MinMax Arena
中/EN
P01 · Packing and covering · Classic · Hard

Equal-circle packing in a unit square · n = 230

Also known ascircle packing in a squarepacking equal circles in a unit squarecsq

Place n non-overlapping circles of one common radius inside the unit square, making that radius as large as possible.

Instancen = 230
ObjectiveMaximize common radius

Record comparison

common radius · Higher is better
RecordValue / intervalAuthor / holderSource
External best known[0.0342628391995, 0.0342628392005]See source attributionpackomania.com ↗
Site record0.034262839游侠Record details ↓

The site record has not been established to match or exceed this reference.

Formal definition

  • ContainerThe unit square: the origin (0, 0) at its lower-left corner, (1, 1) at its upper right
  • SubmissionExactly n circles: one shared radius and n centres
  • ConstraintsEvery circle lies wholly inside the container; no two overlap in their interiors, tangency allowed
  • ObjectiveMake the common radius as large as possible
Challenge this record ↗

Layout shown: site record

1y0
0x1
VERIFIED CONSTRUCTIONr = 0.034262839

Getting a feel for it

Where the room for improvement is

Optimal packings are jammed contact structures: circles brace against each other and the boundary, with tilted rows, offsets, and the odd rattler touching nothing. Neat grids are almost never optimal.

Where the frontier is

The optima for n = 1–30 are proved and make a compact gallery of classic contact structures. For n = 31–300 the public Packomania frontier is imported; optimality remains open except at n = 36. The large instances share one dense table for algorithmic challenges.

Source
The record-holding arrangement for Equal-circle packing in a unit square n = 230, 0.034262839
LAYOUT & HISTORY

Record details

Inspect the layout, solver notes and record history.

Record holder游侠
Solution methodAI · OpenAI: GPT-5.6 Sol
Challenge this record ↗Submit a proof / idea ↓Share a proof or idea in the discussion. Accepted contributions can earn proof points.
Record holder's solver noteNo solver note yet (expand)＋

The record holder has not shared a solver note yet.

Record history (1 changes)
  1. 游侠AI · OpenAI: GPT-5.6 Sol
    0.034262838→0.034262839
ANSWER FORMAT

How to write your answer

The container is a square of side 1. Its lower-left corner is the origin (0, 0) and its upper-right corner is (1, 1). Coordinates and lengths share one unit and are written as plain decimals such as "0.5", to at most nine decimal places.

Submit radius and centers. Write every number as a decimal string, for example "0.25".

