Mathematics

[Harut]

WARNING!!!

 

the monitor has nothing to do with you not being able to understand the question, especially the third paragraph.

breaking it will NOT give you the solution!!!

[Guest Fadi]

Your first question is rather easy if I understand it well.

 

(22/60) = (x/12)

 

x = 4.4

 

4 + 4/10

 

(4/10) = (y/60)

 

y = 24

 

Answer 4:24 (AM ? or PM ? )

 

As for your other question...

 

I don't understand the question, and I may be angree against you, for having given ounces as units ? You Americans WILL never learn the international system

 

Well I will try to understand the question first and answer then. And you are right I have broked that monitor and still the new one isnt better, still it dosnt give me the answer.

 

[ April 11, 2002, 07:51 AM: Message edited by: Domino ]

[Azat]

Hey that is a fun question Harut. I am glad you did not ask what color is the rope or something like that.

 

Here goes the answer:

 

X = the age of the monkey when the mother was 3 times older than the monkey. That would mean that 3X is the age of the mother at that time. (this is the easy part to understand) You solve the rest. hehehe no I am kidding, I will.

 

When the monkey is three times the mother's age the monkey will be 9X

 

When the mother is 1/2 the monkeys age the mother is 4.5X and since the mother is twice as old as the monkey or 2X older than the monkey is 2.5X when the mother is 4.5X

 

Since the mothers current age is 2 times the age of the monkey in above then the mother is 5X currently and the monkey is 3X because it is 2X younger.

 

We know that they are 4 years old combined so 3X+5X=4 and X=.5

 

"Monkey's weight in pounds is the same as the mother's age in years", so 2.5*16=40 ounces

 

Sandbag=40 ounces

 

Weight of rope and sandbag = 1.5 times weight of monkey and because monkey and sandbad weight the same then the rope must be halt the weight of monkey. 20 ounces

 

rope is 4 ounces per foot thus the rope is 5 feet long.

 

Cool problem Harut jan.

[Harut]

very good people.

 

those last two problems that i posted where from LACC 16th Annual Math contest, which i took part too. unfortunately got only the fifth place.

 

the following problem is also from there.

========================

 

Suppose a runner running at 10 miles per hour and a bicyclist riding 20 miles per hour are headed toward each other. At the instant they are 15 miles apart a humming bird passes the runner flying in the direction of the bicyclist. The humming bird is flying 30 miles per hour. When it reaches the bicyclist, without slowing down the humming bird reverses direction and flies back toward the runner. When the humming bird reaches the runner, it again reverses direction without any slowing and heads back toward the bicyclist. The hummingbird continues this pattern, going back and forth between the runner and the bicyclist, until the distance between the runner and the bicyclist has closed to zero. What is the total distance traveled by the humming bird from the time the runner and bicyclist are 15 miles apart until they meet?

 

This problem is mentioned in the biography of Nobel prize winner John Forbes Nash. In the early 1950's the problem was presented to John von Neumann, a professor at Princeton and the most famous mathematician in the world at that time. Amazingly von Neumann was able to solve the problem as an infinite sum in his head (without pencil or paper) within a few seconds! Nash, who was a 22 year old graduate student at Princeton also solved the problem in his head within a few seconds. However, Nash's solution was much simpler than von Neumann's.

[Harut]

here is one more for today.

==================

 

A jailer in a prison with infinitely many cells decides to release some of the prisoners. The jailer first unlocks the doors of all the cells. Next he reverses the locks on the door of every second cell (cell numbers 2, 4, 6,...); so, the even numbered cells are now locked again. Next he reverses the locks on the door of every third cell (cell numbers 3, 6, 9,...). Cell 3 was unlocked and is now reversed back to locked. Cell 6, however, had last been locked; so, it is now reversed back to unlocked. Next the jailer reverses the locks on the doors of every fourth cell, then every fifth cell,.... The process continues without end. Which cells will remain unlocked?

[Azat]

I am having a hard time figuring out what the formula is but I can tell you the cells that will be unlocked.

 

1, 4, 9, 16, 25, 36...

 

oh wait, as I was writting these numbers I think I may have it. the numbers are 1^2, 2^2, 3^2, 4^2 and so on. Hence if you tell give me "n", I will find the largest whole number whose square is smaller then "n" and that is the number of doors that will remain unlocked.

 

Right?

[Azat]

hey, what happened to my answer for the previous problem. Did someone delete it?

[Azat]

what I had said for the bike problem went something like this.

 

----------------

 

Harut jan, either I am not reading the problem right or it is a very simple problem to solve.

 

(20 MPH) bike | 15 mile distance | human(10 MPH)

 

thus it would take them 30 minutes to meet since combiled they are traveling at 30 miles an hour and need to travel 15 miles.

 

And no matter what direction the stupid bird is traveling, it would travel 15 miles in 30 minutes since it is traveling 30 MPH.

 

Am I not getting it?

[Harut]

good job Azat,

 

everything is right.

 

simple stuff sometimes are confusing too.

[Guest Fadi]

Booo... I wanted to answer these questions. Bad Azat, you took them all off.

------------

 

Now I have a question for Harut, its not really mathematic but logic.

 

A king is very seak, and has not children that will replace him if ever he die, and has also no family. He then decide to make the next King, the most intelligent person in his Kingdom, many come to be tested, at the end there is 3 person left, and you are one of those

 

Now the king the tree of you in triangle, and place a ball in each of those heads(3), the bag from where he took the balls out to put them in these heads(3) conatained many balls, one of the balls in, was black and the rest white.

 

Now the question is, how can you know what is the color of the ball on the top of your head, you see the balls on the head of the two others, and the tree of you are placed on triagle, you see both of them have white balls on their heads, now you don't know if the balls on your head is the black one or one of those white one. The king answer, the first one that scream the color of the ball on top of his head is made king, but if you are mistaken you get your head cut.

