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

Equal-circle packing in a unit circle · n = 285

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 = 285
ObjectiveMaximize common radius

Record comparison

common radius · Higher is better
RecordValue / intervalAuthor / holderSource
External best known[0.0543457271745, 0.0543457271755]See source attributionpackomania.com ↗
Site recordNo player record yet——

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: starter layout

2y0
0x2
VERIFIED CONSTRUCTIONr = 0.054345726

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 current arrangement for Equal-circle packing in a unit circle n = 285
LAYOUT & HISTORY

Starter layout

Inspect the layout, solver notes and record history.

Challenge this record ↗Submit a proof / idea ↓Share a proof or idea in the discussion. Accepted contributions can earn proof points.
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".

Starter answer

{
  "centers": [
    [
      "0.987570151",
      "0.054427421"
    ],
    [
      "1.0961547",
      "0.059246963"
    ],
    [
      "0.879149809",
      "0.06209956"
    ],
    [
      "1.203468977",
      "0.076494516"
    ],
    [
      "0.767448997",
      "0.083429097"
    ],
    [
      "0.66397661",
      "0.116749704"
    ],
    [
      "1.371873567",
      "0.130533466"
    ],
    [
      "1.043319077",
      "0.154232378"
    ],
    [
      "1.268362174",
      "0.16368801"
    ],
    [
      "0.84080251",
      "0.163801659"
    ],
    [
      "1.150633354",
      "0.171479932"
    ],
    [
      "0.538111366",
      "0.17482069"
    ],
    [
      "0.943911639",
      "0.198186826"
    ],
    [
      "0.743368421",
      "0.211972506"
    ],
    [
      "1.43589915",
      "0.218366017"
    ],
    [
      "0.635290409",
      "0.223504012"
    ],
    [
      "1.544272445",
      "0.226676323"
    ],
    [
      "0.44647473",
      "0.23327203"
    ],
    [
      "1.332387757",
      "0.25152056"
    ],
    [
      "1.224309745",
      "0.263052066"
    ],
    [
      "1.116231733",
      "0.274583572"
    ],
    [
      "1.008128834",
      "0.285879381"
    ],
    [
      "1.629414583",
      "0.294238506"
    ],
    [
      "0.900076256",
      "0.297646826"
    ],
    [
      "0.362150554",
      "0.301852389"
    ],
    [
      "0.791998244",
      "0.309178332"
    ],
    [
      "0.568189701",
      "0.309382599"
    ],
    [
      "0.683920233",
      "0.320709838"
    ],
    [
      "1.504583113",
      "0.327862237"
    ],
    [
      "1.396494017",
      "0.339294813"
    ],
    [
      "0.463704974",
      "0.340589088"
    ],
    [
      "1.288426582",
      "0.350925024"
    ],
    [
      "1.180348571",
      "0.36245653"
    ],
    [
      "1.70624171",
      "0.371124296"
    ],
    [
      "1.072270559",
      "0.373988036"
    ],
    [
      "0.964182023",
      "0.38542133"
    ],
    [
      "1.589725251",
      "0.39542442"
    ],
    [
      "0.856114536",
      "0.397051048"
    ],
    [
      "0.322937549",
      "0.403223847"
    ],
    [
      "0.748036524",
      "0.408582554"
    ],
    [
      "0.639958512",
      "0.42011406"
    ],
    [
      "0.531406622",
      "0.425620371"
    ],
    [
      "1.460530177",
      "0.427226069"
    ],
    [
      "1.352452165",
      "0.438757575"
    ],
    [
      "0.424106572",
      "0.442956214"
    ],
    [
      "1.244374154",
      "0.450289081"
    ],
    [
      "0.227291685",
      "0.454854273"
    ],
    [
      "1.773738886",
      "0.456317979"
    ],
    [
      "1.136296142",
      "0.461820587"
    ],
    [
      "1.02821813",
      "0.473352093"
    ],
    [
      "0.920140119",
      "0.484883599"
    ],
    [
      "1.631520039",
      "0.495759"
    ],
    [
      "0.812062107",
      "0.496415105"
    ],
    [
      "0.703984095",
      "0.507946611"
    ],
    [
      "1.52455576",
      "0.51505862"
    ],
    [
      "0.595906083",
      "0.519478117"
    ],
    [
      "1.416477748",
      "0.526590126"
    ],
    [
      "0.487828072",
      "0.531009623"
    ],
    [
      "1.308399737",