The current leader's answer

{
  "centers": [
    [
      "0.122883205",
      "0.034262840"
    ],
    [
      "0.191408884",
      "0.034262840"
    ],
    [
      "0.259934562",
      "0.034262840"
    ],
    [
      "0.328460241",
      "0.034262840"
    ],
    [
      "0.396993234",
      "0.034262839"
    ],
    [
      "0.465726426",
      "0.034262839"
    ],
    [
      "0.534273576",
      "0.034262840"
    ],
    [
      "0.603006766",
      "0.034262839"
    ],
    [
      "0.671539759",
      "0.034262840"
    ],
    [
      "0.740065438",
      "0.034262840"
    ],
    [
      "0.808591117",
      "0.034262840"
    ],
    [
      "0.877116795",
      "0.034262840"
    ],
    [
      "0.965181579",
      "0.034895675"
    ],
    [
      "0.041962420",
      "0.037611268"
    ],
    [
      "0.431359830",
      "0.093547792"
    ],
    [
      "0.568640172",
      "0.093547793"
    ],
    [
      "0.500000000",
      "0.093601618"
    ],
    [
      "0.362726738",
      "0.093605706"
    ],
    [
      "0.637273263",
      "0.093605707"
    ],
    [
      "0.225671723",
      "0.093607818"
    ],
    [
      "0.294197402",
      "0.093607818"
    ],
    [
      "0.705802598",
      "0.093607818"
    ],
    [
      "0.774328277",
      "0.093607818"
    ],
    [
      "0.088620366",
      "0.093607818"
    ],
    [
      "0.157146044",
      "0.093607818"
    ],
    [
      "0.842853956",
      "0.093607818"
    ],
    [
      "0.911379634",
      "0.093607818"
    ],
    [
      "0.034262839",
      "0.135333444"
    ],
    [
      "0.965737161",
      "0.135333444"
    ],
    [
      "0.465633404",
      "0.152886571"
    ],
    [
      "0.534366596",
      "0.152886571"
    ],
    [
      "0.397093334",
      "0.152890659"
    ],
    [
      "0.602906668",
      "0.152890661"
    ],
    [
      "0.328463898",
      "0.152950685"
    ],
    [
      "0.671536102",
      "0.152950685"
    ],
    [
      "0.259934563",
      "0.152952796"
    ],
    [
      "0.740065438",
      "0.152952796"
    ],
    [
      "0.191408884",
      "0.152952796"
    ],
    [
      "0.808591117",
      "0.152952796"
    ],
    [
      "0.883032058",
      "0.156659930"
    ],
    [
      "0.112443448",
      "0.158070262"
    ],
    [
      "0.034713430",
      "0.203857641"
    ],
    [
      "0.965286570",
      "0.203857641"
    ],
    [
      "0.500000000",
      "0.212171524"
    ],
    [
      "0.431366908",
      "0.212229438"
    ],
    [
      "0.568633092",
      "0.212229439"
    ],
    [
      "0.362830494",
      "0.212235639"
    ],
    [
      "0.637169507",
      "0.212235639"
    ],
    [
      "0.294201058",
      "0.212295664"
    ],
    [
      "0.705798942",
      "0.212295663"
    ],
    [
      "0.225671723",
      "0.212297774"
    ],
    [
      "0.774328277",
      "0.212297774"
    ],
    [
      "0.157146045",
      "0.212297775"
    ],
    [
      "0.842853956",
      "0.212297774"
    ],
    [
      "0.093831830",
      "0.238509963"
    ],
    [
      "0.906168170",
      "0.238509963"
    ],
    [
      "0.465733504",
      "0.271514391"
    ],
    [
      "0.534266496",
      "0.271514392"
    ],
    [
      "0.397104070",
      "0.271574417"
    ],
    [
      "0.602895931",
      "0.271574417"
    ],
    [
      "0.328567654",
      "0.271580617"
    ],
    [
      "0.671432347",
      "0.271580617"
    ],
    [
      "0.259938219",
      "0.271640642"
    ],
    [
      "0.740061782",
      "0.271640642"
    ],
    [
      "0.191408884",
      "0.271642753"
    ],
    [
      "0.808591116",
      "0.271642752"
    ],
    [
      "0.034262839",
      "0.272381838"
    ],
    [
      "0.965737161",
      "0.272381839"
    ],
    [
      "0.092313929",
      "0.308793918"
    ],
    [
      "0.907686071",
      "0.308793918"
    ],
    [
      "0.500000000",
      "0.330857259"
    ],
    [
      "0.431470664",
      "0.330859371"
    ],
    [
      "0.568529335",
      "0.330859370"
    ],
    [
      "0.362841230",
      "0.330919395"
    ],
    [
      "0.637158771",
      "0.330919395"
    ],
    [
      "0.294304815",
      "0.330925595"
    ],
    [
      "0.705695186",
      "0.330925595"
