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

Equal-circle packing in a unit circle · n = 222

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 = 222
ObjectiveMaximize common radius

Record comparison

common radius · Higher is better
RecordValue / intervalAuthor / holderSource
External best known[0.0613546248065, 0.0613546248075]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 = 0.061354624

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 = 222
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": [
    [
      "0.976269619",
      "0.061654643"
    ],
    [
      "0.854064712",
      "0.07276862"
    ],
    [
      "1.16391431",
      "0.075777495"
    ],
    [
      "0.732044326",
      "0.100651379"
    ],
    [
      "1.380350265",
      "0.141868998"
    ],
    [
      "0.611047447",
      "0.145733618"
    ],
    [
      "1.064179989",
      "0.147266131"
    ],
    [
      "1.258265578",
      "0.15423384"
    ],
    [
      "0.949059167",
      "0.189748554"
    ],
    [
      "0.826376723",
      "0.19231332"
    ],
    [
      "1.497289708",
      "0.203910755"
    ],
    [
      "0.512754433",
      "0.219191383"
    ],
    [
      "0.707280347",
      "0.221870265"
    ],
    [
      "1.158531257",
      "0.225722476"
    ],
    [
      "1.390393506",
      "0.264166558"
    ],
    [
      "1.043410435",
      "0.268204899"
    ],
    [
      "0.40357423",
      "0.275202483"
    ],
    [
      "1.265956962",
      "0.288156904"
    ],
    [
      "1.612945356",
      "0.28912071"
    ],
    [
      "0.928289613",
      "0.310687322"
    ],
    [
      "0.80560717",
      "0.313252088"
    ],
    [
      "0.626195294",
      "0.313972242"
    ],
    [
      "1.496024664",
      "0.326613483"
    ],
    [
      "0.506671366",
      "0.341749762"
    ],
    [
      "1.156327067",
      "0.348411927"
    ],
    [
      "1.699846763",
      "0.375776666"
    ],
    [
      "1.365799158",
      "0.38438585"
    ],
    [
      "1.041206245",
      "0.39089435"
    ],
    [
      "0.716237309",
      "0.397338876"
    ],
    [
      "0.397491164",
      "0.397760861"
    ],
    [
      "0.274935521",
      "0.4038988"
    ],
    [
      "1.575432709",
      "0.420165192"
    ],
    [
      "1.250678336",
      "0.426868272"
    ],
    [
      "0.926085423",
      "0.433376773"
    ],
    [
      "0.599018679",
      "0.433634231"
    ],
    [
      "1.460311887",
      "0.462647615"
    ],
    [
      "1.135557514",
      "0.469350695"
    ],
    [
      "0.810832868",
      "0.475500504"
    ],
    [
      "0.486391357",
      "0.482344048"
    ],
    [
      "1.792482276",
      "0.496982124"
    ],
    [
      "1.669783978",
      "0.498621537"
    ],
    [
      "1.345029604",
      "0.505324617"
    ],
    [
      "1.020436691",
      "0.511833118"
    ],
    [
      "0.695843779",
      "0.518341619"
    ],
    [
      "0.248566084",
      "0.523741249"
    ],
    [
      "0.371270535",
      "0.524826471"
    ],
    [
      "1.554663156",
      "0.54110396"
    ],
    [
      "1.229908782",
      "0.54780704"
    ],
    [
      "0.905315869",
      "0.554315541"
    ],
    [
      "0.580722956",
      "0.560824042"
    ],
    [
      "1.439542334",
      "0.583586383"
    ],
    [
      "1.11478796",
      "0.590289463"
    ],
    [
      "0.790195047",
      "0.596797964"
    ],
    [
      "0.151444539",
      "0.598741019"
    ],
    [
      "0.465602134",
      "0.603306464"
    ],
    [
      "1.851329337",
      "0.604660271"