      "0.538121632"
    ],
    [
      "0.379710833",
      "0.542167356"
    ],
    [
      "1.200321725",
      "0.549653137"
    ],
    [
      "1.723955783",
      "0.55293824"
    ],
    [
      "0.271673258",
      "0.554071752"
    ],
    [
      "1.834323602",
      "0.554956625"
    ],
    [
      "0.163125351",
      "0.559656015"
    ],
    [
      "1.092243713",
      "0.561184643"
    ],
    [
      "0.984165702",
      "0.572716149"
    ],
    [
      "0.87608769",
      "0.584247655"
    ],
    [
      "0.768009678",
      "0.595779161"
    ],
    [
      "1.593965745",
      "0.598920609"
    ],
    [
      "0.659931666",
      "0.607310667"
    ],
    [
      "1.480503331",
      "0.614422676"
    ],
    [
      "0.551853655",
      "0.618842173"
    ],
    [
      "1.37242532",
      "0.625954182"
    ],
    [
      "0.443775643",
      "0.630373679"
    ],
    [
      "1.264347308",
      "0.637485688"
    ],
    [
      "0.335697631",
      "0.641905185"
    ],
    [
      "1.156269296",
      "0.649017194"
    ],
    [
      "0.222235418",
      "0.650869129"
    ],
    [
      "1.880015498",
      "0.653947544"
    ],
    [
      "1.75588046",
      "0.656835532"
    ],
    [
      "1.048191285",
      "0.6605487"
    ],
    [
      "0.114570071",
      "0.668039527"
    ],
    [
      "0.940113273",
      "0.672080206"
    ],
    [
      "0.832035261",
      "0.683611712"
    ],
    [
      "1.652606926",
      "0.690723721"
    ],
    [
      "0.723957249",
      "0.695143218"
    ],
    [
      "1.544528914",
      "0.702255227"
    ],
    [
      "0.615879238",
      "0.706674724"
    ],
    [
      "1.436450903",
      "0.713786733"
    ],
    [
      "0.507801226",
      "0.71820623"
    ],
    [
      "1.328372891",
      "0.725318239"
    ],
    [
      "0.399723214",
      "0.729737736"
    ],
    [
      "1.220294879",
      "0.736849745"
    ],
    [
      "0.291645202",
      "0.741269242"
    ],
    [
      "1.819906043",
      "0.744668082"
    ],
    [
      "1.112216867",
      "0.748381251"
    ],
    [
      "0.183528794",
      "0.752435017"
    ],
    [
      "1.004138856",
      "0.759912757"
    ],
    [
      "0.896060844",
      "0.771444263"
    ],
    [
      "1.716632509",
      "0.778556272"
    ],
    [
      "0.787982832",
      "0.782975769"
    ],
    [
      "0.079422193",
      "0.783670379"
    ],
    [
      "1.920870164",
      "0.784918283"
    ],
    [
      "1.608554497",
      "0.790087778"
    ],
    [
      "0.679904821",
      "0.794507275"
    ],
    [
      "1.500476486",
      "0.801619284"
    ],
    [
      "0.571826809",
      "0.806038781"
    ],
    [
      "1.392398474",
      "0.81315079"
    ],
    [
      "0.463748797",
      "0.817570287"
    ],
    [
      "1.284320462",
      "0.824682296"
    ],
    [
      "0.355670785",
      "0.829101793"
    ],
    [
      "1.17624245",
      "0.836213802"
    ],
    [
      "0.247325334",
      "0.84052708"
    ],
    [
      "1.068164439",
      "0.847745308"
    ],
    [
      "0.960086427",
      "0.859276814"
    ],
    [
      "1.788906358",
      "0.860699537"
    ],
    [
      "0.852008415",
      "0.87080832"
    ],
    [
      "1.67258008",
      "0.877920329"
    ],
    [
      "0.743930404",
      "0.882339826"
    ],
    [
      "0.10794332",
      "0.888553064"
    ],
    [
      "1.564502069",
      "0.889451835"
    ],
    [
      "1.939467662",
      "0.892006869"
    ],
    [
      "0.635852392",
      "0.893871332"
    ],
    [
      "1.456424057",
      "0.900983341"
    ],
    [
      "0.52777438",
      "0.905402838"
    ],
    [
      "1.348346045",
      "0.912514846"
    ],
    [
      "0.419696368",
      "0.916934344"
    ],
    [
      "1.240268033",
      "0.924046352"
    ],
    [
      "0.311618357",
      "0.928465849"
    ],
    [
      "1.132190022",
      "0.935577858"
    ],
    [
      "0.203565193",
      "0.940227909"
    ],
    [
      "1.02411201",
      "0.947109364"
    ],
    [
      "1.84858393",
      "0.951622132"
    ],
    [
      "0.916033998",
      "0.95864087"