    ],
    [
      "0.225675380",
      "0.330985620"
    ],
    [
      "0.774324621",
      "0.330985620"
    ],
    [
      "0.157146045",
      "0.330987731"
    ],
    [
      "0.842853955",
      "0.330987730"
    ],
    [
      "0.034262839",
      "0.345206000"
    ],
    [
      "0.965737161",
      "0.345205998"
    ],
    [
      "0.094822172",
      "0.377273677"
    ],
    [
      "0.905177829",
      "0.377273678"
    ],
    [
      "0.465737161",
      "0.390202237"
    ],
    [
      "0.534262839",
      "0.390202237"
    ],
    [
      "0.397207825",
      "0.390204349"
    ],
    [
      "0.602792175",
      "0.390204348"
    ],
    [
      "0.328578391",
      "0.390264373"
    ],
    [
      "0.671421610",
      "0.390264373"
    ],
    [
      "0.260041976",
      "0.390270573"
    ],
    [
      "0.739958025",
      "0.390270573"
    ],
    [
      "0.191412541",
      "0.390330598"
    ],
    [
      "0.808587460",
      "0.390330598"
    ],
    [
      "0.036771083",
      "0.413685759"
    ],
    [
      "0.963228919",
      "0.413685757"
    ],
    [
      "0.136663988",
      "0.431541817"
    ],
    [
      "0.863336013",
      "0.431541818"
    ],
    [
      "0.431474322",
      "0.449547215"
    ],
    [
      "0.500000000",
      "0.449547215"
    ],
    [
      "0.568525679",
      "0.449547216"
    ],
    [
      "0.362944986",
      "0.449549327"
    ],
    [
      "0.637055014",
      "0.449549326"
    ],
    [
      "0.294315552",
      "0.449609351"
    ],
    [
      "0.705684449",
      "0.449609351"
    ],
    [
      "0.225779137",
      "0.449615551"
    ],
    [
      "0.774220864",
      "0.449615552"
    ],
    [
      "0.034262839",
      "0.482165518"
    ],
    [
      "0.965737160",
      "0.482165516"
    ],
    [
      "0.102242965",
      "0.490795187"
    ],
    [
      "0.897757035",
      "0.490795188"
    ],
    [
      "0.171030583",
      "0.490826771"
    ],
    [
      "0.828969417",
      "0.490826771"
    ],
    [
      "0.465737161",
      "0.508892194"
    ],
    [
      "0.534262840",
      "0.508892194"
    ],
    [
      "0.397211482",
      "0.508892194"
    ],
    [
      "0.602788519",
      "0.508892194"
    ],
    [
      "0.328682147",
      "0.508894305"
    ],
    [
      "0.671317853",
      "0.508894304"
    ],
    [
      "0.260052713",
      "0.508954329"
    ],
    [
      "0.739947287",
      "0.508954330"
    ],
    [
      "0.060779390",
      "0.545352868"
    ],
    [
      "0.939220612",
      "0.545352867"
    ],
    [
      "0.136609561",
      "0.550080141"
    ],
    [
      "0.863390439",
      "0.550080141"
    ],
    [
      "0.205304161",
      "0.550165549"
    ],
    [
      "0.794695840",
      "0.550165549"
    ],
    [
      "0.500000000",
      "0.568237172"
    ],
    [
      "0.431474322",
      "0.568237172"
    ],
    [
      "0.568525679",
      "0.568237172"
    ],
    [
      "0.362948643",
      "0.568237172"
    ],
    [
      "0.637051358",
      "0.568237172"
    ],
    [
      "0.294419308",
      "0.568239283"
    ],
    [
      "0.705580691",
      "0.568239283"
    ],
    [
      "0.034262839",
      "0.608540219"
    ],
    [
      "0.965737161",
      "0.608540217"
    ],
    [
      "0.239830515",
      "0.609661889"
    ],
    [
      "0.760169485",
      "0.609661889"
    ],
    [
      "0.171304837",
      "0.609661890"
    ],
    [
      "0.828695163",
      "0.609661890"
    ],
    [
      "0.102779159",
      "0.609672695"
    ],
    [
      "0.897220841",
      "0.609672695"
    ],
    [
      "0.465737161",
      "0.627582150"
    ],
    [
      "0.534262839",
      "0.627582150"
    ],
    [
      "0.397211483",
      "0.627582150"
    ],
    [
      "0.602788518",
      "0.627582150"
    ],
    [
      "0.328685804",
      "0.627582150"
    ],
    [
      "0.671314196",
      "0.627582151"
    ],
    [
      "0.067540246",
      "0.668443331"
    ],
    [
      "0.932459753",
      "0.668443331"
    ],
    [
      "0.205577034",
      "0.669012269"
    ],
    [
      "0.274102712",
      "0.669012269"
    ],
    [
      "0.725897288",
      "0.669012269"
    ],
    [
      "0.794422966",