    ],
    [
      "1.649014424",
      "0.619560305"
    ],
    [
      "1.32426005",
      "0.626263385"
    ],
    [
      "0.999667138",
      "0.632771886"
    ],
    [
      "0.675074225",
      "0.639280387"
    ],
    [
      "0.350481152",
      "0.645788453"
    ],
    [
      "1.533893602",
      "0.662042728"
    ],
    [
      "1.209139228",
      "0.668745808"
    ],
    [
      "0.884546316",
      "0.675254309"
    ],
    [
      "1.755244224",
      "0.680983342"
    ],
    [
      "0.559953403",
      "0.68176281"
    ],
    [
      "0.23536049",
      "0.68827131"
    ],
    [
      "1.41877278",
      "0.704525151"
    ],
    [
      "1.094018406",
      "0.711228231"
    ],
    [
      "0.769425493",
      "0.717736732"
    ],
    [
      "0.110664264",
      "0.71790673"
    ],
    [
      "0.444832581",
      "0.724245232"
    ],
    [
      "1.869384499",
      "0.726033955"
    ],
    [
      "1.62824487",
      "0.740499073"
    ],
    [
      "1.303490497",
      "0.747202153"
    ],
    [
      "0.978897584",
      "0.753710654"
    ],
    [
      "0.654304671",
      "0.760219155"
    ],
    [
      "0.329711759",
      "0.766727655"
    ],
    [
      "1.513124048",
      "0.782981496"
    ],
    [
      "1.188369675",
      "0.789684576"
    ],
    [
      "0.863776762",
      "0.796193077"
    ],
    [
      "1.734474671",
      "0.80192211"
    ],
    [
      "0.539183849",
      "0.802701577"
    ],
    [
      "0.214590936",
      "0.809210078"
    ],
    [
      "1.398003226",
      "0.825463919"
    ],
    [
      "1.073248853",
      "0.832166999"
    ],
    [
      "0.076155294",
      "0.835703663"
    ],
    [
      "1.924177238",
      "0.835830656"
    ],
    [
      "0.74865594",
      "0.8386755"
    ],
    [
      "0.424063027",
      "0.845184"
    ],
    [
      "1.607967548",
      "0.861521344"
    ],
    [
      "1.282720943",
      "0.868140921"
    ],
    [
      "0.95812803",
      "0.874649422"
    ],
    [
      "0.633535118",
      "0.881157922"
    ],
    [
      "0.308940803",
      "0.887668109"
    ],
    [
      "1.815956292",
      "0.893673433"
    ],
    [
      "1.492354495",
      "0.903920264"
    ],
    [
      "1.167600121",
      "0.910623344"
    ],
    [
      "0.843007208",
      "0.917131845"
    ],
    [
      "0.164525264",
      "0.921241272"
    ],
    [
      "0.518414295",
      "0.923640345"
    ],
    [
      "1.702318817",
      "0.939977689"
    ],
    [
      "1.377233673",
      "0.946402687"
    ],
    [
      "1.052479299",
      "0.953105767"
    ],
    [
      "1.937695956",
      "0.957792963"
    ],
    [
      "0.727886386",
      "0.959614268"
    ],
    [
      "0.403293473",
      "0.966122768"
    ],
    [
      "1.586707259",
      "0.982374809"
    ],
    [
      "0.061433944",
      "0.987797562"
    ],
    [
      "1.261951389",
      "0.989079689"
    ],
    [
      "0.937358477",
      "0.99558819"
    ],
    [
      "0.612765564",
      "1.00209669"
    ],
    [
      "0.288174821",
      "1.00861107"
    ],
    [
      "1.82947501",
      "1.01563574"
    ],
    [
      "1.471584941",
      "1.024859032"
    ],
    [
      "1.146830567",
      "1.031562112"
    ],
    [
      "0.822237655",
      "1.038070613"
    ],
    [
      "0.170619042",
      "1.043799119"
    ],
    [
      "0.497644742",
      "1.044579113"
    ],
    [
      "1.681058528",
      "1.060831154"
    ],
    [
      "1.356464119",
      "1.067341454"
    ],
    [
      "1.031709745",
