MinMax Arena
中/EN
P02 · Packing and covering · Classic · Weak baseline · Hard

Equal-circle packing in a unit circle · n = 229

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 = 229
ObjectiveMaximize common radius

Record comparison

common radius · Higher is better
RecordValue / intervalAuthor / holderSource
External best known[0.0603767584422535107080478845675, 0.0603767584422535107080478845685]See source attributionpackomania.com ↗
Site record0.060376758游侠Record 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 = 0.060376758

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 = 229, 0.060376758
LAYOUT & HISTORY

Record details

Inspect the layout, solver notes and record history.

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

The record holder has not shared a solver note yet.

Record history (1 changes)
  1. 游侠AI · OpenAI: GPT-5.6 Sol
    0.060376757→0.060376758
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": [
    [
      "0.720431029",
      "0.987129349"
    ],
    [
      "0.214642272",
      "0.732847509"
    ],
    [
      "0.713813092",
      "0.552403407"
    ],
    [
      "1.482953135",
      "1.389942810"
    ],
    [
      "1.924104756",
      "0.829934611"
    ],
    [
      "0.983253018",
      "1.168773190"
    ],
    [
      "0.578196249",
      "1.273204777"
    ],
    [
      "0.724680645",
      "1.422491606"
    ],
    [
      "1.590716635",
      "0.551499082"
    ],
    [
      "1.021951658",
      "1.841742117"
    ],
    [
      "0.394946824",
      "0.572263236"
    ],
    [
      "1.336468740",
      "1.240655981"
    ],
    [
      "1.306321937",
      "1.123726164"
    ],
    [
      "1.099450224",
      "1.934345487"
    ],
    [
      "1.190031018",
      "1.551919654"
    ],
    [
      "1.246028333",
      "0.889866530"
    ],
    [
      "1.595041113",
      "0.986937566"
    ],
    [
      "1.069443809",
      "1.084200385"
    ],
    [
      "1.546815268",
      "1.627291967"
    ],
    [
      "1.500863970",
      "0.204998667"
    ],
    [
      "0.185124230",
      "1.181830814"
    ],
    [
      "1.599290729",
      "1.422299822"
    ],
    [
      "1.336684320",
      "1.715601759"
    ],
    [
      "0.312892166",
      "1.210587614"
    ],
    [
      "0.754827447",
      "1.539421423"
    ],
    [
      "0.716594589",
      "0.104135496"
    ],
    [
      "1.685481520",
      "1.337727017"
    ],
    [
      "1.388263113",
      "0.603791102"
    ],
    [
      "1.302072322",
      "0.688363907"
    ],
    [
      "0.396982103",
      "1.005309781"
    ],
    [
      "1.185781402",
      "1.116557397"
    ],
    [
      "1.508850322",
      "1.071510371"
    ],
    [
      "0.514971820",
      "1.040129675"
    ],
    [
      "0.979474010",
      "0.296971137"
    ],
    [
      "1.452806333",
      "1.273012993"
    ],
    [
      "0.601681276",
      "0.955420918"
    ],
    [
      "0.140539723",
      "1.379762911"
    ],
    [
      "1.882835784",
      "1.321702991"
    ],
    [
      "1.707710771",
      "0.581395301"
    ],
    [
      "1.443738258",
      "1.828244043"
    ],
    [
      "1.422659531",
      "1.156083176"
    ],
    [
      "1.099590611",
      "1.201130202"
    ],
    [
      "1.325526325",
      "0.370491556"
    ],
    [
      "0.800003883",
      "0.467830602"
    ],
    [
      "0.428337236",