    ],
    [
      "1.740468996",
      "0.962802172"
    ],
    [
      "0.807955987",
      "0.970172376"
    ],
    [
      "1.628527652",
      "0.977284385"
    ],
    [
      "0.699877975",
      "0.981703882"
    ],
    [
      "0.054495056",
      "0.983195102"
    ],
    [
      "1.52044964",
      "0.988815891"
    ],
    [
      "0.591799963",
      "0.993235388"
    ],
    [
      "1.412371628",
      "1.000347397"
    ],
    [
      "1.945654129",
      "1.000522121"
    ],
    [
      "0.483721951",
      "1.004766894"
    ],
    [
      "1.304293616",
      "1.011878903"
    ],
    [
      "0.375610982",
      "1.016322415"
    ],
    [
      "1.196215605",
      "1.023410409"
    ],
    [
      "0.264153827",
      "1.030465648"
    ],
    [
      "1.088137593",
      "1.034941915"
    ],
    [
      "0.152047178",
      "1.035934368"
    ],
    [
      "0.980059581",
      "1.046473421"
    ],
    [
      "1.800605015",
      "1.053342172"
    ],
    [
      "0.87198157",
      "1.058004927"
    ],
    [
      "1.692553235",
      "1.065116936"
    ],
    [
      "0.763903558",
      "1.069536433"
    ],
    [
      "1.584475223",
      "1.076648442"
    ],
    [
      "0.655825546",
      "1.081067939"
    ],
    [
      "1.476397211",
      "1.088179948"
    ],
    [
      "0.058812123",
      "1.091800788"
    ],
    [
      "0.547747534",
      "1.092599445"
    ],
    [
      "1.899315278",
      "1.098840701"
    ],
    [
      "1.368319199",
      "1.099711454"
    ],
    [
      "0.439669523",
      "1.104130951"
    ],
    [
      "1.260241188",
      "1.11124296"
    ],
    [
      "0.331595845",
      "1.115703002"
    ],
    [
      "1.152163176",
      "1.122774466"
    ],
    [
      "0.212635812",
      "1.126172108"
    ],
    [
      "1.044085164",
      "1.134305972"
    ],
    [
      "0.936007153",
      "1.145837478"
    ],
    [
      "1.75677637",
      "1.15280514"
    ],
    [
      "0.827929141",
      "1.157368984"
    ],
    [
      "1.648500806",
      "1.164480993"
    ],
    [
      "0.719851129",
      "1.16890049"
    ],
    [
      "1.540422794",
      "1.176012499"
    ],
    [
      "0.611773117",
      "1.180431996"
    ],
    [
      "1.432344782",
      "1.187544005"
    ],
    [
      "0.503695106",
      "1.191963502"
    ],
    [
      "1.324266771",
      "1.199075511"
    ],
    [
      "0.075562947",
      "1.199193722"
    ],
    [
      "0.395621428",
      "1.203535553"
    ],
    [
      "1.92319421",
      "1.20487668"
    ],
    [
      "1.216188759",
      "1.210607017"
    ],
    [
      "0.287543416",
      "1.215067059"
    ],
    [
      "1.108110747",
      "1.222138523"
    ],
    [
      "0.17985546",
      "1.229802609"
    ],
    [
      "1.000032735",
      "1.233670029"
    ],
    [
      "1.820604333",
      "1.240781406"
    ],
    [
      "0.891954724",
      "1.245201535"
    ],
    [
      "1.712526389",
      "1.252313544"
    ],
    [
      "0.783876712",
      "1.256733041"
    ],
    [
      "1.604448377",
      "1.26384505"
    ],
    [
      "0.6757987",
      "1.268264547"
    ],
    [
      "1.496370365",
      "1.275376556"
    ],
    [
      "0.567720689",
      "1.279796053"
    ],
    [
      "1.388292354",
      "1.286908061"
    ],
    [
      "0.459647011",
      "1.291368104"
    ],
    [
      "1.280214342",
      "1.298439567"
    ],
    [
      "0.351568999",
      "1.30289961"
    ],
    [
      "1.17213633",
      "1.309971073"
    ],
    [
      "0.107054789",
      "1.310778825"
    ],
    [
      "0.243881043",
      "1.31763516"
    ],
    [
      "1.064058318",
      "1.321502579"
    ],
    [
      "1.887529499",
      "1.326425171"
    ],
    [
      "0.955980307",
      "1.333034085"
    ],
    [
      "1.77989724",
      "1.341562182"
    ],
    [
      "0.847902295",
      "1.344565591"
    ],
    [
      "1.66847396",
      "1.3516776"
    ],
    [
      "0.739824283",
      "1.356097097"
    ],
    [
      "1.560395948",
      "1.363209106"
    ],
    [
      "0.631746272",
      "1.367628603"
    ],
    [
