Friday, 25 October 2013

Dragons take up 1 x 1 squares

Dragons take up 1 x 1 squares in the plane with sides parallel to the coordinate axes such that
the interiors of the squares do not intersect. A dragon can re at another dragoon if the di fference in
the x-coordinates of their centers and the diff erence in the y-coordinates of their centers are both
atmost 6, regardless of any dragons in between. For example, a dragon centered at (4, 5) can fire at
a dragon centered at the origin, but a dragon centered at (7, 0) cannot. A dragon cannot fi re at
itself. What is the maximum number of dragons that can fire at a single dragon simultaneously?

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Define f:RR by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \ 0, ...