      "1.672315874"
    ],
    [
      "0.780607495",
      "1.669220014"
    ],
    [
      "0.226730514",
      "1.295190105"
    ],
    [
      "0.242673378",
      "0.850302474"
    ],
    [
      "0.682990741",
      "1.743891568"
    ],
    [
      "0.810871436",
      "1.337918801"
    ],
    [
      "1.504600706",
      "0.636148114"
    ],
    [
      "1.277890828",
      "0.106431038"
    ],
    [
      "0.366835301",
      "0.888379964"
    ],
    [
      "1.186695143",
      "0.190175755"
    ],
    [
      "0.571578021",
      "0.838479882"
    ],
    [
      "1.215881531",
      "0.772936712"
    ],
    [
      "0.734822316",
      "0.225074452"
    ],
    [
      "0.687915906",
      "0.870835847"
    ],
    [
      "1.651085102",
      "0.785434943"
    ],
    [
      "0.541431219",
      "0.721550065"
    ],
    [
      "0.422977929",
      "0.689718202"
    ],
    [
      "0.485355741",
      "0.923020584"
    ],
    [
      "0.592306119",
      "1.823626826"
    ],
    [
      "0.608343052",
      "1.390134594"
    ],
    [
      "0.634240238",
      "1.071702154"
    ],
    [
      "1.423869129",
      "1.592187337"
    ],
    [
      "0.860297488",
      "0.701690237"
    ],
    [
      "0.927209029",
      "1.370275813"
    ],
    [
      "0.828822607",
      "0.148703240"
    ],
    [
      "0.312678024",
      "1.519207251"
    ],
    [
      "1.771672311",
      "1.253154212"
    ],
    [
      "1.032679070",
      "0.532544626"
    ],
    [
      "0.915101277",
      "0.064220088"
    ],
    [
      "1.478703520",
      "0.954580554"
    ],
    [
      "1.392512729",
      "1.039153359"
    ],
    [
      "0.657055270",
      "0.317688763"
    ],
    [
      "1.880568133",
      "1.200970768"
    ],
    [
      "1.625187915",
      "1.103867383"
    ],
    [
      "1.850446076",
      "0.600458628"
    ],
    [
      "1.065194193",
      "0.648838128"
    ],
    [
      "0.364800021",
      "0.455333419"
    ],
    [
      "0.511284417",
      "0.604620248"
    ],
    [
      "1.760328309",
      "1.132568936"
    ],
    [
      "0.866915425",
      "1.136416178"
    ],
    [
      "0.455208939",
      "0.806090767"
    ],
    [
      "0.859583654",
      "0.265472970"
    ],
    [
      "1.686597612",
      "0.900877256"
    ],
    [
      "1.009150204",
      "0.850340751"
    ],
    [
      "0.627622301",
      "0.636976213"
    ],
    [
      "1.126780198",
      "0.411599226"
    ],
    [
      "1.239410396",
      "0.455140588"
    ],
    [
      "0.979003402",
      "0.733410934"
    ],
    [
      "0.694533843",
      "1.305561789"
    ],
    [
      "0.871165040",
      "1.571778435"
    ],
    [
      "1.569143926",
      "1.305370005"
    ],
    [
      "0.134636405",
      "0.633888425"
    ],
    [
      "0.163958817",
      "0.941874467"
    ],
    [
      "1.938805977",
      "0.969727912"
    ],
    [
      "1.246075007",
      "1.350417032"
    ],
    [
      "1.394771329",
      "0.147329235"
    ],
    [
      "0.945862324",
      "0.180989818"
    ],
    [
      "1.572123105",
      "1.745363662"
    ],
    [
      "1.831580179",
      "1.030827906"
    ],
    [
      "0.244930505",
      "0.440748810"
    ],
    [
      "1.715628322",
      "1.454656834"
    ],
    [
      "0.545353210",
      "1.583921275"
    ],
    [
      "0.450990812",
      "0.370760614"
