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The consecutive sides of an equiangular hexagon measure $$x$$, $$y$$, 2, 2006, 3, 2007 units
In an equiangular hexagon with consecutive sides $$a_1, \ldots, a_6$$, opposite sides satisfy $$a_1 - a_4 = a_5 - a_2 = a_3 - a_6$$. Here $$a_3 - a_6 = 2 - 2007 = -2005$$, so $$x - 2006 = -2005$$ gives $$x = 1$$ and $$3 - y = -2005$$ gives $$y = 2008$$. The sides are 1, 2008, 2, 2006, 3, 2007, so the smallest is $$x$$ and the greatest is $$y$$.
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