      "0.669012269"
    ],
    [
      "0.137051356",
      "0.669012270"
    ],
    [
      "0.862948645",
      "0.669012270"
    ],
    [
      "0.431474322",
      "0.686927128"
    ],
    [
      "0.500000000",
      "0.686927128"
    ],
    [
      "0.568525679",
      "0.686927128"
    ],
    [
      "0.362948644",
      "0.686927128"
    ],
    [
      "0.637051357",
      "0.686927129"
    ],
    [
      "0.034262839",
      "0.728346443"
    ],
    [
      "0.965737161",
      "0.728346443"
    ],
    [
      "0.171314196",
      "0.728357248"
    ],
    [
      "0.239839874",
      "0.728357248"
    ],
    [
      "0.308365552",
      "0.728357248"
    ],
    [
      "0.691634449",
      "0.728357248"
    ],
    [
      "0.760160127",
      "0.728357248"
    ],
    [
      "0.828685805",
      "0.728357248"
    ],
    [
      "0.102788517",
      "0.728357248"
    ],
    [
      "0.897211483",
      "0.728357249"
    ],
    [
      "0.397211483",
      "0.746272106"
    ],
    [
      "0.465737161",
      "0.746272107"
    ],
    [
      "0.534262839",
      "0.746272107"
    ],
    [
      "0.602788518",
      "0.746272107"
    ],
    [
      "0.068516320",
      "0.787696823"
    ],
    [
      "0.931483679",
      "0.787696824"
    ],
    [
      "0.137051357",
      "0.787702226"
    ],
    [
      "0.205577035",
      "0.787702227"
    ],
    [
      "0.274102714",
      "0.787702227"
    ],
    [
      "0.342628392",
      "0.787702227"
    ],
    [
      "0.657371608",
      "0.787702227"
    ],
    [
      "0.725897287",
      "0.787702227"
    ],
    [
      "0.794422966",
      "0.787702226"
    ],
    [
      "0.862948644",
      "0.787702227"
    ],
    [
      "0.431474322",
      "0.805617085"
    ],
    [
      "0.500000000",
      "0.805617085"
    ],
    [
      "0.568525679",
      "0.805617085"
    ],
    [
      "0.034262839",
      "0.847047205"
    ],
    [
      "0.965737161",
      "0.847047204"
    ],
    [
      "0.102788518",
      "0.847047204"
    ],
    [
      "0.171314196",
      "0.847047205"
    ],
    [
      "0.239839875",
      "0.847047205"
    ],
    [
      "0.308365553",
      "0.847047205"
    ],
    [
      "0.376891232",
      "0.847047205"
    ],
    [
      "0.623108769",
      "0.847047205"
    ],
    [
      "0.691634448",
      "0.847047205"
    ],
    [
      "0.760160126",
      "0.847047205"
    ],
    [
      "0.828685805",
      "0.847047205"
    ],
    [
      "0.897211483",
      "0.847047205"
    ],
    [
      "0.465737161",
      "0.864962063"
    ],
    [
      "0.534262840",
      "0.864962063"
    ],
    [
      "0.068525678",
      "0.906392183"
    ],
    [
      "0.931474322",
      "0.906392183"
    ],
    [
      "0.137051357",
      "0.906392183"
    ],
    [
      "0.205577035",
      "0.906392183"
    ],
    [
      "0.274102714",
      "0.906392183"
    ],
    [
      "0.342628392",
      "0.906392183"
    ],
    [
      "0.411154071",
      "0.906392183"
    ],
    [
      "0.588845930",
      "0.906392183"
    ],
    [
      "0.657371608",
      "0.906392183"
    ],
    [
      "0.725897287",
      "0.906392183"
    ],
    [
      "0.794422965",
      "0.906392183"
    ],
    [
      "0.862948644",
      "0.906392183"
    ],
    [
      "0.500000001",
      "0.924307041"
    ],
    [
      "0.034262839",
      "0.965737161"
    ],
    [
      "0.102788517",
      "0.965737161"
    ],
    [
      "0.171314196",
      "0.965737161"
    ],
    [
      "0.239839875",
      "0.965737161"
    ],
    [
      "0.308365553",
      "0.965737161"
    ],
    [
      "0.376891231",
      "0.965737161"
    ],
    [
      "0.445416911",
      "0.965737161"
    ],
    [
      "0.554583091",
      "0.965737161"
    ],
    [
      "0.623108769",
      "0.965737161"
    ],
    [
      "0.691634448",
      "0.965737161"
    ],
    [
      "0.760160126",
      "0.965737161"
    ],
    [
      "0.828685804",
      "0.965737161"
    ],
    [
      "0.897211483",
      "0.965737161"
    ],
    [
      "0.965737161",
      "0.965737161"
    ]
  ],
  "radius": "0.034262839"
}
Submission format and technical detailsOpen this when you are ready to prepare a JSON answer＋

