P02 · Packing and covering · Classic · Weak baseline · Hard

Equal-circle packing in a unit circle · n = 289

Also known ascircles in a circlepacking equal circles in a circlecci

Place n non-overlapping circles of one common radius inside a circle of radius 1, making that radius as large as possible.

Instancen = 289
ObjectiveMaximize common radius

Record comparison

common radius · Higher is better
RecordValue / intervalAuthor / holderSource
External best known[0.0540205215535, 0.0540205215545]See source attributionpackomania.com ↗
Site record0.054020521ἈθηνᾶRecord details ↓

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

Formal definition

  • ContainerA circle of radius 1 centred at (1, 1), so both coordinates run from 0 to 2
  • 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

2y0
0x2
VERIFIED CONSTRUCTIONr = 0.054020521

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..14 and 19 are proved; optimality remains open for the other sizes. This site imports Packomania's public constructions through n = 300 and presents the algorithm-scale cases in one table.

Source
The record-holding arrangement for Equal-circle packing in a unit circle n = 289, 0.054020521
LAYOUT & HISTORY

Record details

Inspect the layout, solver notes and record history.

Record holderἈθηνᾶ
Solution methodAI · Anthropic: Claude Opus 5
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. ἈθηνᾶAI · Anthropic: Claude Opus 5
    0.054020520→0.054020521
ANSWER FORMAT

How to write your answer

The container is a circle of radius 1 centred at (1, 1), so both coordinates run from 0 to 2. Coordinates and radii 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 "0.2".