    ],
    [
      "1.534747508",
      "0.753077931"
    ],
    [
      "0.668636656",
      "1.623994228"
    ],
    [
      "1.039297007",
      "0.967270568"
    ],
    [
      "0.069972176",
      "0.866059408"
    ],
    [
      "0.901311843",
      "1.688708252"
    ],
    [
      "0.569661779",
      "1.702202741"
    ],
    [
      "1.332219124",
      "0.805293724"
    ],
    [
      "0.306573186",
      "0.654552433"
    ],
    [
      "1.673103147",
      "0.344390368"
    ],
    [
      "0.892812611",
      "0.817983739"
    ],
    [
      "0.481137615",
      "0.487690431"
    ],
    [
      "1.766245438",
      "0.687013030"
    ],
    [
      "0.548049447",
      "1.156274960"
    ],
    [
      "1.564894311",
      "0.870007748"
    ],
    [
      "0.280644510",
      "0.972952769"
    ],
    [
      "0.431966316",
      "0.251515151"
    ],
    [
      "0.916341477",
      "0.500187614"
    ],
    [
      "0.060385079",
      "1.003954194"
    ],
    [
      "0.897062227",
      "1.253345996"
    ],
    [
      "0.398868815",
      "1.434634445"
    ],
    [
      "0.332841317",
      "0.338787752"
    ],
    [
      "1.155634600",
      "0.999627580"
    ],
    [
      "0.552589594",
      "0.257121988"
    ],
    [
      "1.073693425",
      "1.519562642"
    ],
    [
      "1.103840227",
      "1.636492459"
    ],
    [
      "0.905614065",
      "1.809385105"
    ],
    [
      "1.538997124",
      "1.188440188"
    ],
    [
      "1.125487798",
      "0.882697763"
    ],
    [
      "1.665980275",
      "1.662829168"
    ],
    [
      "1.333854065",
      "1.878312757"
    ],
    [
      "1.043546622",
      "1.402632825"
    ],
    [
      "0.311999643",
      "1.639958862"
    ],
    [
      "1.302316630",
      "0.225005103"
    ],
    [
      "0.947799195",
      "1.937788980"
    ],
    [
      "0.806621820",
      "0.902556544"
    ],
    [
      "1.418409915",
      "0.720720919"
    ],
    [
      "0.836768622",
      "1.019486361"
    ],
    [
      "0.478977158",
      "1.781937999"
    ],
    [
      "1.066574472",
      "0.177829245"
    ],
    [
      "1.362365926",
      "0.922223542"
    ],
    [
      "1.035813424",
      "0.061059515"
    ],
    [
      "1.675104588",
      "0.465127297"
    ],
    [
      "1.013399820",
      "1.285703008"
    ],
    [
      "1.396762344",
      "1.474515616"
    ],
    [
      "0.922959413",
      "0.934913556"
    ],
    [
      "1.276175135",
      "1.006796347"
    ],
    [
      "1.100186158",
      "0.293810564"
    ],
    [
      "1.006068050",
      "0.414759799"
    ],
    [
      "0.334604292",
      "0.772007399"
    ],
    [
      "0.694177722",
      "1.888461913"
    ],
    [
      "0.196340435",
      "1.486850223"
    ],
    [
      "1.512734799",
      "1.508205857"
    ],
    [
      "0.454912803",
      "1.233131823"
    ],
    [
      "0.070793791",
      "1.139039673"
    ],
    [
      "1.408409271",
      "0.282674535"
    ],
    [
      "1.245356684",
      "1.796156653"
    ],
    [
      "1.457216099",
      "1.708245045"
    ],
    [
      "0.664387040",
      "1.188631972"
    ],
    [
      "1.358041448",
      "0.486785058"
    ],
    [
      "0.946488279",
      "0.617117432"
    ],
    [
      "1.448556717",
      "0.837650736"
    ],
    [
      "0.399112092",
      "1.126044511"
    ],
    [