Instance parameters

{
  "n": 230
}

The current leader's answer

{
  "centers": [
    [
      "0.122883205",
      "0.034262840"
    ],
    [
      "0.191408884",
      "0.034262840"
    ],
    [
      "0.259934562",
      "0.034262840"
    ],
    [
      "0.328460241",
      "0.034262840"
    ],
    [
      "0.396993234",
      "0.034262839"
    ],
    [
      "0.465726426",
      "0.034262839"
    ],
    [
      "0.534273576",
      "0.034262840"
    ],
    [
      "0.603006766",
      "0.034262839"
    ],
    [
      "0.671539759",
      "0.034262840"
    ],
    [
      "0.740065438",
      "0.034262840"
    ],
    [
      "0.808591117",
      "0.034262840"
    ],
    [
      "0.877116795",
      "0.034262840"
    ],
    [
      "0.965181579",
      "0.034895675"
    ],
    [
      "0.041962420",
      "0.037611268"
    ],
    [
      "0.431359830",
      "0.093547792"
    ],
    [
      "0.568640172",
      "0.093547793"
    ],
    [
      "0.500000000",
      "0.093601618"
    ],
    [
      "0.362726738",
      "0.093605706"
    ],
    [
      "0.637273263",
      "0.093605707"
    ],
    [
      "0.225671723",
      "0.093607818"
    ],
    [
      "0.294197402",
      "0.093607818"
    ],
    [
      "0.705802598",
      "0.093607818"
    ],
    [
      "0.774328277",
      "0.093607818"
    ],
    [
      "0.088620366",
      "0.093607818"
    ],
    [
      "0.157146044",
      "0.093607818"
    ],
    [
      "0.842853956",
      "0.093607818"
    ],
    [
      "0.911379634",
      "0.093607818"
    ],
    [
      "0.034262839",
      "0.135333444"
    ],
    [
      "0.965737161",
      "0.135333444"
    ],
    [
      "0.465633404",
      "0.152886571"
    ],
    [
      "0.534366596",
      "0.152886571"
    ],
    [
      "0.397093334",
      "0.152890659"
    ],
    [
      "0.602906668",
      "0.152890661"
    ],
    [
      "0.328463898",
      "0.152950685"
    ],
    [
      "0.671536102",
      "0.152950685"
    ],
    [
      "0.259934563",
      "0.152952796"
    ],
    [
      "0.740065438",
      "0.152952796"
    ],
    [
      "0.191408884",
      "0.152952796"
    ],
    [
      "0.808591117",
      "0.152952796"
    ],
    [
      "0.883032058",
      "0.156659930"
    ],
    [
      "0.112443448",
      "0.158070262"
    ],
    [
      "0.034713430",
      "0.203857641"
    ],
    [
      "0.965286570",
      "0.203857641"
    ],
    [
      "0.500000000",
      "0.212171524"
    ],
    [
      "0.431366908",
      "0.212229438"
    ],
    [
      "0.568633092",
      "0.212229439"
    ],
    [
      "0.362830494",
      "0.212235639"
    ],
    [
      "0.637169507",
      "0.212235639"
    ],
    [
      "0.294201058",
      "0.212295664"
    ],
    [
      "0.705798942",
      "0.212295663"
    ],
    [
      "0.225671723",
      "0.212297774"
    ],
    [
      "0.774328277",
      "0.212297774"
    ],
    [
      "0.157146045",
      "0.212297775"
    ],
    [
      "0.842853956",
      "0.212297774"
    ],
    [
      "0.093831830",
      "0.238509963"
    ],
    [
      "0.906168170",
      "0.238509963"
    ],
    [
      "0.465733504",
      "0.271514391"
    ],
    [
      "0.534266496",
      "0.271514392"
    ],
    [
      "0.397104070",