      "1.452317937",
      "1.374740612"
    ],
    [
      "0.522087366",
      "1.380334582"
    ],
    [
      "1.344239925",
      "1.386272118"
    ],
    [
      "1.236161913",
      "1.397803624"
    ],
    [
      "0.155490778",
      "1.408677829"
    ],
    [
      "0.375527886",
      "1.408917552"
    ],
    [
      "1.128083901",
      "1.40933513"
    ],
    [
      "1.02000589",
      "1.420866636"
    ],
    [
      "0.26783993",
      "1.423653101"
    ],
    [
      "1.841682712",
      "1.431053303"
    ],
    [
      "0.911927878",
      "1.432398142"
    ],
    [
      "1.732611128",
      "1.439428703"
    ],
    [
      "0.803849866",
      "1.443929648"
    ],
    [
      "1.624467074",
      "1.451140037"
    ],
    [
      "0.695771855",
      "1.455461154"
    ],
    [
      "1.51634352",
      "1.462573163"
    ],
    [
      "0.587693843",
      "1.46699266"
    ],
    [
      "0.463928191",
      "1.472156925"
    ],
    [
      "1.408265508",
      "1.474104669"
    ],
    [
      "1.300187496",
      "1.485636175"
    ],
    [
      "1.192109484",
      "1.497167681"
    ],
    [
      "1.084031473",
      "1.508699187"
    ],
    [
      "0.331902602",
      "1.511458604"
    ],
    [
      "0.205292156",
      "1.512544092"
    ],
    [
      "0.975953461",
      "1.520230693"
    ],
    [
      "0.867875449",
      "1.531762199"
    ],
    [
      "1.777370837",
      "1.538476169"
    ],
    [
      "0.759797438",
      "1.543293705"
    ],
    [
      "1.579713153",
      "1.550880138"
    ],
    [
      "0.651719426",
      "1.554825211"
    ],
    [
      "0.529534668",
      "1.558815003"
    ],
    [
      "1.472873131",
      "1.570856173"
    ],
    [
      "0.421728169",
      "1.572656642"
    ],
    [
      "1.364213079",
      "1.573468726"
    ],
    [
      "1.256135067",
      "1.585000232"
    ],
    [
      "1.681348721",
      "1.589403424"
    ],
    [
      "1.148057056",
      "1.596531738"
    ],
    [
      "0.269354827",
      "1.600349594"
    ],
    [
      "1.039986998",
      "1.608138037"
    ],
    [
      "0.931901032",
      "1.61959475"
    ],
    [
      "0.82382302",
      "1.631126256"
    ],
    [
      "0.713207072",
      "1.644963034"
    ],
    [
      "0.593560251",
      "1.646647553"
    ],
    [
      "1.542839524",
      "1.65403391"
    ],
    [
      "0.485753752",
      "1.660489193"
    ],
    [
      "0.359180394",
      "1.661547632"
    ],
    [
      "1.428822961",
      "1.670309615"
    ],
    [
      "1.32016065",
      "1.672832782"
    ],
    [
      "1.212399906",
      "1.68702624"
    ],
    [
      "1.644774919",
      "1.691756682"
    ],
    [
      "1.104073448",
      "1.695926277"
    ],
    [
      "0.895962368",
      "1.722172743"
    ],
    [
      "0.787884356",
      "1.733704249"
    ],
    [
      "1.003587976",
      "1.73735697"
    ],
    [
      "0.423205977",
      "1.749380183"
    ],
    [
      "0.606154968",
      "1.75460683"
    ],
    [
      "1.561138343",
      "1.761173938"
    ],
    [
      "1.376031107",
      "1.766065418"
    ],
    [
      "1.165944335",
      "1.785289723"
    ],
    [
      "1.273376757",
      "1.801785393"
    ],
    [
      "0.703729587",
      "1.802492381"
    ],
    [
      "0.51300569",
      "1.810616152"
    ],
    [
      "1.470088734",
      "1.820535548"
    ],
    [
      "0.848975134",
      "1.823602798"
    ],
    [
      "1.065274574",
      "1.826847728"
    ],
    [
      "0.956964107",
      "1.835940301"
    ],
    [
      "0.613472174",
      "1.863051704"
    ],
    [
      "1.361590026",
      "1.873793258"
    ],
    [
      "1.151503254",
      "1.893017563"
    ],
    [
      "0.732982285",
      "1.907173381"
    ],
    [
      "1.258935675",
      "1.909513232"
    ],
    [
      "0.83884225",
      "1.931820897"
    ],
    [
      "1.055522593",
      "1.944022905"
    ],
    [
      "0.946831223",
      "1.9441584"
    ]
  ],
  "radius": "0.054345726"
}
Submission format and technical detailsOpen this when you are ready to prepare a JSON answer+