      "1.074044535"
    ],
    [
      "0.707116832",
      "1.080553035"
    ],
    [
      "1.934305059",
      "1.085222295"
    ],
    [
      "0.382526089",
      "1.087067415"
    ],
    [
      "1.565937706",
      "1.103313577"
    ],
    [
      "1.241181836",
      "1.110018457"
    ],
    [
      "0.067939618",
      "1.110989116"
    ],
    [
      "0.916588923",
      "1.116526958"
    ],
    [
      "0.59199601",
      "1.123035458"
    ],
    [
      "1.782964285",
      "1.129188865"
    ],
    [
      "0.260641081",
      "1.13730788"
    ],
    [
      "1.450815387",
      "1.145797799"
    ],
    [
      "1.126061014",
      "1.15250088"
    ],
    [
      "0.801468101",
      "1.15900938"
    ],
    [
      "0.476877358",
      "1.16552376"
    ],
    [
      "1.66540815",
      "1.182752921"
    ],
    [
      "1.335694565",
      "1.188280222"
    ],
    [
      "1.010940192",
      "1.194983303"
    ],
    [
      "0.686347279",
      "1.201491803"
    ],
    [
      "1.915313721",
      "1.206586066"
    ],
    [
      "0.361756536",
      "1.208006183"
    ],
    [
      "0.137567744",
      "1.212031107"
    ],
    [
      "1.545168152",
      "1.224252345"
    ],
    [
      "1.220412282",
      "1.230957225"
    ],
    [
      "0.895819369",
      "1.237465726"
    ],
    [
      "0.571228626",
      "1.243980105"
    ],
    [
      "1.800754337",
      "1.25060169"
    ],
    [
      "0.250557567",
      "1.259894035"
    ],
    [
      "1.430045834",
      "1.266736567"
    ],
    [
      "1.10529146",
      "1.273439648"
    ],
    [
      "0.780698547",
      "1.279948148"
    ],
    [
      "0.456107804",
      "1.286462528"
    ],
    [
      "1.63951942",
      "1.30270869"
    ],
    [
      "1.314925012",
      "1.30921899"
    ],
    [
      "0.990170638",
      "1.315922071"
    ],
    [
      "0.665579895",
      "1.322436451"
    ],
    [
      "0.122727994",
      "1.333839735"
    ],
    [
      "0.344908835",
      "1.33835038"
    ],
    [
      "1.524398598",
      "1.345191113"
    ],
    [
      "1.870252136",
      "1.351733366"
    ],
    [
      "1.199642728",
      "1.351895993"
    ],
    [
      "0.875049816",
      "1.358404493"
    ],
    [
      "1.747434052",
      "1.361120951"
    ],
    [
      "0.550459073",
      "1.364918873"
    ],
    [
      "1.409278586",
      "1.387675731"
    ],
    [
      "0.232761503",
      "1.388155359"
    ],
    [
      "1.084521906",
      "1.394378416"
    ],
    [
      "0.759931163",
      "1.400892796"
    ],
    [
      "0.439260104",
      "1.416806726"
    ],
    [
      "1.294155458",
      "1.430157758"
    ],
    [
      "1.638833401",
      "1.431555653"
    ],
    [
      "0.969401084",
      "1.436860838"
    ],
    [
      "0.644462706",
      "1.443795141"
    ],
    [
      "1.816931851",
      "1.462252628"
    ],
    [
      "0.327112771",
      "1.466611704"
    ],
    [
      "1.515137983",
      "1.467550424"
    ],
    [
      "1.178873175",
      "1.472834761"
    ],
    [
      "0.854282432",
      "1.479349141"
    ],
    [
      "1.388506726",
      "1.508614103"
    ],
    [
      "0.211333166",
      "1.508979141"
    ],
    [
      "1.063752353",
      "1.515317184"
    ],
    [
      "0.5119108",
      "1.515697757"
    ],
    [
      "0.73916161",
      "1.521831563"
    ],
    [
      "1.724257148",
      "1.542682469"
    ],
    [
      "1.273385904",
      "1.551096526"
    ],
    [
      "1.602084071",
      "1.554141057"
    ],
