Problem Reference

(ported from wiki)

Certain notable problems that I don’t want to look through a zillion pages to find.

• Iran TST 1996, notoriously reposted at least 35 times on AoPS (okay, many of these are actually modifications):

  If \(x, y, z > 0\) then

  \[(xy+yz+zx)\left(\frac{1}{(x+y)^2} + \frac{1}{(y+z)^2} + \frac{1}{(z+x)^2}\right) \geq \frac{9}{4}\]
• ISL 1988 #4: if \(1, 2, \ldots, n^2\) are placed in a \(n \times n\) chessboard, some two adjacent numbers differ by at least \(n\)
• USAMO 1995.2: any positive rational can be obtained from applying some sequence of \(\sin, \cos, \tan, \arcsin, \arccos, \arctan\) to 0
• USAMO 1996.6: there’s a set \(S\) such that for any integer \(n\), \(a + 2b = n\) has exactly one solution for \(a, b \in S\)
• APMO 1994.4: there exists an infinite set of points, no three collinear, such that the distance between any two points is rational
• TT 2009 Fall Senior A (PDF).6: Anna and Ben on Archipelago; .7: Ali Baba vs the rotating round table. Extension: ELMO 2012.6
• TT 2010 Fall Senior A (PDF).7: diagonal bisecting important rectangles.
• TT 2001 Spring Senior A (PDF).7: hiring programmers to get “geniuses”