alfa has to be double that of the right but still less that the middle

so if you equal the left hand 30 and the right hand 15....90-45=45 therefore alfa has to be 45 degrees... i guess

halamadrid2 wrote:

Kamina wrote:A little bit geometry

You're given a square. One side is divided into 3 even pieces and the other in 4 ( see in the pic, viva MS Paint ). If you connect two ends like in the pic, you'll get a plane angle. The question, what angle is it?

requirements: junior high school

ok i am not very good with this...

that top triangle has two equal division... i.e. its a right angle therefore the top corner is 90 degrees

the bottom one is a right angle as well so it has 90 degrees angle on the bottom hand corner

since the top triangle is double the size of the bottom triangle the the angle on the left side of alfa has to be double that of the right but still less that the middle

so if you equal the left hand 30 and the right hand 15....90-45=45 therefore alfa has to be 45 degrees... i guess

Hala, the worthy disciple Great job on solving the problem geometrically

A question, do you have any idea how to solve it through calculation? You don't need to solve it that way but just give a hint how it could be solved through calculation if you get the idea
For future reference write 90 degree as 90° that way you can avoud writing degree all the time for angles

Mole visited the thread and was annoyed

He proposed a question which doesn't require any knowledge in maths:[/color]

What's between mountain and valley?

requirements: none

Kamina wrote:

halamadrid2 wrote:

Kamina wrote:A little bit geometry

You're given a square. One side is divided into 3 even pieces and the other in 4 ( see in the pic, viva MS Paint ). If you connect two ends like in the pic, you'll get a plane angle. The question, what angle is it?

requirements: junior high school

ok i am not very good with this...

that top triangle has two equal division... i.e. its a right angle therefore the top corner is 90 degrees

the bottom one is a right angle as well so it has 90 degrees angle on the bottom hand corner

since the top triangle is double the size of the bottom triangle the the angle on the left side of alfa has to be double that of the right but still less that the middle

so if you equal the left hand 30 and the right hand 15....90-45=45 therefore alfa has to be 45 degrees... i guess

Hala, the worthy disciple Great job on solving the problem geometrically

A question, do you have any idea how to solve it through calculation? You don't need to solve it that way but just give a hint how it could be solved through calculation if you get the idea
For future reference write 90 degree as 90° that way you can avoud writing degree all the time for angles

pi / 2 - arctg(2/3) - arctg(1/4) = answer = around 43 degrees

spanky489 wrote:

Kamina wrote:

halamadrid2 wrote:

Kamina wrote:A little bit geometry

You're given a square. One side is divided into 3 even pieces and the other in 4 ( see in the pic, viva MS Paint ). If you connect two ends like in the pic, you'll get a plane angle. The question, what angle is it?

requirements: junior high school

ok i am not very good with this...

that top triangle has two equal division... i.e. its a right angle therefore the top corner is 90 degrees

the bottom one is a right angle as well so it has 90 degrees angle on the bottom hand corner

since the top triangle is double the size of the bottom triangle the the angle on the left side of alfa has to be double that of the right but still less that the middle

so if you equal the left hand 30 and the right hand 15....90-45=45 therefore alfa has to be 45 degrees... i guess

Hala, the worthy disciple Great job on solving the problem geometrically

A question, do you have any idea how to solve it through calculation? You don't need to solve it that way but just give a hint how it could be solved through calculation if you get the idea
For future reference write 90 degree as 90° that way you can avoud writing degree all the time for angles

pi / 2 - arctg(2/3) - arctg(1/4) = answer = around 43 degrees

There's a way to get 45° exactly

Fun and somewhat logical question:

How would a mathematician catch a lion in an instant in a desert if he's got a 4x4 meter cage ?

requirements: sense of humor and some basic knowledge in maths theorie

lol i actually dont know babun... was thinking of 1/2 sine something but my mind has just gone blank... could you show us

Kamina wrote:Mole visited the thread and was annoyed

He proposed a question which doesn't require any knowledge in maths:[/color]

What's between mountain and valley?

requirements: none

grass i suppose or mud