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

Equal-circle packing in a unit circle · n = 270

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 = 270
ObjectiveMaximize common radius

Record comparison

common radius · Higher is better
RecordValue / intervalAuthor / holderSource
External best known[0.0559056939488112315540846418595, 0.0559056939488112315540846418605]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 = 0.055905693

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 = 270
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": [
    [
      "1.063255922",
      "0.058027205"
    ],
    [
      "0.936744078",
      "0.059137337"
    ],
    [
      "1.174176665",
      "0.07211178"
    ],
    [
      "0.823019376",
      "0.073562459"
    ],
    [
      "0.712103576",
      "0.100872808"
    ],
    [
      "1.312208451",
      "0.109023041"
    ],
    [
      "1.001477108",
      "0.151221436"
    ],
    [
      "1.415354297",
      "0.152182291"
    ],
    [
      "0.579937176",
      "0.154505303"
    ],
    [
      "1.220972839",
      "0.173659328"
    ],
    [
      "1.109373884",
      "0.180548425"
    ],
    [
      "0.787579962",
      "0.183365847"
    ],
    [
      "0.898746244",
      "0.195359355"
    ],
    [
      "1.512674283",
      "0.207233238"
    ],
    [
      "0.678400701",
      "0.207483796"
    ],
    [
      "0.482924848",
      "0.210096622"
    ],
    [
      "1.403191269",
      "0.263330153"
    ],
    [
      "1.291050064",
      "0.265027787"
    ],
    [
      "0.393165142",
      "0.276767317"
    ],
    [
      "1.179446273",
      "0.277473252"
    ],
    [
      "1.067847318",
      "0.284362348"
    ],
    [
      "0.956248362",
      "0.291251445"
    ],
    [
      "0.844442755",
      "0.294792903"
    ],
    [
      "0.733050452",
      "0.305029637"
    ],
    [
      "1.564198325",
      "0.30646559"
    ],
    [
      "0.620958038",
      "0.307037265"
    ],
    [
      "0.509596945",
      "0.318680165"
    ],
    [
      "1.67183979",
      "0.336716233"
    ],
    [
      "1.464405754",
      "0.35689603"
    ],
    [
      "1.352768085",
      "0.363126391"
    ],
    [
      "1.241211883",
      "0.370676234"
    ],
    [
      "1.129612928",
      "0.37756533"
    ],
    [
      "0.354575125",
      "0.381708239"
    ],
    [
      "1.018013972",
      "0.384454427"
    ],
    [
      "0.906415017",
      "0.391343523"
    ],
    [
      "0.794816062",
      "0.398232619"
    ],
    [
      "0.683217107",
      "0.405121716"
    ],
    [
      "0.571600862",
      "0.411724782"
    ],
    [
      "0.460019902",
      "0.41889944"
    ],
    [
      "1.748313144",
      "0.424502187"
    ],
    [
      "0.251387274",
      "0.424766965"
    ],
    [
      "1.637774359",
      "0.443211927"
    ],
    [
      "1.526175125",
      "0.45009652"
    ],
    [
      "1.414576448",
      "0.45699012"
    ],
    [
      "1.302977493",
      "0.463879216"
    ],
    [
      "1.191378538",
      "0.470768312"
    ],
    [
      "1.079779582",
      "0.477657409"
    ],
    [
      "0.968180627",
      "0.484546505"
    ],
    [
      "0.856581672",
      "0.491435601"
    ],
    [
      "0.744982717",
      "0.498324698"
    ],
    [
      "0.633383761",
      "0.505213794"
    ],
    [
      "0.521784806",
      "0.51210289"
    ],
    [
      "0.408960411",
      "0.518376686"
    ],
    [
      "0.185704481",
      "0.522258577"
    ],
    [
      "0.297429257",
      "0.526658683"
    ],
    [
      "1.709159192",
      "0.52927"
    ],
    [
      "1.820883968",
      "0.533670106"
    ],
    [
      "1.587941013",
      "0.543304006"
    ],
    [
      "1.476342058",