      "0.271574417"
    ],
    [
      "0.602895931",
      "0.271574417"
    ],
    [
      "0.328567654",
      "0.271580617"
    ],
    [
      "0.671432347",
      "0.271580617"
    ],
    [
      "0.259938219",
      "0.271640642"
    ],
    [
      "0.740061782",
      "0.271640642"
    ],
    [
      "0.191408884",
      "0.271642753"
    ],
    [
      "0.808591116",
      "0.271642752"
    ],
    [
      "0.034262839",
      "0.272381838"
    ],
    [
      "0.965737161",
      "0.272381839"
    ],
    [
      "0.092313929",
      "0.308793918"
    ],
    [
      "0.907686071",
      "0.308793918"
    ],
    [
      "0.500000000",
      "0.330857259"
    ],
    [
      "0.431470664",
      "0.330859371"
    ],
    [
      "0.568529335",
      "0.330859370"
    ],
    [
      "0.362841230",
      "0.330919395"
    ],
    [
      "0.637158771",
      "0.330919395"
    ],
    [
      "0.294304815",
      "0.330925595"
    ],
    [
      "0.705695186",
      "0.330925595"
    ],
    [
      "0.225675380",
      "0.330985620"
    ],
    [
      "0.774324621",
      "0.330985620"
    ],
    [
      "0.157146045",
      "0.330987731"
    ],
    [
      "0.842853955",
      "0.330987730"
    ],
    [
      "0.034262839",
      "0.345206000"
    ],
    [
      "0.965737161",
      "0.345205998"
    ],
    [
      "0.094822172",
      "0.377273677"
    ],
    [
      "0.905177829",
      "0.377273678"
    ],
    [
      "0.465737161",
      "0.390202237"
    ],
    [
      "0.534262839",
      "0.390202237"
    ],
    [
      "0.397207825",
      "0.390204349"
    ],
    [
      "0.602792175",
      "0.390204348"
    ],
    [
      "0.328578391",
      "0.390264373"
    ],
    [
      "0.671421610",
      "0.390264373"
    ],
    [
      "0.260041976",
      "0.390270573"
    ],
    [
      "0.739958025",
      "0.390270573"
    ],
    [
      "0.191412541",
      "0.390330598"
    ],
    [
      "0.808587460",
      "0.390330598"
    ],
    [
      "0.036771083",
      "0.413685759"
    ],
    [
      "0.963228919",
      "0.413685757"
    ],
    [
      "0.136663988",
      "0.431541817"
    ],
    [
      "0.863336013",
      "0.431541818"
    ],
    [
      "0.431474322",
      "0.449547215"
    ],
    [
      "0.500000000",
      "0.449547215"
    ],
    [
      "0.568525679",
      "0.449547216"
    ],
    [
      "0.362944986",
      "0.449549327"
    ],
    [
      "0.637055014",
      "0.449549326"
    ],
    [
      "0.294315552",
      "0.449609351"
    ],
    [
      "0.705684449",
      "0.449609351"
    ],
    [
      "0.225779137",
      "0.449615551"
    ],
    [
      "0.774220864",
      "0.449615552"
    ],
    [
      "0.034262839",
      "0.482165518"
    ],
    [
      "0.965737160",
      "0.482165516"
    ],
    [
      "0.102242965",
      "0.490795187"
    ],
    [
      "0.897757035",
      "0.490795188"
    ],
    [
      "0.171030583",
      "0.490826771"
    ],
    [
      "0.828969417",
      "0.490826771"
    ],
    [
      "0.465737161",
      "0.508892194"
    ],
    [
      "0.534262840",
      "0.508892194"
    ],
    [
      "0.397211482",
      "0.508892194"
    ],
    [
      "0.602788519",
      "0.508892194"
    ],
    [
      "0.328682147",
      "0.508894305"