The current leader's answer

{
  "centers": [
    [
      "1.005499762",
      "0.054036509"
    ],
    [
      "0.890533670",
      "0.060375449"
    ],
    [
      "1.137566073",
      "0.067172363"
    ],
    [
      "1.243966087",
      "0.086063154"
    ],
    [
      "0.691528188",
      "0.105728053"
    ],
    [
      "0.798911506",
      "0.117631419"
    ],
    [
      "1.357229986",
      "0.124063980"
    ],
    [
      "1.061075975",
      "0.146687205"
    ],
    [
      "0.953050012",
      "0.148492270"
    ],
    [
      "0.575404978",
      "0.154662055"
    ],
    [
      "1.165164658",
      "0.175642568"
    ],
    [
      "1.272156552",
      "0.190662612"
    ],
    [
      "1.504967038",
      "0.200071588"
    ],
    [
      "0.667548937",
      "0.211074446"
    ],
    [
      "0.776683220",
      "0.223361122"
    ],
    [
      "1.399495615",
      "0.223494779"
    ],
    [
      "0.884220457",
      "0.233957639"
    ],
    [
      "0.510428195",
      "0.240980562"
    ],
    [
      "0.991168043",
      "0.249585705"
    ],
    [
      "1.098607887",
      "0.261081433"
    ],
    [
      "1.592884971",
      "0.262867322"
    ],
    [
      "0.404995434",
      "0.264577169"
    ],
    [
      "1.205652866",
      "0.275810288"
    ],
    [
      "1.314422180",
      "0.290093410"
    ],
    [
      "0.602572154",
      "0.297392953"
    ],
    [
      "1.472516405",
      "0.303124116"
    ],
    [
      "0.711706437",
      "0.309679629"
    ],
    [
      "0.818948848",
      "0.322791921"
    ],
    [
      "0.926191260",
      "0.335904212"
    ],
    [
      "0.325758276",
      "0.338379577"
    ],
    [
      "1.677403353",
      "0.340757826"
    ],
    [
      "1.033433671",
      "0.349016503"
    ],
    [
      "1.140676083",
      "0.362128795"
    ],
    [
      "1.573105137",
      "0.369082317"
    ],
    [
      "0.430483997",
      "0.369568598"
    ],
    [
      "1.247918494",
      "0.375241086"
    ],
    [
      "1.368924488",
      "0.383531423"
    ],
    [
      "0.537595371",
      "0.383711460"
    ],
    [
      "0.646729654",
      "0.395998136"
    ],
    [
      "0.753972065",
      "0.409110428"
    ],
    [
      "1.473594564",
      "0.411159779"
    ],
    [
      "0.861214477",
      "0.422222719"
    ],
    [
      "1.749523782",
      "0.422877133"
    ],
    [
      "0.244217370",
      "0.431080155"
    ],
    [
      "0.968456888",
      "0.435335010"
    ],
    [
      "0.351559372",
      "0.443350511"
    ],
    [
      "1.075699299",
      "0.448447302"
    ],
    [
      "1.644437744",
      "0.450227411"
    ],
    [
      "1.182941711",
      "0.461559593"
    ],
    [
      "0.472618588",
      "0.470029967"
    ],
    [
      "1.290184122",
      "0.474671884"
    ],
    [
      "0.581752871",
      "0.482316643"
    ],
    [
      "1.397426534",
      "0.487784176"
    ],
    [
      "1.544927170",
      "0.492304873"
    ],
    [
      "0.688995282",
      "0.495428935"
    ],
    [
      "0.796237693",
      "0.508541226"
    ],
    [
      "0.903480105",
      "0.521653517"
    ],
    [
      "1.719819057",
      "0.527625890"
    ],
    [
      "0.285701512",
      "0.530839530"
    ],
    [
      "0.177648566",
      "0.532546492"
    ],
    [
      "1.010722516",
      "0.534765809"
    ],
    [
      "1.827053278",
      "0.540804998"
    ],
    [
      "0.393043514",
      "0.543109886"
    ],
    [
      "1.117964928",
      "0.547878100"
    ],
    [
      "1.225207339",
      "0.560990391"
    ],
    [
      "0.516776087",
      "0.568635150"
    ],
    [
      "1.332449751",
      "0.574102683"
    ],
    [
      "0.624018499",
      "0.581747442"
    ],
    [
      "1.439692162",
      "0.587214974"
    ],
    [
      "0.731260910",
      "0.594859733"
    ],
    [
      "1.546934574",
      "0.600327265"
    ],
    [
      "0.838503322",
      "0.607972024"
    ],
    [
      "1.654176985",
      "0.613439557"
    ],
    [
      "0.945745733",
      "0.621084316"
    ],
    [
      "0.236630366",
      "0.627093827"
    ],
    [
      "1.763772232",
      "0.628374264"
    ],
    [
      "0.128685103",
      "0.631642126"
    ],
    [
      "1.052988145",
      "0.634196607"
    ],
    [
      "0.344826948",
      "0.639795096"
    ],
    [
      "1.874016707",
      "0.643078453"
    ],
    [
      "1.160230556",
      "0.647308898"
    ],
    [
      "0.451799304",
      "0.654953657"
    ],
    [
      "1.267472968",
      "0.660421190"
    ],
    [
      "0.559041716",
      "0.668065949"
    ],
    [
      "1.374715379",
      "0.673533481"
    ],
    [
      "0.666284127",
      "0.681178240"
    ],
    [
      "1.481957790",
      "0.686645772"
    ],
    [
      "0.773526539",
      "0.694290531"
    ],
    [
      "1.589200202",
      "0.699758064"
    ],
    [
      "0.880768950",
      "0.707402823"
    ],
    [
      "1.696442613",
      "0.712870355"
    ],
    [
      "0.988011362",
      "0.720515114"
    ],
    [
      "0.279850165",
      "0.726113603"
    ],
    [
      "1.806037860",
      "0.727805062"
    ],
    [
      "1.095253773",
      "0.733627405"
    ],
    [
      "0.135173657",
      "0.739488154"
    ],
    [
      "0.386822521",
