Mathematics

[wh00t]

Offer the janitor a thermometer in exchange for the height of the building.

[ThornyRose]

Erm, no... I had some more creative stuff on my mind.
I know it's not about math, but... Maybe we might come up with more than six or so ways and exchange some funny stuff...

[Harut]

thanks for the problems Azat.

but wait at least couple of days before giving the answers, please.

[Azat]

Very good Harut.

I thought this was the hardest and the others are just tricky.

I have few more in my old emails. My friend and I use to email each other these type of problems long time ago. Now I need to go and dig them out.

[Azat]

Hey Thorny, good question.

Lets see.
1. Can you go to the top and measure the temperature and measure the temperature at the bottom and figure out the height because the temperature goes down X degrees for each Y meters?

2. You can possibly boil water on top of the roof and measure the temperature of the water at the boiling point. Water boils at lower temperature at higher altitude and based on the boiling point you can determine the height.

3. Drop the thermometer from the roof and measure the time it takes for it to hit the ground and based on the time and theory of acceleration you can get the height.

Okay, I have to admit, I have no clue. I need some hints.

[Azat]

Okay Harut and Thorny,

 

Today I am going to be a cheap home owner(I am playing myself)

 

I am going to hire you two to plant 5 rows of trees for me. 4 trees per row. But remember I am cheep so I can only afford to buy 10 trees.

 

How are you guys going to plant the 10 trees such that it is 5 rows of 4 trees each.

 

 

Hey Thorny, I am still waiting for your hints on the height of the building.

 

Azat

[Azat]

Okay, create a grid on a football field. 5 by 5. 25 equal squares.

 

If you draw this grid, the square in the upper left-hand corner we could say is one, and the one next to it is two, three, four, five, and then the line below that is six, seven, eight, nine, 10, 11, 12... All the way to 25.

 

Now put a person in each square. You have to move each person from the square they are into the square of one of his adjacent squares. So number one can move to square number two, or number six, for example.

 

Number two can move to number one. Or number three, or number seven.

 

So, here's the question. What is the fewest number of total moves that will allow every person to move to an adjacent square?

[Armine]

Here's a problem you guys can also try..it's called the Magic Plant.

 

Monday morning Jack plants a magic bean. When Jack waters the plant on Tuesday morning it has grown to a height of 4ft. When Jack waters the plant on Wednesday moring it is 6ft tall. When Jack waters the plant on Thursday morning it is 7ft tall.

If Jack's magic plant continues to grow at the same rate, how many days will it take Jack's magic plant to grow to a height of 8ft?

 

[ September 30, 2001: Message edited by: Armo ]

[Harut]

Armo jan, inchkan el jres meka 8 fti chi hasni.
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it won't be 8 ft tall ever.
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i can now see that you are studying calculas.

[Harut]

i don't know how Thorny wants to do it, but i'll plant them it STAR shape.
^^^^^^*^^^^^^^
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i think you can see 5 lines

[Azat]

You're hired. I just hope you don't charge too much money.

[Harut]

Azat jan, bayts du shat shustri es.
et inchi tverov cheir grel?
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i got this one too.
the items they needed are the numbers for the doors

1 is $2
2 is $2
12 is $4
144 is $6
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i liked this one, Azat.

[Harut]

no, at all. i offer very cheap labor.
let's see. one tree costs $20.
you need 5 rows, 4 tree on each. that would be $400.

[Azat]

Okay Harut,

I am sure this is going to be easy for you as well.

 

Remember the balls from the previous question? You take 1 ball from each bag and mix them. Such that 49 are the same weight and 1 is just a little heavier. Now you have a have to find which one is the heavy ball with my balance scale.

 

You only have 5 dollars and I charge a dollar each time you use the balance scale(to pay the tree gardener ). How do you find the heavy ball? To make it harder for you. You also want to buy Thorny ice cream and that costs a dollar. How can you do both? Buy the ice cream and find the heavy ball?

[Azat]

I use to have this small paperbag Armenian book(green cover) that had all kinds of cool math and logic puzzles in it. I would love to find it's name and see if I can buy it from some place. It was originally published in the Soviet era, probably in mid 70s.

 

Does anyone know any info on this book?

 

Azat

[ThornyRose]

Azat, I'm sorry, but we are in different time zones - in fact, you asked the question with the rows and Harut answered it before I could even think! I saw the answer this morning (your night), but my provider was too slow for me to comment.



I couldn't remember all the answers, but you had all the brainy ones anyway!
This was what I prepared shortly after I put up the question (all of this assuming you DO have a ruler or a household measurer [sorry I haven't added that!]):

One way is to measure the temperature at the bottom of the building and at the very top – the difference will enable you to calculate the height.