    [
      "0.9486337",
      "1.557805486"
    ],
    [
      "0.624288788",
      "1.564980085"
    ],
    [
      "0.399763468",
      "1.565502735"
    ],
    [
      "1.483621339",
      "1.586143262"
    ],
    [
      "1.158103621",
      "1.593773529"
    ],
    [
      "0.833512878",
      "1.600287909"
    ],
    [
      "0.284469091",
      "1.607511858"
    ],
    [
      "1.367737173",
      "1.629552871"
    ],
    [
      "1.042984969",
      "1.636261831"
    ],
    [
      "0.718640057",
      "1.64343643"
    ],
    [
      "0.485128082",
      "1.65365285"
    ],
    [
      "1.673094037",
      "1.654216751"
    ],
    [
      "1.252616351",
      "1.672035294"
    ],
    [
      "0.927864147",
      "1.678744254"
    ],
    [
      "0.603519235",
      "1.685918852"
    ],
    [
      "0.369833704",
      "1.695661973"
    ],
    [
      "1.462851785",
      "1.707082029"
    ],
    [
      "1.137583309",
      "1.714754836"
    ],
    [
      "0.812991325",
      "1.721892775"
    ],
    [
      "1.581999375",
      "1.736431849"
    ],
    [
      "1.346967619",
      "1.750491639"
    ],
    [
      "1.022464657",
      "1.757243138"
    ],
    [
      "0.697870503",
      "1.764375198"
    ],
    [
      "0.47277529",
      "1.776534946"
    ],
    [
      "1.232180397",
      "1.793867364"
    ],
    [
      "0.907503361",
      "1.800155378"
    ],
    [
      "0.586118775",
      "1.823797202"
    ],
    [
      "1.442082232",
      "1.828020797"
    ],
    [
      "1.116819932",
      "1.835694664"
    ],
    [
      "1.327811453",
      "1.876126552"
    ],
    [
      "0.815469962",
      "1.881318261"
    ],
    [
      "0.692891553",
      "1.886983395"
    ],
    [
      "1.210723669",
      "1.914686108"
    ],
    [
      "0.925479436",
      "1.935682545"
    ],
    [
      "1.048176551",
      "1.937408214"
    ]
  ],
  "radius": "0.061354624"
}
Submission format and technical detailsOpen this when you are ready to prepare a JSON answer+

Instance parameters

{
  "n": 222
}

Starter answer

{
  "centers": [
    [
      "0.976269619",
      "0.061654643"
    ],
    [
      "0.854064712",
      "0.07276862"
    ],
    [
      "1.16391431",
      "0.075777495"
    ],
    [
      "0.732044326",
      "0.100651379"
    ],
    [
      "1.380350265",
      "0.141868998"
    ],
    [
      "0.611047447",
      "0.145733618"
    ],
    [
      "1.064179989",
      "0.147266131"
    ],
    [
      "1.258265578",
      "0.15423384"
    ],
    [
      "0.949059167",
      "0.189748554"
    ],
    [
      "0.826376723",
      "0.19231332"
    ],
    [
      "1.497289708",
      "0.203910755"
    ],
    [
      "0.512754433",
      "0.219191383"
    ],
    [
      "0.707280347",
      "0.221870265"
    ],
    [
      "1.158531257",
      "0.225722476"
    ],
    [
      "1.390393506",
      "0.264166558"
    ],
    [
      "1.043410435",
      "0.268204899"
    ],
    [
      "0.40357423",
      "0.275202483"
    ],
    [
      "1.265956962",
      "0.288156904"
    ],
    [
      "1.612945356",
      "0.28912071"
    ],
    [
      "0.928289613",
      "0.310687322"
    ],
    [
      "0.80560717",
      "0.313252088"
    ],
    [
      "0.626195294",
      "0.313972242"
    ],
    [
      "1.496024664",
      "0.326613483"
    ],
    [
      "0.506671366",
      "0.341749762"
    ],
    [
      "1.156327067",
      "0.348411927"
    ],
    [
      "1.699846763",
      "0.375776666"
    ],
    [
      "1.365799158",
      "0.38438585"