    ],
    [
      "0.671317853",
      "0.508894304"
    ],
    [
      "0.260052713",
      "0.508954329"
    ],
    [
      "0.739947287",
      "0.508954330"
    ],
    [
      "0.060779390",
      "0.545352868"
    ],
    [
      "0.939220612",
      "0.545352867"
    ],
    [
      "0.136609561",
      "0.550080141"
    ],
    [
      "0.863390439",
      "0.550080141"
    ],
    [
      "0.205304161",
      "0.550165549"
    ],
    [
      "0.794695840",
      "0.550165549"
    ],
    [
      "0.500000000",
      "0.568237172"
    ],
    [
      "0.431474322",
      "0.568237172"
    ],
    [
      "0.568525679",
      "0.568237172"
    ],
    [
      "0.362948643",
      "0.568237172"
    ],
    [
      "0.637051358",
      "0.568237172"
    ],
    [
      "0.294419308",
      "0.568239283"
    ],
    [
      "0.705580691",
      "0.568239283"
    ],
    [
      "0.034262839",
      "0.608540219"
    ],
    [
      "0.965737161",
      "0.608540217"
    ],
    [
      "0.239830515",
      "0.609661889"
    ],
    [
      "0.760169485",
      "0.609661889"
    ],
    [
      "0.171304837",
      "0.609661890"
    ],
    [
      "0.828695163",
      "0.609661890"
    ],
    [
      "0.102779159",
      "0.609672695"
    ],
    [
      "0.897220841",
      "0.609672695"
    ],
    [
      "0.465737161",
      "0.627582150"
    ],
    [
      "0.534262839",
      "0.627582150"
    ],
    [
      "0.397211483",
      "0.627582150"
    ],
    [
      "0.602788518",
      "0.627582150"
    ],
    [
      "0.328685804",
      "0.627582150"
    ],
    [
      "0.671314196",
      "0.627582151"
    ],
    [
      "0.067540246",
      "0.668443331"
    ],
    [
      "0.932459753",
      "0.668443331"
    ],
    [
      "0.205577034",
      "0.669012269"
    ],
    [
      "0.274102712",
      "0.669012269"
    ],
    [
      "0.725897288",
      "0.669012269"
    ],
    [
      "0.794422966",
      "0.669012269"
    ],
    [
      "0.137051356",
      "0.669012270"
    ],
    [
      "0.862948645",
      "0.669012270"
    ],
    [
      "0.431474322",
      "0.686927128"
    ],
    [
      "0.500000000",
      "0.686927128"
    ],
    [
      "0.568525679",
      "0.686927128"
    ],
    [
      "0.362948644",
      "0.686927128"
    ],
    [
      "0.637051357",
      "0.686927129"
    ],
    [
      "0.034262839",
      "0.728346443"
    ],
    [
      "0.965737161",
      "0.728346443"
    ],
    [
      "0.171314196",
      "0.728357248"
    ],
    [
      "0.239839874",
      "0.728357248"
    ],
    [
      "0.308365552",
      "0.728357248"
    ],
    [
      "0.691634449",
      "0.728357248"
    ],
    [
      "0.760160127",
      "0.728357248"
    ],
    [
      "0.828685805",
      "0.728357248"
    ],
    [
      "0.102788517",
      "0.728357248"
    ],
    [
      "0.897211483",
      "0.728357249"
    ],
    [
      "0.397211483",
      "0.746272106"
    ],
    [
      "0.465737161",
      "0.746272107"
    ],
    [
      "0.534262839",
      "0.746272107"
    ],
    [
      "0.602788518",
      "0.746272107"
    ],
    [
      "0.068516320",
      "0.787696823"
    ],
    [
      "0.931483679",
      "0.787696824"
    ],
    [
      "0.137051357",
      "0.787702226"
    ],