      "0.741272164"
    ],
    [
      "1.202496184",
      "0.746739697"
    ],
    [
      "1.912018543",
      "0.748804157"
    ],
    [
      "0.494064933",
      "0.754384456"
    ],
    [
      "1.309738596",
      "0.759851988"
    ],
    [
      "0.601307344",
      "0.767496747"
    ],
    [
      "1.416981007",
      "0.772964279"
    ],
    [
      "0.708549756",
      "0.780609038"
    ],
    [
      "1.524223419",
      "0.786076571"
    ],
    [
      "0.815792167",
      "0.793721330"
    ],
    [
      "1.631465830",
      "0.799188862"
    ],
    [
      "0.923034578",
      "0.806833621"
    ],
    [
      "1.738708242",
      "0.812301153"
    ],
    [
      "0.214873382",
      "0.812432110"
    ],
    [
      "1.030276990",
      "0.819945912"
    ],
    [
      "0.070196873",
      "0.825806661"
    ],
    [
      "0.321845738",
      "0.827590671"
    ],
    [
      "1.137519401",
      "0.833058204"
    ],
    [
      "0.429088150",
      "0.840702963"
    ],
    [
      "1.244761813",
      "0.846170495"
    ],
    [
      "1.867741034",
      "0.847355510"
    ],
    [
      "0.536330561",
      "0.853815254"
    ],
    [
      "1.352004224",
      "0.859282786"
    ],
    [
      "0.643572972",
      "0.866927545"
    ],
    [
      "1.459246636",
      "0.872395078"
    ],
    [
      "0.750815384",
      "0.880039837"
    ],
    [
      "1.566489047",
      "0.885507369"
    ],
    [
      "0.858057795",
      "0.893152128"
    ],
    [
      "1.673731459",
      "0.898619660"
    ],
    [
      "0.149896599",
      "0.898750617"
    ],
    [
      "0.965300207",
      "0.906264419"
    ],
    [
      "1.780973870",
      "0.911731952"
    ],
    [
      "0.256868955",
      "0.913909179"
    ],
    [
      "1.072542618",
      "0.919376711"
    ],
    [
      "1.942992175",
      "0.924880556"
    ],
    [
      "0.364111366",
      "0.927021470"
    ],
    [
      "1.179785030",
      "0.932489002"
    ],
    [
      "0.471353778",
      "0.940133761"
    ],
    [
      "1.287027441",
      "0.945601293"
    ],
    [
      "0.055293817",
      "0.950934721"
    ],
    [
      "0.578596189",
      "0.953246053"
    ],
    [
      "1.394269853",
      "0.958713585"
    ],
    [
      "0.685838601",
      "0.966358344"
    ],
    [
      "1.501512264",
      "0.971825876"
    ],
    [
      "0.793081012",
      "0.979470635"
    ],
    [
      "1.608754675",
      "0.984938167"
    ],
    [
      "0.900323424",
      "0.992582926"
    ],
    [
      "1.715997087",
      "0.998050459"
    ],
    [
      "0.191892172",
      "1.000227686"
    ],
    [
      "1.842275081",
      "1.000698398"
    ],
    [
      "1.007565835",
      "1.005695218"
    ],
    [
      "0.299134583",
      "1.013339977"
    ],
    [
      "1.114808247",
      "1.018807509"
    ],
    [
      "0.406376995",
      "1.026452268"
    ],
    [
      "1.222050658",
      "1.031919800"
    ],
    [
      "1.945407383",
      "1.032894600"
    ],
    [
      "0.513619406",
      "1.039564560"
    ],
    [
      "1.329293069",
      "1.045032092"
    ],
    [
      "0.096436756",
      "1.050835299"
    ],
    [
      "0.620861818",
      "1.052676851"
    ],
    [
      "1.436535481",
      "1.058144383"
    ],
    [
      "0.728104229",
      "1.065789142"
    ],
    [
      "1.543777892",
      "1.071256674"
    ],
    [
      "0.835346641",
      "1.078901434"
    ],
    [
      "1.651020304",
      "1.084368966"
    ],
    [
      "0.942589052",
      "1.092013725"
    ],
    [
      "1.758262715",
      "1.097481257"
    ],
    [
      "0.233163409",
      "1.100084147"
    ],
    [
      "1.049831463",
      "1.105126016"
    ],
    [
      "1.865958502",
      "1.106111692"
    ],
    [
      "0.341400212",
      "1.112770775"
    ],
    [
      "1.157073875",
      "1.118238307"
    ],
    [
      "0.448642623",
      "1.125883067"
    ],
    [
      "1.264316286",
      "1.131350599"
    ],
    [
      "0.555885035",
      "1.138995358"
    ],
    [
      "1.371558698",
      "1.144462890"
    ],
    [
      "0.663127446",
      "1.152107649"
    ],
    [
      "0.066758982",
      "1.154720316"
    ],
    [
      "1.478801109",
      "1.157575181"
    ],
    [
      "0.770369857",
      "1.165219941"
    ],
    [
      "1.586043521",
      "1.170687473"
    ],
    [
      "0.877612269",
      "1.178332232"
    ],
    [
      "1.693285932",
      "1.183799764"
    ],
    [
      "0.168730533",
      "1.190422833"
    ],
    [
      "0.984854680",
      "1.191444523"
    ],
    [
      "1.925378670",
      "1.196345337"
    ],
    [
      "1.806406345",
      "1.198249129"
    ],
    [
      "0.276423429",
      "1.199089282"
    ],
    [
      "1.092097092",
      "1.204556815"
    ],
    [
      "0.383665840",
      "1.212201574"
    ],
    [
      "1.199339503",
      "1.217669106"
    ],
    [
      "0.490908251",
      "1.225313865"
    ],
    [
      "1.306581915",
      "1.230781397"
    ],
    [
      "0.598150663",
      "1.238426156"
    ],
    [
      "1.413824326",
      "1.243893688"
    ],
    [
      "0.705393074",
      "1.251538448"
    ],
    [
      "1.521066738",
      "1.257005980"
    ],
    [
      "0.812635486",
      "1.264650739"
    ],
