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If I have a disk $d$ where each point of the disk is contained in at least $k$ other disks, then at least how many other disks does $d$ intersect?

Given, that all the disks (including $d$) have the same radius, and no two disks have the same coordiante.

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yes $d$ too has same radius, but I'm not sure if I understand your remark. –  stefan Sep 14 '11 at 3:34
    
Oh, I think I get it: each point in $d$ is contained in at least $k$ other disks, but not necessarily the same disks. –  anon Sep 14 '11 at 3:41
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A simple upper limit is $3k$. Each disk passes through the center of $d$ and is clocked from the first one by $\frac{2\pi}{3k}$. If one of the covering disks is allowed to match $d$ we get $3k-2$. But one can probably do better.

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