Mathematics

[Azat]

A teenage boy(oh lets call him Harut) smitten with a teenage girl in his school in Yerevan makes his feelings known. Overjoyed at finding them reciprocated, he took a pen knife to a young hardwood tree in the vicinity and carved their initials within a heart 1.5 meters up on the tree's trunk, as boys will do.

 

Few days later the girl dumped him. She went away and got married. The boy, devastated, was inconsolable. Bidding his family farewell, he took his small savings, that he got from selling copies of Tata songs which he had gotten off of Napster.

 

He buys a ticket, goes to the United States and becomes a computer programmer(geek) and makes millions working for some dot com(those were the days).

 

5 years later, he returns to Yerevan and imagine his joy when he discovers that his old sweetheart is living there, now single again.

 

One thing leads to another. The flame reignited and one day they searched for their tree. It wasn't hard to find.

 

Here's the question. It had been 5 years since he had carved their initials.

 

If the tree had added 35% to its height in the first 3 years of his absence, 10% in the following year, and two and a half percent in last year, how far up the trunk did they have to look to find the carving with their initials?

[Harut]

es inch patmutyunner es patmum, Azat jan? knerek, huzvetsi.

 

i think the initials would still be at 1.5 meters.

[Azat]

Darn, again it did not work. I thought I would put all that stuff there to fool you but you are one sharp cookie. Even when love stories are involved you do not get fooled.

Don't worry Harut, I am sure someday I will come up with one of these that will fool you.

[Harut]

Azat jan, inch uzum es ara, menak te shat mi latsatsra.

[Harut]

Azat!!!!! esents chi lini. inch eghar? mi ban ches aselu?

[Azat]

Harut,
If once in a long while you would answer one, just one, of my questions incorrectly, I would post more of these, but this way it is no fun for me too.

I'll to post a couple. I remembered few the other day, but they have skipped my mind now. Will post in the near future.

[Sip]

This will help you remember. It has very nice music so make sure you turn on your speakers. ... then CLICK HERE.

[Azat]

Thanks Sip. I now remember everything to the day I was born.

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Okay this question is not Math related, but it is an interesting puzzle.

 

At an antique auction in NY they claim to have some rare and priceless antiques. They claim to have stuff that collectors would really want, and one of the items that comes up for auction is a child's sled, a hand-made sled, a wooden sled that the auctioneer claimed was made by none other than George Washington himself.

 

He turns the sled over and carved into one of the wooden slats is "G. Washington, September 10, 1752."

 

When someone in the crowd stands up and says it's a fake.

 

He was right and how did he know?

 

Additional Information for you:

George Washington's birthday is 1732, so that would make him 20 years old and it should all fit. At the age of 20 he had not started his military career as of yet.

[Harut]

i knew it.

i just didn't answer it correctly so Azat will post more questions.

[Sip]

Ok then here's another one (assuming the previous one is solved):

 

Four bugs are placed at the corners of a square. Each bug walks always directly toward the next bug in the clockwise direction. How far do the bugs walk before they meet?

[Azat]

Here is the answer to the GW puzzle

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The date, September 10, 1752, does not exist. In fact the dates September 3 through September 13, 1752 were omitted from the calendar in many Protestant countries (including England and thus the American colonies). Thanks to John Bruce for giving me the correct dates.

Pope Gregory revised the calendar in 1552 to realign the equinox dates. Older calendars had used, for example, a year length of 365 days instead of a more accurate 365.25 days (but see below). So in 1552 10 days were omitted from the year (there were additional revisions too). The protestant countries avoided this Papal correction until 1752 and had to omit 11 days because of a leap year issue in 1600

 

The length of the year is 365 days, 5 hrs. 48 min. 46 sec. (365.2422 days), or about 365 1/4 days

 

The Gregorian calendar corrects for the non-integral number of days in the year first by adding a 'leap-day' every four years. This correction makes the average year 365.25 days long. If that was the only correction our years would be one day too long every 128 years. We make a further correction by making only century years divisible by 400 leap years (so 2000 was a leap year while 1700, 1800 and 1900 were not). A little calculation shows that these corrections make the average year 365.2425 days long instead of the more accurate 365.2422 days. But with these corrections the calendar will be only one day off in about 3333 years.