    ],
    [
      "1.041206245",
      "0.39089435"
    ],
    [
      "0.716237309",
      "0.397338876"
    ],
    [
      "0.397491164",
      "0.397760861"
    ],
    [
      "0.274935521",
      "0.4038988"
    ],
    [
      "1.575432709",
      "0.420165192"
    ],
    [
      "1.250678336",
      "0.426868272"
    ],
    [
      "0.926085423",
      "0.433376773"
    ],
    [
      "0.599018679",
      "0.433634231"
    ],
    [
      "1.460311887",
      "0.462647615"
    ],
    [
      "1.135557514",
      "0.469350695"
    ],
    [
      "0.810832868",
      "0.475500504"
    ],
    [
      "0.486391357",
      "0.482344048"
    ],
    [
      "1.792482276",
      "0.496982124"
    ],
    [
      "1.669783978",
      "0.498621537"
    ],
    [
      "1.345029604",
      "0.505324617"
    ],
    [
      "1.020436691",
      "0.511833118"
    ],
    [
      "0.695843779",
      "0.518341619"
    ],
    [
      "0.248566084",
      "0.523741249"
    ],
    [
      "0.371270535",
      "0.524826471"
    ],
    [
      "1.554663156",
      "0.54110396"
    ],
    [
      "1.229908782",
      "0.54780704"
    ],
    [
      "0.905315869",
      "0.554315541"
    ],
    [
      "0.580722956",
      "0.560824042"
    ],
    [
      "1.439542334",
      "0.583586383"
    ],
    [
      "1.11478796",
      "0.590289463"
    ],
    [
      "0.790195047",
      "0.596797964"
    ],
    [
      "0.151444539",
      "0.598741019"
    ],
    [
      "0.465602134",
      "0.603306464"
    ],
    [
      "1.851329337",
      "0.604660271"
    ],
    [
      "1.649014424",
      "0.619560305"
    ],
    [
      "1.32426005",
      "0.626263385"
    ],
    [
      "0.999667138",
      "0.632771886"
    ],
    [
      "0.675074225",
      "0.639280387"
    ],
    [
      "0.350481152",
      "0.645788453"
    ],
    [
      "1.533893602",
      "0.662042728"
    ],
    [
      "1.209139228",
      "0.668745808"
    ],
    [
      "0.884546316",
      "0.675254309"
    ],
    [
      "1.755244224",
      "0.680983342"
    ],
    [
      "0.559953403",
      "0.68176281"
    ],
    [
      "0.23536049",
      "0.68827131"
    ],
    [
      "1.41877278",
      "0.704525151"
    ],
    [
      "1.094018406",
      "0.711228231"
    ],
    [
      "0.769425493",
      "0.717736732"
    ],
    [
      "0.110664264",
      "0.71790673"
    ],
    [
      "0.444832581",
      "0.724245232"
    ],
    [
      "1.869384499",
      "0.726033955"
    ],
    [
      "1.62824487",
      "0.740499073"
    ],
    [
      "1.303490497",
      "0.747202153"
    ],
    [
      "0.978897584",
      "0.753710654"
    ],
    [
      "0.654304671",
      "0.760219155"
    ],
    [
      "0.329711759",
      "0.766727655"
    ],
    [
      "1.513124048",
      "0.782981496"
    ],
    [
      "1.188369675",
      "0.789684576"
    ],
    [
      "0.863776762",
      "0.796193077"
    ],
    [
      "1.734474671",
      "0.80192211"
    ],
    [
      "0.539183849",
      "0.802701577"
    ],
    [
      "0.214590936",
      "0.809210078"
    ],
    [
      "1.398003226",
      "0.825463919"
    ],
    [
      "1.073248853",
      "0.832166999"
    ],
    [
      "0.076155294",
      "0.835703663"
    ],
    [
      "1.924177238",
      "0.835830656"
    ],
    [
      "0.74865594",
      "0.8386755"
    ],
    [
      "0.424063027",
      "0.845184"
    ],
    [
      "1.607967548",
      "0.861521344"
    ],
    [
      "1.282720943",
      "0.868140921"
    ],
    [
      "0.95812803",