Instance parameters

{
  "n": 285
}

Starter answer

{
  "centers": [
    [
      "0.987570151",
      "0.054427421"
    ],
    [
      "1.0961547",
      "0.059246963"
    ],
    [
      "0.879149809",
      "0.06209956"
    ],
    [
      "1.203468977",
      "0.076494516"
    ],
    [
      "0.767448997",
      "0.083429097"
    ],
    [
      "0.66397661",
      "0.116749704"
    ],
    [
      "1.371873567",
      "0.130533466"
    ],
    [
      "1.043319077",
      "0.154232378"
    ],
    [
      "1.268362174",
      "0.16368801"
    ],
    [
      "0.84080251",
      "0.163801659"
    ],
    [
      "1.150633354",
      "0.171479932"
    ],
    [
      "0.538111366",
      "0.17482069"
    ],
    [
      "0.943911639",
      "0.198186826"
    ],
    [
      "0.743368421",
      "0.211972506"
    ],
    [
      "1.43589915",
      "0.218366017"
    ],
    [
      "0.635290409",
      "0.223504012"
    ],
    [
      "1.544272445",
      "0.226676323"
    ],
    [
      "0.44647473",
      "0.23327203"
    ],
    [
      "1.332387757",
      "0.25152056"
    ],
    [
      "1.224309745",
      "0.263052066"
    ],
    [
      "1.116231733",
      "0.274583572"
    ],
    [
      "1.008128834",
      "0.285879381"
    ],
    [
      "1.629414583",
      "0.294238506"
    ],
    [
      "0.900076256",
      "0.297646826"
    ],
    [
      "0.362150554",
      "0.301852389"
    ],
    [
      "0.791998244",
      "0.309178332"
    ],
    [
      "0.568189701",
      "0.309382599"
    ],
    [
      "0.683920233",
      "0.320709838"
    ],
    [
      "1.504583113",
      "0.327862237"
    ],
    [
      "1.396494017",
      "0.339294813"
    ],
    [
      "0.463704974",
      "0.340589088"
    ],
    [
      "1.288426582",
      "0.350925024"
    ],
    [
      "1.180348571",
      "0.36245653"
    ],
    [
      "1.70624171",
      "0.371124296"
    ],
    [
      "1.072270559",
      "0.373988036"
    ],
    [
      "0.964182023",
      "0.38542133"
    ],
    [
      "1.589725251",
      "0.39542442"
    ],
    [
      "0.856114536",
      "0.397051048"
    ],
    [
      "0.322937549",
      "0.403223847"
    ],
    [
      "0.748036524",
      "0.408582554"
    ],
    [
      "0.639958512",
      "0.42011406"
    ],
    [
      "0.531406622",
      "0.425620371"
    ],
    [
      "1.460530177",
      "0.427226069"
    ],
    [
      "1.352452165",
      "0.438757575"
    ],
    [
      "0.424106572",
      "0.442956214"
    ],
    [
      "1.244374154",
      "0.450289081"
    ],
    [
      "0.227291685",
      "0.454854273"
    ],
    [
      "1.773738886",
      "0.456317979"
    ],
    [
      "1.136296142",
      "0.461820587"
    ],
    [
      "1.02821813",
      "0.473352093"
    ],
    [
      "0.920140119",
      "0.484883599"
    ],
    [
      "1.631520039",
      "0.495759"
    ],
    [
      "0.812062107",
      "0.496415105"
    ],
    [
      "0.703984095",
      "0.507946611"
    ],
    [
      "1.52455576",
      "0.51505862"
    ],
    [
      "0.595906083",
      "0.519478117"
    ],
    [
      "1.416477748",
      "0.526590126"
    ],
    [
      "0.487828072",
      "0.531009623"
    ],
    [
      "1.308399737",
      "0.538121632"
    ],
    [
      "0.379710833",
      "0.542167356"
    ],
    [
      "1.200321725",
      "0.549653137"
    ],
    [
      "1.723955783",
      "0.55293824"
    ],
    [
      "0.271673258",
      "0.554071752"
    ],
    [
      "1.834323602",
      "0.554956625"
    ],
    [
      "0.163125351",
      "0.559656015"
    ],
    [
      "1.092243713",
      "0.561184643"
    ],
    [
      "0.984165702",
      "0.572716149"
    ],
    [
      "0.87608769",
      "0.584247655"
    ],
    [
      "0.768009678",
      "0.595779161"
    ],
    [
      "1.593965745",
      "0.598920609"
    ],
    [
      "0.659931666",
      "0.607310667"
