Back-to-back USAMO and IMO problems in one day!

by shiningsunnyday, Jun 23, 2016, 2:47 PM

1997 IMO P4 wrote:
An $ n \times n$ matrix whose entries come from the set $ S = \{1, 2, \ldots , 2n - 1\}$ is called a silver matrix if, for each $ i = 1, 2, \ldots , n$, the $ i$-th row and the $ i$-th column together contain all elements of $ S$. Show that silver matrices exist for infinitely many values of $ n$.
Solution
Remark
Tidbit
P33 of 101 wrote:
Let $m,n$ be distinct positive integers. Find the maximum value of $|x^m-x^n|,$ where $x$ is a real number within $(0,1).$
Solution
Remark
This post has been edited 1 time. Last edited by shiningsunnyday, Jun 23, 2016, 2:48 PM

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According to this, IMO 1/4s are slightly easier than USAMO 1/4s. Don't know why.

Er mainly so most contestants can try to at least get one right.
This post has been edited 1 time. Last edited by shiningsunnyday, Jun 24, 2016, 1:54 AM

by MathAwesome123, Jun 23, 2016, 4:32 PM

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Wait what classes are you taking at AwesomeMath?

Combo 3 and Geo 3
This post has been edited 1 time. Last edited by shiningsunnyday, Jul 1, 2016, 1:57 PM

by pinetree1, Jun 30, 2016, 3:54 PM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

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