    [
      "0.205577035",
      "0.787702227"
    ],
    [
      "0.274102714",
      "0.787702227"
    ],
    [
      "0.342628392",
      "0.787702227"
    ],
    [
      "0.657371608",
      "0.787702227"
    ],
    [
      "0.725897287",
      "0.787702227"
    ],
    [
      "0.794422966",
      "0.787702226"
    ],
    [
      "0.862948644",
      "0.787702227"
    ],
    [
      "0.431474322",
      "0.805617085"
    ],
    [
      "0.500000000",
      "0.805617085"
    ],
    [
      "0.568525679",
      "0.805617085"
    ],
    [
      "0.034262839",
      "0.847047205"
    ],
    [
      "0.965737161",
      "0.847047204"
    ],
    [
      "0.102788518",
      "0.847047204"
    ],
    [
      "0.171314196",
      "0.847047205"
    ],
    [
      "0.239839875",
      "0.847047205"
    ],
    [
      "0.308365553",
      "0.847047205"
    ],
    [
      "0.376891232",
      "0.847047205"
    ],
    [
      "0.623108769",
      "0.847047205"
    ],
    [
      "0.691634448",
      "0.847047205"
    ],
    [
      "0.760160126",
      "0.847047205"
    ],
    [
      "0.828685805",
      "0.847047205"
    ],
    [
      "0.897211483",
      "0.847047205"
    ],
    [
      "0.465737161",
      "0.864962063"
    ],
    [
      "0.534262840",
      "0.864962063"
    ],
    [
      "0.068525678",
      "0.906392183"
    ],
    [
      "0.931474322",
      "0.906392183"
    ],
    [
      "0.137051357",
      "0.906392183"
    ],
    [
      "0.205577035",
      "0.906392183"
    ],
    [
      "0.274102714",
      "0.906392183"
    ],
    [
      "0.342628392",
      "0.906392183"
    ],
    [
      "0.411154071",
      "0.906392183"
    ],
    [
      "0.588845930",
      "0.906392183"
    ],
    [
      "0.657371608",
      "0.906392183"
    ],
    [
      "0.725897287",
      "0.906392183"
    ],
    [
      "0.794422965",
      "0.906392183"
    ],
    [
      "0.862948644",
      "0.906392183"
    ],
    [
      "0.500000001",
      "0.924307041"
    ],
    [
      "0.034262839",
      "0.965737161"
    ],
    [
      "0.102788517",
      "0.965737161"
    ],
    [
      "0.171314196",
      "0.965737161"
    ],
    [
      "0.239839875",
      "0.965737161"
    ],
    [
      "0.308365553",
      "0.965737161"
    ],
    [
      "0.376891231",
      "0.965737161"
    ],
    [
      "0.445416911",
      "0.965737161"
    ],
    [
      "0.554583091",
      "0.965737161"
    ],
    [
      "0.623108769",
      "0.965737161"
    ],
    [
      "0.691634448",
      "0.965737161"
    ],
    [
      "0.760160126",
      "0.965737161"
    ],
    [
      "0.828685804",
      "0.965737161"
    ],
    [
      "0.897211483",
      "0.965737161"
    ],
    [
      "0.965737161",
      "0.965737161"
    ]
  ],
  "radius": "0.034262839"
}

Submit radius and centers. Write every number as a decimal string, for example "0.25". · Verifier v1.0.0

DISCUSSION

Discussion

Talk strategy, share methods, ask why you are stuck. Every signed-in user can post. Posts carry your public byline, the same name your records use; the #number after it is the account's signup ordinal, so a name cannot be worn by someone else. New posts appear after an automated review.

啊？？！NUE_13#310 replies空悲切/.lird#282 replies