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Forum: Competition Questions
Welcome to the Competition Questions forum!
For discussing problems from mathematics competitions.

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while on factorizations.... by drini on 2003-11-29 01:19:12
a fun factorization problem)
(from some russian math olympiad book)

Factor
x^10 + x^5 + 1

neat!
 f
G -----> H G
p \ /_ ----- ~ f(G)
 \ / f ker f
 G/ker f 
[ reply | up ]
probability problem by gongli on 2003-09-02 20:21:26
A professor gave this challenge problem to his students in a probability course.
Prove that the sum of two discrete random variables both defined on the same finite sample space of size N cannot have a uniform distribution.
The professor said that the solution to this problem was known
only for even (or odd) N ( I forget which just now).
Is this true? Is no solution known for general N?

[ reply | up ]
A fun problem by alozano on 2003-08-18 17:15:39
Hi "all",

I came across this amusing problem and I thought a number of you might enjoy solving it:

One day three mathematicians were hanging out, $\mathcal{A}$, $\Sum$, and $\Prod$. $\mathcal{A}$ thought of two natural numbers $x,y$ such that

$$1<x,y \quad and \quad x \cdot y < 100$$

and, in secret he told $\Sum$ their sum ($x+y$), and he told $\Prod$ their product ($x \cdot y$). Then $\Prod$ spoke first:

$\Prod$: I cannot know the numbers $x$ and $y$.

$\Sum$: Hmmm, I knew you would not know the numbers.

$\Prod$: Aha!, then I know the numbers $x$ and $y$!

$\Sum$: I see! then I know the numbers too!

So, what are the numbers $x$ and $y$?

( I believe the problem was proposed by Martin Gardner )
[ reply | up ]
A Competition Announcement by HH on 2002-08-11 21:25:47
I'm not sure that this is what this forum is about, but I've heard about a new competition and so I thought of sharing it. You can find it at:

http://members.aol.com/bitzenbeitz/Contests/Triangles/Description.html
[ reply | up ]

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