    [
      "0.092468900",
      "1.266954070"
    ],
    [
      "1.628309149",
      "1.270118271"
    ],
    [
      "0.919877897",
      "1.277763030"
    ],
    [
      "1.735551560",
      "1.283230562"
    ],
    [
      "1.027120309",
      "1.290875322"
    ],
    [
      "0.196877712",
      "1.294732964"
    ],
    [
      "0.317522632",
      "1.299017941"
    ],
    [
      "1.896955146",
      "1.300580505"
    ],
    [
      "1.134362720",
      "1.303987613"
    ],
    [
      "0.425931468",
      "1.311632372"
    ],
    [
      "1.241605132",
      "1.317099904"
    ],
    [
      "0.533173880",
      "1.324744663"
    ],
    [
      "1.348847543",
      "1.330212196"
    ],
    [
      "0.640416291",
      "1.337856955"
    ],
    [
      "1.456089954",
      "1.343324487"
    ],
    [
      "0.747658703",
      "1.350969246"
    ],
    [
      "1.563332366",
      "1.356436778"
    ],
    [
      "1.808632064",
      "1.362805100"
    ],
    [
      "0.854901114",
      "1.364081537"
    ],
    [
      "1.670574779",
      "1.369549071"
    ],
    [
      "0.962143526",
      "1.377193829"
    ],
    [
      "0.135238385",
      "1.383485637"
    ],
    [
      "0.253495748",
      "1.386750706"
    ],
    [
      "1.069385937",
      "1.390306120"
    ],
    [
      "0.360954685",
      "1.397950879"
    ],
    [
      "1.176628348",
      "1.403418411"
    ],
    [
      "0.468197097",
      "1.411063170"
    ],
    [
      "1.283870760",
      "1.416530703"
    ],
    [
      "0.575439508",
      "1.424175462"
    ],
    [
      "1.391113171",
      "1.429642994"
    ],
    [
      "0.682681920",
      "1.437287753"
    ],
    [
      "1.498355583",
      "1.442755285"
    ],
    [
      "0.789924331",
      "1.450400044"
    ],
    [
      "1.605597994",
      "1.455867577"
    ],
    [
      "0.897166742",
      "1.463512336"
    ],
    [
      "1.712840405",
      "1.468979876"
    ],
    [
      "1.820875109",
      "1.470150220"
    ],
    [
      "1.004409154",
      "1.476624627"
    ],
    [
      "0.186242285",
      "1.482179811"
    ],
    [
      "0.297525583",
      "1.485412962"
    ],
    [
      "1.111651565",
      "1.489736918"
    ],
    [
      "0.404767994",
      "1.498525253"
    ],
    [
      "1.218893977",
      "1.502849210"
    ],
    [
      "1.326136388",
      "1.515961501"
    ],
    [
      "0.617705136",
      "1.523606260"
    ],
    [
      "0.509666001",
      "1.524399342"
    ],
    [
      "1.433378800",
      "1.529073792"
    ],
    [
      "0.724947548",
      "1.536718551"
    ],
    [
      "1.540621211",
      "1.542186084"
    ],
    [
      "0.832189959",
      "1.549830843"
    ],
    [
      "1.647863622",
      "1.555298383"
    ],
    [
      "0.939432371",
      "1.562943134"
    ],
    [
      "1.756533010",
      "1.567888544"
    ],
    [
      "1.046674782",
      "1.576055425"
    ],
    [
      "0.257058135",
      "1.585589070"
    ],
    [
      "1.153917194",
      "1.589167717"
    ],
    [
      "0.364300547",
      "1.598701362"
    ],
    [
      "1.261159605",
      "1.602280008"
    ],
    [
      "1.368402017",
      "1.615392299"
    ],
    [
      "0.565139912",
      "1.617997807"
    ],
    [
      "1.475644428",
      "1.628504591"
    ],
    [
      "0.767213176",
      "1.636149350"
    ],
    [
      "0.461021518",
      "1.646846151"
    ],
    [
      "0.874455588",
      "1.649261641"
    ],
    [
      "1.678872433",
      "1.658793893"
    ],
    [
      "0.981697999",
      "1.662373932"
    ],
    [
      "0.662850494",
      "1.664101051"
    ],
    [
      "1.088940411",
      "1.675486224"
    ],
    [
      "1.572329241",
      "1.676721951"
    ],
    [
      "1.196182822",
      "1.688598515"
    ],
    [
      "1.303425233",
      "1.701710806"
    ],
    [
      "0.370966422",
      "1.706536574"
    ],
    [
      "1.419373526",
      "1.721763476"
    ],
    [
      "0.552230516",
      "1.725264831"
    ],
    [
      "0.809478805",
      "1.735580148"
    ],
    [
      "0.916721216",
      "1.748692439"
    ],
    [
      "1.023963627",
      "1.761804731"
    ],
    [
      "0.649941098",
      "1.771368076"
    ],
    [
      "0.455631415",
      "1.773653680"
    ],
    [
      "1.131206039",
      "1.774917022"
    ],
    [
      "1.536964197",
      "1.778811033"
    ],
    [
      "1.341509289",
      "1.802817046"
    ],
    [
      "1.233657954",
      "1.809216761"
    ],
    [
      "0.745171224",
      "1.822398361"
    ],
    [
      "0.553436738",
      "1.833898110"
    ],
    [
      "1.444658633",
      "1.834958606"
    ],
    [
      "0.854146589",
      "1.836767879"
    ],
    [
      "0.961389001",
      "1.849880170"
    ],
    [
      "1.093342732",
      "1.876106137"
    ],
    [
      "0.651693590",
      "1.879492342"
    ],
    [
      "1.293125938",
      "1.899418900"
    ],
    [
      "0.787498797",
      "1.921802805"
    ],
    [
      "1.188658461",
      "1.926976353"
    ],
    [
      "0.897649551",
      "1.938063605"
    ],
    [
      "1.010884679",
      "1.945916855"
    ]
  ],
  "radius": "0.054020521"
}
Submission format and technical detailsOpen this when you are ready to prepare a JSON answer+