    ],
    [
      "1.480503331",
      "0.614422676"
    ],
    [
      "0.551853655",
      "0.618842173"
    ],
    [
      "1.37242532",
      "0.625954182"
    ],
    [
      "0.443775643",
      "0.630373679"
    ],
    [
      "1.264347308",
      "0.637485688"
    ],
    [
      "0.335697631",
      "0.641905185"
    ],
    [
      "1.156269296",
      "0.649017194"
    ],
    [
      "0.222235418",
      "0.650869129"
    ],
    [
      "1.880015498",
      "0.653947544"
    ],
    [
      "1.75588046",
      "0.656835532"
    ],
    [
      "1.048191285",
      "0.6605487"
    ],
    [
      "0.114570071",
      "0.668039527"
    ],
    [
      "0.940113273",
      "0.672080206"
    ],
    [
      "0.832035261",
      "0.683611712"
    ],
    [
      "1.652606926",
      "0.690723721"
    ],
    [
      "0.723957249",
      "0.695143218"
    ],
    [
      "1.544528914",
      "0.702255227"
    ],
    [
      "0.615879238",
      "0.706674724"
    ],
    [
      "1.436450903",
      "0.713786733"
    ],
    [
      "0.507801226",
      "0.71820623"
    ],
    [
      "1.328372891",
      "0.725318239"
    ],
    [
      "0.399723214",
      "0.729737736"
    ],
    [
      "1.220294879",
      "0.736849745"
    ],
    [
      "0.291645202",
      "0.741269242"
    ],
    [
      "1.819906043",
      "0.744668082"
    ],
    [
      "1.112216867",
      "0.748381251"
    ],
    [
      "0.183528794",
      "0.752435017"
    ],
    [
      "1.004138856",
      "0.759912757"
    ],
    [
      "0.896060844",
      "0.771444263"
    ],
    [
      "1.716632509",
      "0.778556272"
    ],
    [
      "0.787982832",
      "0.782975769"
    ],
    [
      "0.079422193",
      "0.783670379"
    ],
    [
      "1.920870164",
      "0.784918283"
    ],
    [
      "1.608554497",
      "0.790087778"
    ],
    [
      "0.679904821",
      "0.794507275"
    ],
    [
      "1.500476486",
      "0.801619284"
    ],
    [
      "0.571826809",
      "0.806038781"
    ],
    [
      "1.392398474",
      "0.81315079"
    ],
    [
      "0.463748797",
      "0.817570287"
    ],
    [
      "1.284320462",
      "0.824682296"
    ],
    [
      "0.355670785",
      "0.829101793"
    ],
    [
      "1.17624245",
      "0.836213802"
    ],
    [
      "0.247325334",
      "0.84052708"
    ],
    [
      "1.068164439",
      "0.847745308"
    ],
    [
      "0.960086427",
      "0.859276814"
    ],
    [
      "1.788906358",
      "0.860699537"
    ],
    [
      "0.852008415",
      "0.87080832"
    ],
    [
      "1.67258008",
      "0.877920329"
    ],
    [
      "0.743930404",
      "0.882339826"
    ],
    [
      "0.10794332",
      "0.888553064"
    ],
    [
      "1.564502069",
      "0.889451835"
    ],
    [
      "1.939467662",
      "0.892006869"
    ],
    [
      "0.635852392",
      "0.893871332"
    ],
    [
      "1.456424057",
      "0.900983341"
    ],
    [
      "0.52777438",
      "0.905402838"
    ],
    [
      "1.348346045",
      "0.912514846"
    ],
    [
      "0.419696368",
      "0.916934344"
    ],
    [
      "1.240268033",
      "0.924046352"
    ],
    [
      "0.311618357",
      "0.928465849"
    ],
    [
      "1.132190022",
      "0.935577858"
    ],
    [
      "0.203565193",
      "0.940227909"
    ],
    [
      "1.02411201",
      "0.947109364"
    ],
    [
      "1.84858393",
      "0.951622132"
    ],
    [
      "0.916033998",
      "0.95864087"
    ],
    [
      "1.740468996",
      "0.962802172"
    ],
    [
      "0.807955987",
      "0.970172376"
    ],
    [
      "1.628527652",
      "0.977284385"
    ],
    [
      "0.699877975",
      "0.981703882"
    ],
    [
      "0.054495056",
      "0.983195102"
    ],
    [
      "1.52044964",
      "0.988815891"
    ],
    [
      "0.591799963",
      "0.993235388"
    ],
    [
      "1.412371628",
      "1.000347397"