      "0.874649422"
    ],
    [
      "0.633535118",
      "0.881157922"
    ],
    [
      "0.308940803",
      "0.887668109"
    ],
    [
      "1.815956292",
      "0.893673433"
    ],
    [
      "1.492354495",
      "0.903920264"
    ],
    [
      "1.167600121",
      "0.910623344"
    ],
    [
      "0.843007208",
      "0.917131845"
    ],
    [
      "0.164525264",
      "0.921241272"
    ],
    [
      "0.518414295",
      "0.923640345"
    ],
    [
      "1.702318817",
      "0.939977689"
    ],
    [
      "1.377233673",
      "0.946402687"
    ],
    [
      "1.052479299",
      "0.953105767"
    ],
    [
      "1.937695956",
      "0.957792963"
    ],
    [
      "0.727886386",
      "0.959614268"
    ],
    [
      "0.403293473",
      "0.966122768"
    ],
    [
      "1.586707259",
      "0.982374809"
    ],
    [
      "0.061433944",
      "0.987797562"
    ],
    [
      "1.261951389",
      "0.989079689"
    ],
    [
      "0.937358477",
      "0.99558819"
    ],
    [
      "0.612765564",
      "1.00209669"
    ],
    [
      "0.288174821",
      "1.00861107"
    ],
    [
      "1.82947501",
      "1.01563574"
    ],
    [
      "1.471584941",
      "1.024859032"
    ],
    [
      "1.146830567",
      "1.031562112"
    ],
    [
      "0.822237655",
      "1.038070613"
    ],
    [
      "0.170619042",
      "1.043799119"
    ],
    [
      "0.497644742",
      "1.044579113"
    ],
    [
      "1.681058528",
      "1.060831154"
    ],
    [
      "1.356464119",
      "1.067341454"
    ],
    [
      "1.031709745",
      "1.074044535"
    ],
    [
      "0.707116832",
      "1.080553035"
    ],
    [
      "1.934305059",
      "1.085222295"
    ],
    [
      "0.382526089",
      "1.087067415"
    ],
    [
      "1.565937706",
      "1.103313577"
    ],
    [
      "1.241181836",
      "1.110018457"
    ],
    [
      "0.067939618",
      "1.110989116"
    ],
    [
      "0.916588923",
      "1.116526958"
    ],
    [
      "0.59199601",
      "1.123035458"
    ],
    [
      "1.782964285",
      "1.129188865"
    ],
    [
      "0.260641081",
      "1.13730788"
    ],
    [
      "1.450815387",
      "1.145797799"
    ],
    [
      "1.126061014",
      "1.15250088"
    ],
    [
      "0.801468101",
      "1.15900938"
    ],
    [
      "0.476877358",
      "1.16552376"
    ],
    [
      "1.66540815",
      "1.182752921"
    ],
    [
      "1.335694565",
      "1.188280222"
    ],
    [
      "1.010940192",
      "1.194983303"
    ],
    [
      "0.686347279",
      "1.201491803"
    ],
    [
      "1.915313721",
      "1.206586066"
    ],
    [
      "0.361756536",
      "1.208006183"
    ],
    [
      "0.137567744",
      "1.212031107"
    ],
    [
      "1.545168152",
      "1.224252345"
    ],
    [
      "1.220412282",
      "1.230957225"
    ],
    [
      "0.895819369",
      "1.237465726"
    ],
    [
      "0.571228626",
      "1.243980105"
    ],
    [
      "1.800754337",
      "1.25060169"
    ],
    [
      "0.250557567",
      "1.259894035"
    ],
    [
      "1.430045834",
      "1.266736567"
    ],
    [
      "1.10529146",
      "1.273439648"
    ],
    [
      "0.780698547",
      "1.279948148"
    ],
    [
      "0.456107804",
      "1.286462528"
    ],
    [
      "1.63951942",
      "1.30270869"
    ],
    [
      "1.314925012",
      "1.30921899"
    ],
    [
      "0.990170638",
      "1.315922071"
    ],
    [
      "0.665579895",
      "1.322436451"
    ],
    [
      "0.122727994",
      "1.333839735"
    ],
    [