      "1.629437531",
      "1.539229640"
    ],
    [
      "1.769765346",
      "0.807715234"
    ],
    [
      "1.366615542",
      "1.357585798"
    ],
    [
      "1.792183271",
      "0.494690687"
    ],
    [
      "0.165934569",
      "1.062611819"
    ],
    [
      "0.657769104",
      "0.753906030"
    ],
    [
      "1.833795453",
      "0.910094711"
    ],
    [
      "1.095340996",
      "0.765767946"
    ],
    [
      "0.638489854",
      "1.507064411"
    ],
    [
      "1.271925520",
      "0.571434090"
    ],
    [
      "0.515206408",
      "1.466991457"
    ],
    [
      "0.368692878",
      "1.317674926"
    ],
    [
      "0.230648039",
      "0.560654703"
    ],
    [
      "0.773392863",
      "0.350045775"
    ],
    [
      "0.953106216",
      "1.051843373"
    ],
    [
      "0.784862343",
      "1.808726655"
    ],
    [
      "0.485059606",
      "1.350061640"
    ],
    [
      "0.604042843",
      "0.147879254"
    ],
    [
      "1.711378706",
      "1.019294578"
    ],
    [
      "0.282620262",
      "1.093690121"
    ],
    [
      "1.443019569",
      "0.398361782"
    ],
    [
      "0.098933439",
      "1.266403619"
    ],
    [
      "0.957355831",
      "1.487205630"
    ],
    [
      "1.621011805",
      "0.668391106"
    ],
    [
      "1.558766995",
      "0.432770285"
    ],
    [
      "0.774106697",
      "0.786263042"
    ],
    [
      "1.185734728",
      "0.656006895"
    ],
    [
      "1.556765554",
      "0.312033356"
    ],
    [
      "0.282531226",
      "1.402277417"
    ],
    [
      "1.303132740",
      "1.594221100"
    ],
    [
      "1.017649436",
      "1.721065264"
    ],
    [
      "0.841018238",
      "1.454848618"
    ],
    [
      "0.780724634",
      "1.220988984"
    ],
    [
      "0.567683964",
      "0.401849269"
    ],
    [
      "1.745775124",
      "1.571586652"
    ],
    [
      "1.159884216",
      "1.434989837"
    ],
    [
      "1.216941949",
      "1.678793905"
    ],
    [
      "1.126385942",
      "1.775327250"
    ],
    [
      "1.215928205",
      "1.233487214"
    ],
    [
      "1.129737413",
      "1.318060020"
    ],
    [
      "0.683666290",
      "0.435473590"
    ],
    [
      "1.894663328",
      "0.712825200"
    ],
    [
      "0.750577831",
      "1.104059166"
    ],
    [
      "0.889730457",
      "0.382402787"
    ],
    [
      "1.474379041",
      "0.519142070"
    ],
    [
      "0.987502634",
      "1.604135447"
    ],
    [
      "0.094829614",
      "0.747892071"
    ],
    [
      "0.827784026",
      "1.923248001"
    ],
    [
      "1.219433684",
      "0.312822124"
    ],
    [
      "1.218456102",
      "1.913875685"
    ],
    [
      "1.834288060",
      "1.432267589"
    ],
    [
      "0.597475499",
      "0.520046395"
    ],
    [
      "0.743959895",
      "0.669333225"
    ],
    [
      "0.429015617",
      "1.551564263"
    ],
    [
      "1.276221809",
      "1.467346849"
    ],
    [
      "1.153219605",
      "0.539713393"
    ],
    [
      "1.934991901",
      "1.093177145"
    ],
    [
      "1.655334717",
      "1.220797200"
    ],
    [
      "0.830150686",
      "0.584760420"
    ],
    [
      "1.155934095",
      "0.073406025"
    ]
  ],
  "radius": "0.060376758"
}
Submission format and technical detailsOpen this when you are ready to prepare a JSON answer＋

