# 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”

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