Another way:
Tie the thermometer to a string long enough, go to the top of the building, let it down, and then measure the length of the string.

Another:
Put the thermometer on the ground, standing up. Within as small an interval of time as possible (to ensure accuracy), measure the lengths of the shadows of both thermometer and building; also measure the length of the thermometer. Then, with the proportionalities, you have the height of the building!

Yet another:
We now (from the previous step) know the length of the thermometer. We call in the fire-fighters and make use of their ladder to align the thermometer along the building, and count how many thermometers the building makes. Then... We call ourselves Laz!

More:
Go to the top of the building, drop (not “throw”!) the thermometer, record the time it takes to hit the ground and shatter , and then calculate the height, h, of the building from h = 0.5*g*t*t. (OK, I’m beating it outta here! Jumping in the lake! )

[ThornyRose]

I used to like stuff, tricks with numbers, when I was having my secondary education. Learned lotsa li'l tricks with numbers which actually helped me in my calculations on tests (especially multiple-choice ones!) but have since forgotten them all... The only one I remember (at the moment - ) is that with the divisibility of a number by 11 - it is, after all, the most important number in my life (not necessarily a lucky one, though).

[Harut]

Azat jan, i just entered to college. i haven't even finished my first term.
but i've decided to go into computer programming.
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i always liked math and logic.
those kinds of questions and problems always exited me
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Ajan jan, i'm afreid to say but i don't have that much of a logic.
it's probably because of my experience. as i said even in kindergarden, when other kids played with toys, i used to "play" with those kinds of things.

in another hand, my father has a GREAT logic. he barly graduated from school, with the lowest grades possible, but he CAN THINK.
i admire him for that.

i gave him those questions you gave me, the one i already solved, and he got all of them in couple of minutes.
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but i have to say that i'm really good at math. i was always at the top of my class.

[ October 01, 2001: Message edited by: Harut ]

[Harut]

i remember i had one of those book when i was little.
its name was "Haryur Khrakhjakan".
it was very interesting book. it had all kinds of questions, from very primitive to genuis level questions.

i also had a couple of books that were filled with math questions from previous Math Olympiads.
it was a great experience for me to read those books.

i wish i had them with me right now.

[Azat]

Harut jan, I am impressed. What is it you study? Your logic is great.

What is it you study?

[ThornyRose]

Top secret, sorry. Hell, I so desire to let it out so I can speak about it, but it is a proven fact that there are people out there stalking others - never know... (And there has been a case where someone on another forum regurgitated something said right here - made a slip, in effect - and got us all by surprise. Ask Thoth and Ceyhun; they are both witnesses to this.) And it would be very easy to "calculate" who I am... Suffice to say, I am studying engineering.

[Armine]

Ayo Harout Aper Jan I am studying Calculus.

 

as for the question you are correct but i was looking for more of a limit equastion which shows that it will approach 8ft but it will never reach it.

[Harut]

i like programming(even though i haven't really experienced it seriously), and i want to be good at it.
but i don't really like all those extra stuff i have to take even before i get into the field(psychology, business, history, english, and so on)

well, we'll see what will happen.

ps: i'm thinking over the rest of the problems. give me another day.

[Harut]

Armo, you are a fresh mind. give us some problems.

[Harut]

Azat, i think i got this one too.
you didn't mantion if you are providing the wights or not, but i don't even need them.
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here it is.

first i would divide 50 balls into 3 groups of 20, 20, 10.
then i'll pay you $1 and will use the scale. i'll put 1st 20 on one side the other 20 on the other side.
if they balance then the heavier one is in the 3rd group, of 10.

i would divide it into 2 groups of 5, 5.
i'll put them on the scale.
i'll take the heavier one and would divide it into 3 groups of 2, 2, 1.
i'll put 2s on each sides of the scale.
if they balance the one left is the heaver one.
if not i'll take the heaver 2 that would put one on each side and would find the heaver one.


if the 20s don't balance then i'll take the heavier one and would divide it into 3 groups of 7, 7, 6.
i'll put 7s in each side.
if they balance then i'll take the 6 and would divide it into 3, 3.

would put them on balance.
would take the heaver one, would divide into 1, 1, 1.
would wight two of them. and would find the heaver one.

if those 7s don't balace then i'll take the heaver one and would divide it into 3, 3, 1.
would use the 3s
if them balance then the heaver one is the one left.
if not, then i'd take heaver 3 and would divide into 1, 1, 1.
i'd wight two of 1s and would find the heaver ball.
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then i will reward myself with delicious Thorny ice-cream.
don't worry i'll share it with you.

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did i miss anything???