Instance parameters

{
  "n": 229
}

The current leader's answer

{
  "centers": [
    [
      "0.720431029",
      "0.987129349"
    ],
    [
      "0.214642272",
      "0.732847509"
    ],
    [
      "0.713813092",
      "0.552403407"
    ],
    [
      "1.482953135",
      "1.389942810"
    ],
    [
      "1.924104756",
      "0.829934611"
    ],
    [
      "0.983253018",
      "1.168773190"
    ],
    [
      "0.578196249",
      "1.273204777"
    ],
    [
      "0.724680645",
      "1.422491606"
    ],
    [
      "1.590716635",
      "0.551499082"
    ],
    [
      "1.021951658",
      "1.841742117"
    ],
    [
      "0.394946824",
      "0.572263236"
    ],
    [
      "1.336468740",
      "1.240655981"
    ],
    [
      "1.306321937",
      "1.123726164"
    ],
    [
      "1.099450224",
      "1.934345487"
    ],
    [
      "1.190031018",
      "1.551919654"
    ],
    [
      "1.246028333",
      "0.889866530"
    ],
    [
      "1.595041113",
      "0.986937566"
    ],
    [
      "1.069443809",
      "1.084200385"
    ],
    [
      "1.546815268",
      "1.627291967"
    ],
    [
      "1.500863970",
      "0.204998667"
    ],
    [
      "0.185124230",
      "1.181830814"
    ],
    [
      "1.599290729",
      "1.422299822"
    ],
    [
      "1.336684320",
      "1.715601759"
    ],
    [
      "0.312892166",
      "1.210587614"
    ],
    [
      "0.754827447",
      "1.539421423"
    ],
    [
      "0.716594589",
      "0.104135496"
    ],
    [
      "1.685481520",
      "1.337727017"
    ],
    [
      "1.388263113",
      "0.603791102"
    ],
    [
      "1.302072322",
      "0.688363907"
    ],
    [
      "0.396982103",
      "1.005309781"
    ],
    [
      "1.185781402",
      "1.116557397"
    ],
    [
      "1.508850322",
      "1.071510371"
    ],
    [
      "0.514971820",
      "1.040129675"
    ],
    [
      "0.979474010",
      "0.296971137"
    ],
    [
      "1.452806333",
      "1.273012993"
    ],
    [
      "0.601681276",
      "0.955420918"
    ],
    [
      "0.140539723",
      "1.379762911"
    ],
    [
      "1.882835784",
      "1.321702991"
    ],
    [
      "1.707710771",
      "0.581395301"
    ],
    [
      "1.443738258",
      "1.828244043"
    ],
    [
      "1.422659531",
      "1.156083176"
    ],
    [
      "1.099590611",
      "1.201130202"
    ],
    [
      "1.325526325",
      "0.370491556"
    ],
    [
      "0.800003883",
      "0.467830602"
    ],
    [
      "0.428337236",
      "1.672315874"
    ],
    [
      "0.780607495",
      "1.669220014"
    ],
    [
      "0.226730514",
      "1.295190105"
    ],
    [
      "0.242673378",
      "0.850302474"
    ],
    [
      "0.682990741",
      "1.743891568"
    ],
    [
      "0.810871436",
      "1.337918801"
    ],
    [
      "1.504600706",
      "0.636148114"
    ],
    [
      "1.277890828",
      "0.106431038"
    ],
    [
      "0.366835301",
      "0.888379964"
    ],
    [
      "1.186695143",
      "0.190175755"
    ],
    [
      "0.571578021",
      "0.838479882"
    ],
    [
      "1.215881531",
      "0.772936712"
    ],
    [
      "0.734822316",
      "0.225074452"
    ],
    [
      "0.687915906",
      "0.870835847"
    ],
    [
      "1.651085102",
      "0.785434943"
    ],
    [
      "0.541431219",
      "0.721550065"
    ],
    [
      "0.422977929",
      "0.689718202"
    ],
    [
      "0.485355741",
      "0.923020584"
    ],
    [
      "0.592306119",
      "1.823626826"
    ],
    [
      "0.608343052",
      "1.390134594"
    ],
    [
      "0.634240238",
      "1.071702154"
    ],
    [
      "1.423869129",
      "1.592187337"
    ],
    [
      "0.860297488",
      "0.701690237"
    ],
    [
      "0.927209029",
      "1.370275813"
    ],
    [
      "0.828822607",
      "0.148703240"
    ],
    [
      "0.312678024",
      "1.519207251"
    ],
    [
      "1.771672311",
      "1.253154212"
    ],
    [
      "1.032679070",
      "0.532544626"
    ],
    [
      "0.915101277",
      "0.064220088"
    ],
    [
      "1.478703520",
      "0.954580554"
    ],
    [
      "1.392512729",
      "1.039153359"
    ],
    [
      "0.657055270",
      "0.317688763"