    ],
    [
      "1.945654129",
      "1.000522121"
    ],
    [
      "0.483721951",
      "1.004766894"
    ],
    [
      "1.304293616",
      "1.011878903"
    ],
    [
      "0.375610982",
      "1.016322415"
    ],
    [
      "1.196215605",
      "1.023410409"
    ],
    [
      "0.264153827",
      "1.030465648"
    ],
    [
      "1.088137593",
      "1.034941915"
    ],
    [
      "0.152047178",
      "1.035934368"
    ],
    [
      "0.980059581",
      "1.046473421"
    ],
    [
      "1.800605015",
      "1.053342172"
    ],
    [
      "0.87198157",
      "1.058004927"
    ],
    [
      "1.692553235",
      "1.065116936"
    ],
    [
      "0.763903558",
      "1.069536433"
    ],
    [
      "1.584475223",
      "1.076648442"
    ],
    [
      "0.655825546",
      "1.081067939"
    ],
    [
      "1.476397211",
      "1.088179948"
    ],
    [
      "0.058812123",
      "1.091800788"
    ],
    [
      "0.547747534",
      "1.092599445"
    ],
    [
      "1.899315278",
      "1.098840701"
    ],
    [
      "1.368319199",
      "1.099711454"
    ],
    [
      "0.439669523",
      "1.104130951"
    ],
    [
      "1.260241188",
      "1.11124296"
    ],
    [
      "0.331595845",
      "1.115703002"
    ],
    [
      "1.152163176",
      "1.122774466"
    ],
    [
      "0.212635812",
      "1.126172108"
    ],
    [
      "1.044085164",
      "1.134305972"
    ],
    [
      "0.936007153",
      "1.145837478"
    ],
    [
      "1.75677637",
      "1.15280514"
    ],
    [
      "0.827929141",
      "1.157368984"
    ],
    [
      "1.648500806",
      "1.164480993"
    ],
    [
      "0.719851129",
      "1.16890049"
    ],
    [
      "1.540422794",
      "1.176012499"
    ],
    [
      "0.611773117",
      "1.180431996"
    ],
    [
      "1.432344782",
      "1.187544005"
    ],
    [
      "0.503695106",
      "1.191963502"
    ],
    [
      "1.324266771",
      "1.199075511"
    ],
    [
      "0.075562947",
      "1.199193722"
    ],
    [
      "0.395621428",
      "1.203535553"
    ],
    [
      "1.92319421",
      "1.20487668"
    ],
    [
      "1.216188759",
      "1.210607017"
    ],
    [
      "0.287543416",
      "1.215067059"
    ],
    [
      "1.108110747",
      "1.222138523"
    ],
    [
      "0.17985546",
      "1.229802609"
    ],
    [
      "1.000032735",
      "1.233670029"
    ],
    [
      "1.820604333",
      "1.240781406"
    ],
    [
      "0.891954724",
      "1.245201535"
    ],
    [
      "1.712526389",
      "1.252313544"
    ],
    [
      "0.783876712",
      "1.256733041"
    ],
    [
      "1.604448377",
      "1.26384505"
    ],
    [
      "0.6757987",
      "1.268264547"
    ],
    [
      "1.496370365",
      "1.275376556"
    ],
    [
      "0.567720689",
      "1.279796053"
    ],
    [
      "1.388292354",
      "1.286908061"
    ],
    [
      "0.459647011",
      "1.291368104"
    ],
    [
      "1.280214342",
      "1.298439567"
    ],
    [
      "0.351568999",
      "1.30289961"
    ],
    [
      "1.17213633",
      "1.309971073"
    ],
    [
      "0.107054789",
      "1.310778825"
    ],
    [
      "0.243881043",
      "1.31763516"
    ],
    [
      "1.064058318",
      "1.321502579"
    ],
    [
      "1.887529499",
      "1.326425171"
    ],
    [
      "0.955980307",
      "1.333034085"
    ],
    [
      "1.77989724",
      "1.341562182"
    ],
    [
      "0.847902295",
      "1.344565591"
    ],
    [
      "1.66847396",
      "1.3516776"
    ],
    [
      "0.739824283",
      "1.356097097"
    ],
    [
      "1.560395948",
      "1.363209106"
    ],
    [
      "0.631746272",
      "1.367628603"
    ],
    [
      "1.452317937",
      "1.374740612"
    ],
    [
      "0.522087366",
      "1.380334582"
    ],
    [
      "1.344239925",
      "1.386272118"
    ],
    [
      "1.236161913",
