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Euclid
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Martin

Posted: Tue Apr 22, 2003 3:35 pm   Post subject: (No subject)

Question 10:
An integer n is 'savage' if it fits the following cases
The set {1,2,3,...,n} can be divided into three groups so that all of the following is true:

Group A contains only odd numbers
Group B contains only even numbers
Group C contains all of the multiples of three (it can contain other numbers as well)

and
The sum of all three groups is the same.

Now for the actual question (3 parts)
a) Show that 8 is a 'savage' number
b) Prove that for every even 'savage' number, (n+4)/12 is an integer
c) Find every prime 'savage' number less than 100.

Remember, this is math, not computer science. Couldn't even have graphing calculators.

Prince

Posted: Tue Apr 22, 2003 5:00 pm   Post subject: (No subject)

wtf?!?!?!... dats ONE question
Catalyst

Posted: Tue Apr 22, 2003 5:55 pm   Post subject: (No subject)

math contests tend to be like that...
yuethomas

Posted: Tue Apr 22, 2003 8:58 pm   Post subject: (No subject)

I got part a and 3/4 of part b done. Didn't have time to start part c.

(P.S. 8 is a savage number as 1~8 can be divided into
A = {5,7}
B = {4,8}
C = {1,2,3,6} )
Office of the Registar

Posted: Fri Apr 25, 2003 9:06 am   Post subject: (No subject)

i did this math contest and that was the last question rite?
man, i blanked out on that
i guess i needed one more year of experience...
Martin

Posted: Fri Apr 25, 2003 11:32 pm   Post subject: (No subject)

Sad thing is, part a)'s only worth 2 of the 10 marks
Crono

Posted: Sun May 11, 2003 1:39 pm   Post subject: (No subject)

hey i saw tis post n wuz like "woh, tom's here", lol, wut's goin on tom? u comin to waterloo tis year?

euclid wuz easy, but long, i didnt have time to finish the last one, o wellz, i'll b happy wit my 90...lol
bugzpodder

Posted: Thu May 22, 2003 4:19 pm   Post subject: (No subject)

98 on euclid for me ^.^;
hypatia question 3, i think it is if you have a cylinder and sphere, both have the same radius, and the sphere is half the height of the cylinder (or was it the other way around). and you have a plane parallel to the ground level cut through both objects, what value of the height of plane will make the area of the cylinder equal to area of the sphere.

the cylinder part is easy, the sphere, you gotta realize do pythagoras. let the radius of the area be r, and radius of sphere be R. so basically:
r^2+(h-R)^2=R^2

SilverSprite

Posted: Wed Jun 18, 2003 1:10 pm   Post subject: (No subject)

I got 75 on the Euclid.. shitty time limit.. Why did Mr White put me next to the window sooo distracting.. anyways yeah.. I did ok.. I tripled my score from last year:D
Andy

Posted: Wed Jun 18, 2003 2:58 pm   Post subject: (No subject)

hmmm our math exams has 2 questions from the Euclid, lucky me and SilverSprite and Hello and AsianSensation
AsianSensation

Posted: Wed Jun 18, 2003 3:30 pm   Post subject: (No subject)

I sucked big time on the Euclid, I only did 7 questions, got 69, ran out of time, spent all my time doing the hexagon and the cannon one. I redid those questions like 4 times each, cuz i kept on getting different answers, stupid mechanical errors .oh well, just have to learn to work faster next time.
Andy

Posted: Wed Jun 18, 2003 3:49 pm   Post subject: (No subject)

meng the cannon one is easy, y do you think it was on our math exam?
JayLo

Posted: Wed Jun 18, 2003 4:00 pm   Post subject: (No subject)

man! i don't even think our school has Euclid.

Posted: Wed Jun 18, 2003 5:52 pm   Post subject: (No subject)

these contests they are talking about are ones offered by the University of Waterloo...

I only did the open one this year, it was pretty straight forward except for part C and I think one question in part B that had all these angles and something about light reflecting or something... even a couple of the teachers looked at it and were like wtf... I can't remember how I did though, I think like 2nd or 3rd in my school, so not too good I don't think
JayLo

Posted: Wed Jun 18, 2003 5:55 pm   Post subject: (No subject)

so it's purely math? at what level? better start preparing...
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