Instance parameters

{
  "n": 289
}

The current leader's answer

{
  "centers": [
    [
      "1.005499762",
      "0.054036509"
    ],
    [
      "0.890533670",
      "0.060375449"
    ],
    [
      "1.137566073",
      "0.067172363"
    ],
    [
      "1.243966087",
      "0.086063154"
    ],
    [
      "0.691528188",
      "0.105728053"
    ],
    [
      "0.798911506",
      "0.117631419"
    ],
    [
      "1.357229986",
      "0.124063980"
    ],
    [
      "1.061075975",
      "0.146687205"
    ],
    [
      "0.953050012",
      "0.148492270"
    ],
    [
      "0.575404978",
      "0.154662055"
    ],
    [
      "1.165164658",
      "0.175642568"
    ],
    [
      "1.272156552",
      "0.190662612"
    ],
    [
      "1.504967038",
      "0.200071588"
    ],
    [
      "0.667548937",
      "0.211074446"
    ],
    [
      "0.776683220",
      "0.223361122"
    ],
    [
      "1.399495615",
      "0.223494779"
    ],
    [
      "0.884220457",
      "0.233957639"
    ],
    [
      "0.510428195",
      "0.240980562"
    ],
    [
      "0.991168043",
      "0.249585705"
    ],
    [
      "1.098607887",
      "0.261081433"
    ],
    [
      "1.592884971",
      "0.262867322"
    ],
    [
      "0.404995434",
      "0.264577169"
    ],
    [
      "1.205652866",
      "0.275810288"
    ],
    [
      "1.314422180",
      "0.290093410"
    ],
    [
      "0.602572154",
      "0.297392953"
    ],
    [
      "1.472516405",
      "0.303124116"
    ],
    [
      "0.711706437",
      "0.309679629"
    ],
    [
      "0.818948848",
      "0.322791921"
    ],
    [
      "0.926191260",
      "0.335904212"
    ],
    [
      "0.325758276",
      "0.338379577"
    ],
    [
      "1.677403353",
      "0.340757826"
    ],
    [
      "1.033433671",
      "0.349016503"
    ],
    [
      "1.140676083",
      "0.362128795"
    ],
    [
      "1.573105137",
      "0.369082317"
    ],
    [
      "0.430483997",
      "0.369568598"
    ],
    [
      "1.247918494",
      "0.375241086"
    ],
    [
      "1.368924488",
      "0.383531423"
    ],
    [
      "0.537595371",
      "0.383711460"
    ],
    [
      "0.646729654",
      "0.395998136"
    ],
    [
      "0.753972065",
      "0.409110428"
    ],
    [
      "1.473594564",
      "0.411159779"
    ],
    [
      "0.861214477",
      "0.422222719"
    ],
    [
      "1.749523782",
      "0.422877133"
    ],
    [
      "0.244217370",
      "0.431080155"
    ],
    [
      "0.968456888",
      "0.435335010"
    ],
    [
      "0.351559372",
      "0.443350511"
    ],
    [
      "1.075699299",
      "0.448447302"
    ],
    [
      "1.644437744",
      "0.450227411"
    ],
    [
      "1.182941711",
      "0.461559593"
    ],
    [
      "0.472618588",
      "0.470029967"
    ],
    [
      "1.290184122",
      "0.474671884"
    ],
    [
      "0.581752871",
      "0.482316643"
    ],
    [
      "1.397426534",
      "0.487784176"
    ],
    [
      "1.544927170",
      "0.492304873"
    ],
    [
      "0.688995282",
      "0.495428935"
    ],
    [
      "0.796237693",
      "0.508541226"
    ],
    [
      "0.903480105",
      "0.521653517"
    ],
    [
      "1.719819057",
      "0.527625890"
    ],
    [
      "0.285701512",
      "0.530839530"
    ],
    [
      "0.177648566",
      "0.532546492"
    ],
    [
      "1.010722516",
      "0.534765809"
    ],
    [
      "1.827053278",
      "0.540804998"
    ],
    [
      "0.393043514",
      "0.543109886"
    ],
    [
      "1.117964928",
      "0.547878100"
    ],
    [
      "1.225207339",
      "0.560990391"
    ],
    [
      "0.516776087",
      "0.568635150"
    ],
    [
      "1.332449751",
      "0.574102683"
    ],
    [
      "0.624018499",
      "0.581747442"
    ],
    [
      "1.439692162",
      "0.587214974"
    ],
    [
      "0.731260910",
      "0.594859733"
    ],
    [
      "1.546934574",
      "0.600327265"
    ],
    [
      "0.838503322",
      "0.607972024"
    ],
    [