    ],
    [
      "1.880568133",
      "1.200970768"
    ],
    [
      "1.625187915",
      "1.103867383"
    ],
    [
      "1.850446076",
      "0.600458628"
    ],
    [
      "1.065194193",
      "0.648838128"
    ],
    [
      "0.364800021",
      "0.455333419"
    ],
    [
      "0.511284417",
      "0.604620248"
    ],
    [
      "1.760328309",
      "1.132568936"
    ],
    [
      "0.866915425",
      "1.136416178"
    ],
    [
      "0.455208939",
      "0.806090767"
    ],
    [
      "0.859583654",
      "0.265472970"
    ],
    [
      "1.686597612",
      "0.900877256"
    ],
    [
      "1.009150204",
      "0.850340751"
    ],
    [
      "0.627622301",
      "0.636976213"
    ],
    [
      "1.126780198",
      "0.411599226"
    ],
    [
      "1.239410396",
      "0.455140588"
    ],
    [
      "0.979003402",
      "0.733410934"
    ],
    [
      "0.694533843",
      "1.305561789"
    ],
    [
      "0.871165040",
      "1.571778435"
    ],
    [
      "1.569143926",
      "1.305370005"
    ],
    [
      "0.134636405",
      "0.633888425"
    ],
    [
      "0.163958817",
      "0.941874467"
    ],
    [
      "1.938805977",
      "0.969727912"
    ],
    [
      "1.246075007",
      "1.350417032"
    ],
    [
      "1.394771329",
      "0.147329235"
    ],
    [
      "0.945862324",
      "0.180989818"
    ],
    [
      "1.572123105",
      "1.745363662"
    ],
    [
      "1.831580179",
      "1.030827906"
    ],
    [
      "0.244930505",
      "0.440748810"
    ],
    [
      "1.715628322",
      "1.454656834"
    ],
    [
      "0.545353210",
      "1.583921275"
    ],
    [
      "0.450990812",
      "0.370760614"
    ],
    [
      "1.534747508",
      "0.753077931"
    ],
    [
      "0.668636656",
      "1.623994228"
    ],
    [
      "1.039297007",
      "0.967270568"
    ],
    [
      "0.069972176",
      "0.866059408"
    ],
    [
      "0.901311843",
      "1.688708252"
    ],
    [
      "0.569661779",
      "1.702202741"
    ],
    [
      "1.332219124",
      "0.805293724"
    ],
    [
      "0.306573186",
      "0.654552433"
    ],
    [
      "1.673103147",
      "0.344390368"
    ],
    [
      "0.892812611",
      "0.817983739"
    ],
    [
      "0.481137615",
      "0.487690431"
    ],
    [
      "1.766245438",
      "0.687013030"
    ],
    [
      "0.548049447",
      "1.156274960"
    ],
    [
      "1.564894311",
      "0.870007748"
    ],
    [
      "0.280644510",
      "0.972952769"
    ],
    [
      "0.431966316",
      "0.251515151"
    ],
    [
      "0.916341477",
      "0.500187614"
    ],
    [
      "0.060385079",
      "1.003954194"
    ],
    [
      "0.897062227",
      "1.253345996"
    ],
    [
      "0.398868815",
      "1.434634445"
    ],
    [
      "0.332841317",
      "0.338787752"
    ],
    [
      "1.155634600",
      "0.999627580"
    ],
    [
      "0.552589594",
      "0.257121988"
    ],
    [
      "1.073693425",
      "1.519562642"
    ],
    [
      "1.103840227",
      "1.636492459"
    ],
    [
      "0.905614065",
      "1.809385105"
    ],
    [
      "1.538997124",
      "1.188440188"
    ],
    [
      "1.125487798",
      "0.882697763"
    ],
    [
      "1.665980275",
      "1.662829168"
    ],
    [
      "1.333854065",
      "1.878312757"
    ],
    [
      "1.043546622",
      "1.402632825"
    ],
    [
      "0.311999643",
      "1.639958862"
    ],
    [
      "1.302316630",
      "0.225005103"
    ],
    [
      "0.947799195",
      "1.937788980"
    ],
    [
      "0.806621820",
      "0.902556544"
    ],
    [
      "1.418409915",
      "0.720720919"
    ],
    [
      "0.836768622",
      "1.019486361"
    ],
    [
      "0.478977158",
      "1.781937999"
    ],
    [
      "1.066574472",
      "0.177829245"
    ],
    [
      "1.362365926",
      "0.922223542"
    ],
    [
      "1.035813424",
      "0.061059515"
    ],
    [
      "1.675104588",
      "0.465127297"
    ],
    [
      "1.013399820",
      "1.285703008"
    ],
    [
      "1.396762344",
      "1.474515616"
    ],
    [
      "0.922959413",
      "0.934913556"
    ],
    [
      "1.276175135",
      "1.006796347"
    ],
    [