      "1.397803624"
    ],
    [
      "0.155490778",
      "1.408677829"
    ],
    [
      "0.375527886",
      "1.408917552"
    ],
    [
      "1.128083901",
      "1.40933513"
    ],
    [
      "1.02000589",
      "1.420866636"
    ],
    [
      "0.26783993",
      "1.423653101"
    ],
    [
      "1.841682712",
      "1.431053303"
    ],
    [
      "0.911927878",
      "1.432398142"
    ],
    [
      "1.732611128",
      "1.439428703"
    ],
    [
      "0.803849866",
      "1.443929648"
    ],
    [
      "1.624467074",
      "1.451140037"
    ],
    [
      "0.695771855",
      "1.455461154"
    ],
    [
      "1.51634352",
      "1.462573163"
    ],
    [
      "0.587693843",
      "1.46699266"
    ],
    [
      "0.463928191",
      "1.472156925"
    ],
    [
      "1.408265508",
      "1.474104669"
    ],
    [
      "1.300187496",
      "1.485636175"
    ],
    [
      "1.192109484",
      "1.497167681"
    ],
    [
      "1.084031473",
      "1.508699187"
    ],
    [
      "0.331902602",
      "1.511458604"
    ],
    [
      "0.205292156",
      "1.512544092"
    ],
    [
      "0.975953461",
      "1.520230693"
    ],
    [
      "0.867875449",
      "1.531762199"
    ],
    [
      "1.777370837",
      "1.538476169"
    ],
    [
      "0.759797438",
      "1.543293705"
    ],
    [
      "1.579713153",
      "1.550880138"
    ],
    [
      "0.651719426",
      "1.554825211"
    ],
    [
      "0.529534668",
      "1.558815003"
    ],
    [
      "1.472873131",
      "1.570856173"
    ],
    [
      "0.421728169",
      "1.572656642"
    ],
    [
      "1.364213079",
      "1.573468726"
    ],
    [
      "1.256135067",
      "1.585000232"
    ],
    [
      "1.681348721",
      "1.589403424"
    ],
    [
      "1.148057056",
      "1.596531738"
    ],
    [
      "0.269354827",
      "1.600349594"
    ],
    [
      "1.039986998",
      "1.608138037"
    ],
    [
      "0.931901032",
      "1.61959475"
    ],
    [
      "0.82382302",
      "1.631126256"
    ],
    [
      "0.713207072",
      "1.644963034"
    ],
    [
      "0.593560251",
      "1.646647553"
    ],
    [
      "1.542839524",
      "1.65403391"
    ],
    [
      "0.485753752",
      "1.660489193"
    ],
    [
      "0.359180394",
      "1.661547632"
    ],
    [
      "1.428822961",
      "1.670309615"
    ],
    [
      "1.32016065",
      "1.672832782"
    ],
    [
      "1.212399906",
      "1.68702624"
    ],
    [
      "1.644774919",
      "1.691756682"
    ],
    [
      "1.104073448",
      "1.695926277"
    ],
    [
      "0.895962368",
      "1.722172743"
    ],
    [
      "0.787884356",
      "1.733704249"
    ],
    [
      "1.003587976",
      "1.73735697"
    ],
    [
      "0.423205977",
      "1.749380183"
    ],
    [
      "0.606154968",
      "1.75460683"
    ],
    [
      "1.561138343",
      "1.761173938"
    ],
    [
      "1.376031107",
      "1.766065418"
    ],
    [
      "1.165944335",
      "1.785289723"
    ],
    [
      "1.273376757",
      "1.801785393"
    ],
    [
      "0.703729587",
      "1.802492381"
    ],
    [
      "0.51300569",
      "1.810616152"
    ],
    [
      "1.470088734",
      "1.820535548"
    ],
    [
      "0.848975134",
      "1.823602798"
    ],
    [
      "1.065274574",
      "1.826847728"
    ],
    [
      "0.956964107",
      "1.835940301"
    ],
    [
      "0.613472174",
      "1.863051704"
    ],
    [
      "1.361590026",
      "1.873793258"
    ],
    [
      "1.151503254",
      "1.893017563"
    ],
    [
      "0.732982285",
      "1.907173381"
    ],
    [
      "1.258935675",
      "1.909513232"
    ],
    [
      "0.83884225",
      "1.931820897"
    ],
    [
      "1.055522593",
      "1.944022905"
    ],
    [
      "0.946831223",
      "1.9441584"
    ]
  ],
  "radius": "0.054345726"
}

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?