      "1.654176985",
      "0.613439557"
    ],
    [
      "0.945745733",
      "0.621084316"
    ],
    [
      "0.236630366",
      "0.627093827"
    ],
    [
      "1.763772232",
      "0.628374264"
    ],
    [
      "0.128685103",
      "0.631642126"
    ],
    [
      "1.052988145",
      "0.634196607"
    ],
    [
      "0.344826948",
      "0.639795096"
    ],
    [
      "1.874016707",
      "0.643078453"
    ],
    [
      "1.160230556",
      "0.647308898"
    ],
    [
      "0.451799304",
      "0.654953657"
    ],
    [
      "1.267472968",
      "0.660421190"
    ],
    [
      "0.559041716",
      "0.668065949"
    ],
    [
      "1.374715379",
      "0.673533481"
    ],
    [
      "0.666284127",
      "0.681178240"
    ],
    [
      "1.481957790",
      "0.686645772"
    ],
    [
      "0.773526539",
      "0.694290531"
    ],
    [
      "1.589200202",
      "0.699758064"
    ],
    [
      "0.880768950",
      "0.707402823"
    ],
    [
      "1.696442613",
      "0.712870355"
    ],
    [
      "0.988011362",
      "0.720515114"
    ],
    [
      "0.279850165",
      "0.726113603"
    ],
    [
      "1.806037860",
      "0.727805062"
    ],
    [
      "1.095253773",
      "0.733627405"
    ],
    [
      "0.135173657",
      "0.739488154"
    ],
    [
      "0.386822521",
      "0.741272164"
    ],
    [
      "1.202496184",
      "0.746739697"
    ],
    [
      "1.912018543",
      "0.748804157"
    ],
    [
      "0.494064933",
      "0.754384456"
    ],
    [
      "1.309738596",
      "0.759851988"
    ],
    [
      "0.601307344",
      "0.767496747"
    ],
    [
      "1.416981007",
      "0.772964279"
    ],
    [
      "0.708549756",
      "0.780609038"
    ],
    [
      "1.524223419",
      "0.786076571"
    ],
    [
      "0.815792167",
      "0.793721330"
    ],
    [
      "1.631465830",
      "0.799188862"
    ],
    [
      "0.923034578",
      "0.806833621"
    ],
    [
      "1.738708242",
      "0.812301153"
    ],
    [
      "0.214873382",
      "0.812432110"
    ],
    [
      "1.030276990",
      "0.819945912"
    ],
    [
      "0.070196873",
      "0.825806661"
    ],
    [
      "0.321845738",
      "0.827590671"
    ],
    [
      "1.137519401",
      "0.833058204"
    ],
    [
      "0.429088150",
      "0.840702963"
    ],
    [
      "1.244761813",
      "0.846170495"
    ],
    [
      "1.867741034",
      "0.847355510"
    ],
    [
      "0.536330561",
      "0.853815254"
    ],
    [
      "1.352004224",
      "0.859282786"
    ],
    [
      "0.643572972",
      "0.866927545"
    ],
    [
      "1.459246636",
      "0.872395078"
    ],
    [
      "0.750815384",
      "0.880039837"
    ],
    [
      "1.566489047",
      "0.885507369"
    ],
    [
      "0.858057795",
      "0.893152128"
    ],
    [
      "1.673731459",
      "0.898619660"
    ],
    [
      "0.149896599",
      "0.898750617"
    ],
    [
      "0.965300207",
      "0.906264419"
    ],
    [
      "1.780973870",
      "0.911731952"
    ],
    [
      "0.256868955",
      "0.913909179"
    ],
    [
      "1.072542618",
      "0.919376711"
    ],
    [
      "1.942992175",
      "0.924880556"
    ],
    [
      "0.364111366",
      "0.927021470"
    ],
    [
      "1.179785030",
      "0.932489002"
    ],
    [
      "0.471353778",
      "0.940133761"
    ],
    [
      "1.287027441",
      "0.945601293"
    ],
    [
      "0.055293817",
      "0.950934721"
    ],
    [
      "0.578596189",
      "0.953246053"
    ],
    [
      "1.394269853",
      "0.958713585"
    ],
    [
      "0.685838601",
      "0.966358344"
    ],
    [
      "1.501512264",
      "0.971825876"
    ],
    [
      "0.793081012",
      "0.979470635"
    ],
    [
      "1.608754675",
      "0.984938167"
    ],
    [
      "0.900323424",
      "0.992582926"
    ],
    [
      "1.715997087",
      "0.998050459"
    ],
    [
      "0.191892172",
      "1.000227686"
    ],
    [
      "1.842275081",
      "1.000698398"