 

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[ February 04, 2002: Message edited by: Azat ]

[Sip]

Wow, very interesting

[Harut]

Azat jan, i'm not good at US History, but i would say that George Washington got his name only after he started his military career, and his name was not George Washington in 1752.

[Azat]

No, while you are on the right direction to think that there is something wrong with that signature, you are not right about the name.

 

If we do not have an answer I will post it this evening or tomorrow morning.

[Sip]

I was giving some extra time for Harut to figure it out

 

Since it was a "child" sled and George was 20 years old, I'd say there was something fishy about the whole thing

 

Man, how much I wish I were skiing today

[Harut]

i'm just guessing for now.
each has to walk as long as the side of the square.
am i correct?

[Sip]

You are correct. So now you can start to think why

[hasmiek]

i think that would be rather difficult...

 

if the average speed has to be 40 mph and the distance is 40 miles, the car would have one hour to reach it's 'goal'

 

if the car has driven the first 20 miles with the speed of 20mph, it has already taken up the hour....

 

 

man; long time ago that i had to think about this stuff....

[Sip]

I am with hasmiek on this one. It is not easy going 20 miles in 0 time !!! It made me think though ... very confusing in the beginnig.

Harut: About the bugs, they all start off perpendicular to each other. As they are moving, nothing changes this so they always stay perpendicular to each other and they are always walking. So essentially, each bug walks an edge of the square but that square happens to be rotating (and shrinking). We can work the equations with polar coordinates but I thought it was a neat problem when I first saw it

Here's the solution. It's a neat website.

[ February 06, 2002: Message edited by: Sip ]

[hasmiek]

heya Sip

 

i saw that you were into the digital electronics...man, did I have sleepless nights over that in the uni.

I remember that we had to design a coffeemachine which you could programm on how many cups of coffee you wanted. I cant even begin to tell you how frustrated I got in that course. Tell me; is 'assembler' still used to programm Eproms?

[Harut]

the paths of bugs will surely be like spiral, going from each corrner to the center.

 

some calculas can solve the problem.

[nellie]

this is the first time i'm reading this post, sorry for the late response.

 

i've got a question. it's not really hard, but it can be tricky.

 

A car is making a trip of 40 miles. it travels half of the distance at an average speed of 20 mph. In order for it to have an average speed of 40 mph for the entire trip, the car would need to:???

[Sip]

Believe it or not yes! Computers have gotten so amazingly sophisticated but the basics have not changed. I have been working on several projects where we have to go and tweak things at the assembly level ... all these embedded chips that are in everything now (like cel phones, pagers, PDAs, cars, etc etc) are reaching the level where they are actually running software. For now, to get the best performance, software is usually tweaked by hand ... compilers will someday catch up but they are not that good when it comes to the very application specific things that these chips require. So this means that some day we will use high level languages even to program most embedded processors but not yet. Compilers are doing ok for normal PCs so no one touches assembly any more. (maybe for writing device drivers)

For example, right now we are working on this little "sensor" device (Berkeley Mote) that has a 4 bit "processr" running at 4 Mhz and a couple of kilobytes of memory. It is running an operating system called TinyOS which uses about 200 bytes! That's for the WHOLE operating system. Of course it can't do much but with only that much resources you have to go and start messing with every instruction and tweak things by hand (a MAJOR nightmare)

But I personally really like these new PDAs (like IPAQs). They are so unbelievably capable. The ones I am playing with run at 206 Mhz and have 64MB of RAM, running linux and we can do pretty much everything a PC can do with it. It doesn't have EEPROMs though ... most of them now have FLASH memory (same thing).

[Azat]

[Azat]

Harut, for this math question you are going to need a super computer, a slide ruler and a Chinese abacus. But I am sure you will get the answer.

 

If you want you can get Sip to write a program using Assembly to help you resolve this question.

 

Okay here is the question:

 

(x+a)(x-(x+c)(x-d)(x+e)... All the way to ...(x-z)

What is the answer to this long polynomial.

 

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Is that all I wrote in my previous post? I am a bonehead.

 

I think I meant to say that we use to use Assembler all the time in a previous job where we wrote low lever monitoring tools for Mainframes and Unix server.