      "0.344908835",
      "1.33835038"
    ],
    [
      "1.524398598",
      "1.345191113"
    ],
    [
      "1.870252136",
      "1.351733366"
    ],
    [
      "1.199642728",
      "1.351895993"
    ],
    [
      "0.875049816",
      "1.358404493"
    ],
    [
      "1.747434052",
      "1.361120951"
    ],
    [
      "0.550459073",
      "1.364918873"
    ],
    [
      "1.409278586",
      "1.387675731"
    ],
    [
      "0.232761503",
      "1.388155359"
    ],
    [
      "1.084521906",
      "1.394378416"
    ],
    [
      "0.759931163",
      "1.400892796"
    ],
    [
      "0.439260104",
      "1.416806726"
    ],
    [
      "1.294155458",
      "1.430157758"
    ],
    [
      "1.638833401",
      "1.431555653"
    ],
    [
      "0.969401084",
      "1.436860838"
    ],
    [
      "0.644462706",
      "1.443795141"
    ],
    [
      "1.816931851",
      "1.462252628"
    ],
    [
      "0.327112771",
      "1.466611704"
    ],
    [
      "1.515137983",
      "1.467550424"
    ],
    [
      "1.178873175",
      "1.472834761"
    ],
    [
      "0.854282432",
      "1.479349141"
    ],
    [
      "1.388506726",
      "1.508614103"
    ],
    [
      "0.211333166",
      "1.508979141"
    ],
    [
      "1.063752353",
      "1.515317184"
    ],
    [
      "0.5119108",
      "1.515697757"
    ],
    [
      "0.73916161",
      "1.521831563"
    ],
    [
      "1.724257148",
      "1.542682469"
    ],
    [
      "1.273385904",
      "1.551096526"
    ],
    [
      "1.602084071",
      "1.554141057"
    ],
    [
      "0.9486337",
      "1.557805486"
    ],
    [
      "0.624288788",
      "1.564980085"
    ],
    [
      "0.399763468",
      "1.565502735"
    ],
    [
      "1.483621339",
      "1.586143262"
    ],
    [
      "1.158103621",
      "1.593773529"
    ],
    [
      "0.833512878",
      "1.600287909"
    ],
    [
      "0.284469091",
      "1.607511858"
    ],
    [
      "1.367737173",
      "1.629552871"
    ],
    [
      "1.042984969",
      "1.636261831"
    ],
    [
      "0.718640057",
      "1.64343643"
    ],
    [
      "0.485128082",
      "1.65365285"
    ],
    [
      "1.673094037",
      "1.654216751"
    ],
    [
      "1.252616351",
      "1.672035294"
    ],
    [
      "0.927864147",
      "1.678744254"
    ],
    [
      "0.603519235",
      "1.685918852"
    ],
    [
      "0.369833704",
      "1.695661973"
    ],
    [
      "1.462851785",
      "1.707082029"
    ],
    [
      "1.137583309",
      "1.714754836"
    ],
    [
      "0.812991325",
      "1.721892775"
    ],
    [
      "1.581999375",
      "1.736431849"
    ],
    [
      "1.346967619",
      "1.750491639"
    ],
    [
      "1.022464657",
      "1.757243138"
    ],
    [
      "0.697870503",
      "1.764375198"
    ],
    [
      "0.47277529",
      "1.776534946"
    ],
    [
      "1.232180397",
      "1.793867364"
    ],
    [
      "0.907503361",
      "1.800155378"
    ],
    [
      "0.586118775",
      "1.823797202"
    ],
    [
      "1.442082232",
      "1.828020797"
    ],
    [
      "1.116819932",
      "1.835694664"
    ],
    [
      "1.327811453",
      "1.876126552"
    ],
    [
      "0.815469962",
      "1.881318261"
    ],
    [
      "0.692891553",
      "1.886983395"
    ],
    [
      "1.210723669",
      "1.914686108"
    ],
    [
      "0.925479436",
      "1.935682545"
    ],
    [
      "1.048176551",
      "1.937408214"
    ]
  ],
  "radius": "0.061354624"
}

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?