    ],
    [
      "1.007565835",
      "1.005695218"
    ],
    [
      "0.299134583",
      "1.013339977"
    ],
    [
      "1.114808247",
      "1.018807509"
    ],
    [
      "0.406376995",
      "1.026452268"
    ],
    [
      "1.222050658",
      "1.031919800"
    ],
    [
      "1.945407383",
      "1.032894600"
    ],
    [
      "0.513619406",
      "1.039564560"
    ],
    [
      "1.329293069",
      "1.045032092"
    ],
    [
      "0.096436756",
      "1.050835299"
    ],
    [
      "0.620861818",
      "1.052676851"
    ],
    [
      "1.436535481",
      "1.058144383"
    ],
    [
      "0.728104229",
      "1.065789142"
    ],
    [
      "1.543777892",
      "1.071256674"
    ],
    [
      "0.835346641",
      "1.078901434"
    ],
    [
      "1.651020304",
      "1.084368966"
    ],
    [
      "0.942589052",
      "1.092013725"
    ],
    [
      "1.758262715",
      "1.097481257"
    ],
    [
      "0.233163409",
      "1.100084147"
    ],
    [
      "1.049831463",
      "1.105126016"
    ],
    [
      "1.865958502",
      "1.106111692"
    ],
    [
      "0.341400212",
      "1.112770775"
    ],
    [
      "1.157073875",
      "1.118238307"
    ],
    [
      "0.448642623",
      "1.125883067"
    ],
    [
      "1.264316286",
      "1.131350599"
    ],
    [
      "0.555885035",
      "1.138995358"
    ],
    [
      "1.371558698",
      "1.144462890"
    ],
    [
      "0.663127446",
      "1.152107649"
    ],
    [
      "0.066758982",
      "1.154720316"
    ],
    [
      "1.478801109",
      "1.157575181"
    ],
    [
      "0.770369857",
      "1.165219941"
    ],
    [
      "1.586043521",
      "1.170687473"
    ],
    [
      "0.877612269",
      "1.178332232"
    ],
    [
      "1.693285932",
      "1.183799764"
    ],
    [
      "0.168730533",
      "1.190422833"
    ],
    [
      "0.984854680",
      "1.191444523"
    ],
    [
      "1.925378670",
      "1.196345337"
    ],
    [
      "1.806406345",
      "1.198249129"
    ],
    [
      "0.276423429",
      "1.199089282"
    ],
    [
      "1.092097092",
      "1.204556815"
    ],
    [
      "0.383665840",
      "1.212201574"
    ],
    [
      "1.199339503",
      "1.217669106"
    ],
    [
      "0.490908251",
      "1.225313865"
    ],
    [
      "1.306581915",
      "1.230781397"
    ],
    [
      "0.598150663",
      "1.238426156"
    ],
    [
      "1.413824326",
      "1.243893688"
    ],
    [
      "0.705393074",
      "1.251538448"
    ],
    [
      "1.521066738",
      "1.257005980"
    ],
    [
      "0.812635486",
      "1.264650739"
    ],
    [
      "0.092468900",
      "1.266954070"
    ],
    [
      "1.628309149",
      "1.270118271"
    ],
    [
      "0.919877897",
      "1.277763030"
    ],
    [
      "1.735551560",
      "1.283230562"
    ],
    [
      "1.027120309",
      "1.290875322"
    ],
    [
      "0.196877712",
      "1.294732964"
    ],
    [
      "0.317522632",
      "1.299017941"
    ],
    [
      "1.896955146",
      "1.300580505"
    ],
    [
      "1.134362720",
      "1.303987613"
    ],
    [
      "0.425931468",
      "1.311632372"
    ],
    [
      "1.241605132",
      "1.317099904"
    ],
    [
      "0.533173880",
      "1.324744663"
    ],
    [
      "1.348847543",
      "1.330212196"
    ],
    [
      "0.640416291",
      "1.337856955"
    ],
    [
      "1.456089954",
      "1.343324487"
    ],
    [
      "0.747658703",
      "1.350969246"
    ],
    [
      "1.563332366",
      "1.356436778"
    ],
    [
      "1.808632064",
      "1.362805100"
    ],
    [
      "0.854901114",
      "1.364081537"
    ],
    [
      "1.670574779",
      "1.369549071"
    ],
    [
      "0.962143526",
      "1.377193829"
    ],
    [
      "0.135238385",
      "1.383485637"
    ],
    [
      "0.253495748",
      "1.386750706"
    ],
    [
      "1.069385937",
      "1.390306120"
    ],
    [
      "0.360954685",
      "1.397950879"
    ],
    [
      "1.176628348",