      "1.100186158",
      "0.293810564"
    ],
    [
      "1.006068050",
      "0.414759799"
    ],
    [
      "0.334604292",
      "0.772007399"
    ],
    [
      "0.694177722",
      "1.888461913"
    ],
    [
      "0.196340435",
      "1.486850223"
    ],
    [
      "1.512734799",
      "1.508205857"
    ],
    [
      "0.454912803",
      "1.233131823"
    ],
    [
      "0.070793791",
      "1.139039673"
    ],
    [
      "1.408409271",
      "0.282674535"
    ],
    [
      "1.245356684",
      "1.796156653"
    ],
    [
      "1.457216099",
      "1.708245045"
    ],
    [
      "0.664387040",
      "1.188631972"
    ],
    [
      "1.358041448",
      "0.486785058"
    ],
    [
      "0.946488279",
      "0.617117432"
    ],
    [
      "1.448556717",
      "0.837650736"
    ],
    [
      "0.399112092",
      "1.126044511"
    ],
    [
      "1.629437531",
      "1.539229640"
    ],
    [
      "1.769765346",
      "0.807715234"
    ],
    [
      "1.366615542",
      "1.357585798"
    ],
    [
      "1.792183271",
      "0.494690687"
    ],
    [
      "0.165934569",
      "1.062611819"
    ],
    [
      "0.657769104",
      "0.753906030"
    ],
    [
      "1.833795453",
      "0.910094711"
    ],
    [
      "1.095340996",
      "0.765767946"
    ],
    [
      "0.638489854",
      "1.507064411"
    ],
    [
      "1.271925520",
      "0.571434090"
    ],
    [
      "0.515206408",
      "1.466991457"
    ],
    [
      "0.368692878",
      "1.317674926"
    ],
    [
      "0.230648039",
      "0.560654703"
    ],
    [
      "0.773392863",
      "0.350045775"
    ],
    [
      "0.953106216",
      "1.051843373"
    ],
    [
      "0.784862343",
      "1.808726655"
    ],
    [
      "0.485059606",
      "1.350061640"
    ],
    [
      "0.604042843",
      "0.147879254"
    ],
    [
      "1.711378706",
      "1.019294578"
    ],
    [
      "0.282620262",
      "1.093690121"
    ],
    [
      "1.443019569",
      "0.398361782"
    ],
    [
      "0.098933439",
      "1.266403619"
    ],
    [
      "0.957355831",
      "1.487205630"
    ],
    [
      "1.621011805",
      "0.668391106"
    ],
    [
      "1.558766995",
      "0.432770285"
    ],
    [
      "0.774106697",
      "0.786263042"
    ],
    [
      "1.185734728",
      "0.656006895"
    ],
    [
      "1.556765554",
      "0.312033356"
    ],
    [
      "0.282531226",
      "1.402277417"
    ],
    [
      "1.303132740",
      "1.594221100"
    ],
    [
      "1.017649436",
      "1.721065264"
    ],
    [
      "0.841018238",
      "1.454848618"
    ],
    [
      "0.780724634",
      "1.220988984"
    ],
    [
      "0.567683964",
      "0.401849269"
    ],
    [
      "1.745775124",
      "1.571586652"
    ],
    [
      "1.159884216",
      "1.434989837"
    ],
    [
      "1.216941949",
      "1.678793905"
    ],
    [
      "1.126385942",
      "1.775327250"
    ],
    [
      "1.215928205",
      "1.233487214"
    ],
    [
      "1.129737413",
      "1.318060020"
    ],
    [
      "0.683666290",
      "0.435473590"
    ],
    [
      "1.894663328",
      "0.712825200"
    ],
    [
      "0.750577831",
      "1.104059166"
    ],
    [
      "0.889730457",
      "0.382402787"
    ],
    [
      "1.474379041",
      "0.519142070"
    ],
    [
      "0.987502634",
      "1.604135447"
    ],
    [
      "0.094829614",
      "0.747892071"
    ],
    [
      "0.827784026",
      "1.923248001"
    ],
    [
      "1.219433684",
      "0.312822124"
    ],
    [
      "1.218456102",
      "1.913875685"
    ],
    [
      "1.834288060",
      "1.432267589"
    ],
    [
      "0.597475499",
      "0.520046395"
    ],
    [
      "0.743959895",
      "0.669333225"
    ],
    [
      "0.429015617",
      "1.551564263"
    ],
    [
      "1.276221809",
      "1.467346849"
    ],
    [
      "1.153219605",
      "0.539713393"
    ],
    [
      "1.934991901",
      "1.093177145"
    ],
    [
      "1.655334717",
      "1.220797200"
    ],
    [
      "0.830150686",
      "0.584760420"
    ],
    [
      "1.155934095",
      "0.073406025"
    ]
  ],
  "radius": "0.060376758"
}

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?