 

Now the intelligent Harut wait 3 second, and scream the color of the ball on his head and he is made king. How you knew the color of the ball you have on your head ? Only the two others see the color of the ball on your head, not you.

 

[ April 02, 2002, 06:33 AM: Message edited by: Domino ]

[Sip]

Wow ... everything solved already!

 

Von Neumann was a really cool guy ... one of the founding fathers of today's computer architectures (your PC basically follows the Von Neumann Architecture)

 

But I think the original problem had trains and a fly or a bee if I remember correctly. It is pretty funny how he summed the series in his head.

[Harut]

the first thing that came up to me is this.

 

if those two other guys are so smart that made it to final, and they don't shout out their balls' colors at once, then, they too see white color on my head and on the head of the other.

because if i had black on my head then those two would call out immidiatly because they would see that the black one is on my head.

====

[Guest Fadi]

Has someone told you, you were smart ?

 

You got it right... You are sure that the ball on your head is white...

 

If of course the other two were selected without cheating, if yes, then you could have some problem. Right ?

 

Now another of that style.

 

You have been sentenced to death unfairly, and jailed untill you are executed. On the trial you perform so well that the Judge not wanting to take back his previous decision because of his ego say that he will give you a chance. He say that there will be a bag in it there will be 2 balls, one white and the other black, if you chose the white ball you are free, if you chose the black one, snipers that are placed around you will shut you.

 

Now you are on the jail waiting for the next day, that you are supposed to take the fatal decision... at night one of the gards come and say you that you have no chance, the judge ego could not afford to set you free, and for this they have put on that bag 2 black balls, and that no one will believe if you tell this to others, and that the snippers at the top will just shut you after they see you have made the wrong decision, and that you have no right to pull of the two balls, because they will shut you right away.

 

Now you think about the situation all the night.

 

At the morning they send you to the position where the snippers are waiting to shut you, they give you the bag with the two balls. You put your hand in it, and you say something, and take of one ball, open your hand, and you are set free.

 

What I ask you, is what you said. Don't forget that no one will believe you if you claim there is two black balls.

 

[ April 02, 2002, 05:40 PM: Message edited by: Domino ]

[Azat]

Dear Domino, his head is big enough. No need to tell him those things.

[Harut]

Domino, i say "krakoghi marik@"

if this is not it than let me think a little more.

[Harut]

or i can say "let's change the rules. if i take out the black one set me free. if i get the white one shoot me!"

[MosJan]

es xpelu gorts ka ??? dzen haneq um ???

[Harut]

relax Movses, i got everything under control.

[Sip]

I think he guy probably says "I pick the one that's in the bag" and takes out one ball ...

 

----

Harut, if the other 2 people were me and Azat, we would not say anything even if there was a black ball on your head. Then it would be really funny to see what happens to your "very smart" head after you guess wrong !!!

[Guest Fadi]

Harut Sip answer is the good one. No changing rules I tough this one was easier then the other.

 

Sip if you and Azat were the two other ones, your action to see Harut smart head(I wonder why you put it under quotation marks, are you questioning it ? ) blow, will cost your both heads, after that I blow them Don't forget that Harut is the one supposed to do my Comp. homeworks. (Even if I dont believe that I have to do other programming courses, Thanks Evil)

[Edit]

Hi:)

2+2=5,

How it happens????????????

[Azat]

Domino, I had heard a question very similar to the King question a while back. Here it is.

 

--------

 

There are three very qualified applicants for a job at Harut Software Inc, and the president of the company, Harut, has interviewed all of them extensively. He calls them all in and says "Sip, Azat, Domino please have a seat. I can't figure out which one of you to hire, so I'm going to administer one final test, and whoever comes up with the answer first gets the job." And the test is fair. No one will be at a disadvantage. In fact, the only one who will be at an advantage is the one who has the superior intellect, and that's the person, of course, that I want to hire.

 

Here's the test: I have in front of me four hats. They're all identical, except that three of them are black and one of them is white. I'm going to blindfold all of you, and then I'm going to place one of the hats on each of your heads. Then I'll take the fourth hat and remove it from the room. Then my assistants, Movses and Tooth, will help me remove your blindfolds simultaneously so that you will see the other two participants and their hats. So each person is facing the other two people. The first person to identify the color of his hat wins the job.

 

So they put the blindfolds on. He goes around and puts the three hats on, throws the fourth one into the hallway. As they're getting ready to remove the blindfolds, Sip raises his hand and says "I know what color my hat is, it's black."

 

The question is how does Sip know it is black?

[Azat]

You are absolutely correct.

 

Now only you would see that x-x=0. hehehe

[Guest Fadi]

Azat, I never said x-x do not give zero... I said in fact it gives zero, what I said is that x-x multiplied with other ellements will not necessary give zero...

 

here just one example amoungs others.

 

a(x-x)

 

Those that give zero ? It appears to, but wait and see what I will fix for a, and you shall judge after.

 

a = x/(x-x)

 

Now replace a in the equation.

 

((x-x)x)/(x-x)

 

And what is the answer ?

 

The answer is x, I just have taken away this x-x...

 

This is what I ment, I never said that x-x do not give zero, what I said is that it is not because there is a x-x in the product you posted that it will necessary mean the answer is zero.

 

[ April 08, 2002, 09:33 AM: Message edited by: Domino ]

[Edit]

Azat,qo kam Haruti glxark@ spitak a,ev qani vor menak mi glxarkn er spitak,et mekn el qo kam Haruti glxin a,nshanakum a Sipi glxin@ piti sev lini.