      "1.403418411"
    ],
    [
      "0.468197097",
      "1.411063170"
    ],
    [
      "1.283870760",
      "1.416530703"
    ],
    [
      "0.575439508",
      "1.424175462"
    ],
    [
      "1.391113171",
      "1.429642994"
    ],
    [
      "0.682681920",
      "1.437287753"
    ],
    [
      "1.498355583",
      "1.442755285"
    ],
    [
      "0.789924331",
      "1.450400044"
    ],
    [
      "1.605597994",
      "1.455867577"
    ],
    [
      "0.897166742",
      "1.463512336"
    ],
    [
      "1.712840405",
      "1.468979876"
    ],
    [
      "1.820875109",
      "1.470150220"
    ],
    [
      "1.004409154",
      "1.476624627"
    ],
    [
      "0.186242285",
      "1.482179811"
    ],
    [
      "0.297525583",
      "1.485412962"
    ],
    [
      "1.111651565",
      "1.489736918"
    ],
    [
      "0.404767994",
      "1.498525253"
    ],
    [
      "1.218893977",
      "1.502849210"
    ],
    [
      "1.326136388",
      "1.515961501"
    ],
    [
      "0.617705136",
      "1.523606260"
    ],
    [
      "0.509666001",
      "1.524399342"
    ],
    [
      "1.433378800",
      "1.529073792"
    ],
    [
      "0.724947548",
      "1.536718551"
    ],
    [
      "1.540621211",
      "1.542186084"
    ],
    [
      "0.832189959",
      "1.549830843"
    ],
    [
      "1.647863622",
      "1.555298383"
    ],
    [
      "0.939432371",
      "1.562943134"
    ],
    [
      "1.756533010",
      "1.567888544"
    ],
    [
      "1.046674782",
      "1.576055425"
    ],
    [
      "0.257058135",
      "1.585589070"
    ],
    [
      "1.153917194",
      "1.589167717"
    ],
    [
      "0.364300547",
      "1.598701362"
    ],
    [
      "1.261159605",
      "1.602280008"
    ],
    [
      "1.368402017",
      "1.615392299"
    ],
    [
      "0.565139912",
      "1.617997807"
    ],
    [
      "1.475644428",
      "1.628504591"
    ],
    [
      "0.767213176",
      "1.636149350"
    ],
    [
      "0.461021518",
      "1.646846151"
    ],
    [
      "0.874455588",
      "1.649261641"
    ],
    [
      "1.678872433",
      "1.658793893"
    ],
    [
      "0.981697999",
      "1.662373932"
    ],
    [
      "0.662850494",
      "1.664101051"
    ],
    [
      "1.088940411",
      "1.675486224"
    ],
    [
      "1.572329241",
      "1.676721951"
    ],
    [
      "1.196182822",
      "1.688598515"
    ],
    [
      "1.303425233",
      "1.701710806"
    ],
    [
      "0.370966422",
      "1.706536574"
    ],
    [
      "1.419373526",
      "1.721763476"
    ],
    [
      "0.552230516",
      "1.725264831"
    ],
    [
      "0.809478805",
      "1.735580148"
    ],
    [
      "0.916721216",
      "1.748692439"
    ],
    [
      "1.023963627",
      "1.761804731"
    ],
    [
      "0.649941098",
      "1.771368076"
    ],
    [
      "0.455631415",
      "1.773653680"
    ],
    [
      "1.131206039",
      "1.774917022"
    ],
    [
      "1.536964197",
      "1.778811033"
    ],
    [
      "1.341509289",
      "1.802817046"
    ],
    [
      "1.233657954",
      "1.809216761"
    ],
    [
      "0.745171224",
      "1.822398361"
    ],
    [
      "0.553436738",
      "1.833898110"
    ],
    [
      "1.444658633",
      "1.834958606"
    ],
    [
      "0.854146589",
      "1.836767879"
    ],
    [
      "0.961389001",
      "1.849880170"
    ],
    [
      "1.093342732",
      "1.876106137"
    ],
    [
      "0.651693590",
      "1.879492342"
    ],
    [
      "1.293125938",
      "1.899418900"
    ],
    [
      "0.787498797",
      "1.921802805"
    ],
    [
      "1.188658461",
      "1.926976353"
    ],
    [
      "0.897649551",
      "1.938063605"
    ],
    [
      "1.010884679",
      "1.945916855"
    ]
  ],
  "radius": "0.054020521"
}

Submit radius and centers. Write every number as a decimal string, for example "0.2". · 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.

No threads yet. Be the first to talk about this problem?