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    \$\begingroup\$ Out of curiosity, is this related to a problem of broader mathematical interest or just a fun puzzle? \$\endgroup\$ Commented Mar 28, 2021 at 19:50
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    \$\begingroup\$ @Jonah—just a puzzle! But I did publish an OEIS sequence back in 2017 about a related problem: A289523. \$\endgroup\$ Commented Mar 28, 2021 at 19:52
  • \$\begingroup\$ Thank you for an interesting challenge! Little later I'd like post here full answer on Mathematica, may be not for real challenge, just for survey. But for now I've found some intriguing detail: Input: RegionIntersection[Circle[{6,-6}, 3],Circle[{3,-2},2] Output: Point[{21/5,-(18/5)}] So the question arose: should tangent circles be considered an overlap? Looks like all answers here suppose "not" and include (6,-6). \$\endgroup\$ Commented Jan 13, 2023 at 10:29
  • \$\begingroup\$ @lesobrod—it's been a while since I've thought about this, but I think the circles should have radius \$\sqrt{3}\$ and \$\sqrt{2}\$ in order for their areas to be \$3\pi\$ and \$2\pi\$ respectively. \$\endgroup\$ Commented Jan 13, 2023 at 16:29
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    \$\begingroup\$ @lesobrod—That's two embarrassing oversights! I suppose to keep things consistent with how things have been, it's only fair to say that for the purposes of this challenge, tangent circles don't overlap. I've modified the question to specify "open" circles (which are, mathematically speaking, really open disks.) – \$\endgroup\$ Commented Jan 14, 2023 at 23:57