      "0.550193102"
    ],
    [
      "1.364743103",
      "0.557082198"
    ],
    [
      "1.253144148",
      "0.563971295"
    ],
    [
      "1.141545192",
      "0.570860391"
    ],
    [
      "1.029946237",
      "0.577749487"
    ],
    [
      "0.918347282",
      "0.584638584"
    ],
    [
      "0.806748327",
      "0.59152768"
    ],
    [
      "0.695149371",
      "0.598416776"
    ],
    [
      "0.583550416",
      "0.605305872"
    ],
    [
      "0.471951461",
      "0.612194969"
    ],
    [
      "0.360352506",
      "0.619084065"
    ],
    [
      "0.237756266",
      "0.621215124"
    ],
    [
      "1.761210977",
      "0.628226547"
    ],
    [
      "1.649706624",
      "0.636506988"
    ],
    [
      "1.872472785",
      "0.639298879"
    ],
    [
      "0.127449164",
      "0.639691245"
    ],
    [
      "1.538107668",
      "0.643396084"
    ],
    [
      "1.426508713",
      "0.65028518"
    ],
    [
      "1.314909758",
      "0.657174277"
    ],
    [
      "1.203310802",
      "0.664063373"
    ],
    [
      "1.091711847",
      "0.670952469"
    ],
    [
      "0.980112892",
      "0.677841566"
    ],
    [
      "0.868513937",
      "0.684730662"
    ],
    [
      "0.756914981",
      "0.691619758"
    ],
    [
      "0.645316026",
      "0.698508855"
    ],
    [
      "0.533717071",
      "0.705397951"
    ],
    [
      "0.422118116",
      "0.712287047"
    ],
    [
      "0.31051916",
      "0.719176144"
    ],
    [
      "0.198920205",
      "0.72606524"
    ],
    [
      "1.712618814",
      "0.728957069"
    ],
    [
      "1.599873278",
      "0.736599066"
    ],
    [
      "1.488274323",
      "0.743488163"
    ],
    [
      "0.089659513",
      "0.749811558"
    ],
    [
      "1.85816881",
      "0.750191542"
    ],
    [
      "1.376675368",
      "0.750377259"
    ],
    [
      "1.265076413",
      "0.757266355"
    ],
    [
      "1.153477457",
      "0.764155452"
    ],
    [
      "1.041878502",
      "0.771044548"
    ],
    [
      "0.930279547",
      "0.777933644"
    ],
    [
      "0.818680591",
      "0.78482274"
    ],
    [
      "0.707081636",
      "0.791711837"
    ],
    [
      "0.595482681",
      "0.798600933"
    ],
    [
      "0.483883726",
      "0.805490029"
    ],
    [
      "0.37228477",
      "0.812379126"
    ],
    [
      "0.260682054",
      "0.819270715"
    ],
    [
      "1.773237896",
      "0.822913797"
    ],
    [
      "1.661638888",
      "0.829802048"
    ],
    [
      "1.929755305",
      "0.836081938"
    ],
    [
      "1.550039933",
      "0.836691145"
    ],
    [
      "1.438440978",
      "0.843580241"
    ],
    [
      "1.326842023",
      "0.850469337"
    ],
    [
      "1.215243067",
      "0.857358434"
    ],
    [
      "0.11728242",
      "0.858157123"
    ],
    [
      "1.103644112",
      "0.86424753"
    ],
    [
      "0.992045157",
      "0.871136626"
    ],
    [
      "0.880446202",
      "0.878025723"
    ],
    [
      "0.768847246",
      "0.884914819"
    ],
    [
      "0.657248291",
      "0.891803915"
    ],
    [
      "0.545649336",
      "0.898693012"
    ],
    [
      "0.43405038",
      "0.905582108"
    ],
    [
      "0.322451425",
      "0.912471204"
    ],
    [
      "1.835241813",
      "0.915958414"
    ],
    [
      "0.210852748",
      "0.919364804"
    ],
    [
      "1.723660852",
      "0.923133073"
    ],
    [
      "1.611805543",
      "0.929894127"
    ],
    [
      "1.500206588",
      "0.936783223"
    ],
    [
      "1.388607633",
      "0.943672319"
    ],
    [
      "1.942613968",
      "0.947151472"
    ],
    [
      "1.277008677",
      "0.950561416"
    ],
    [
      "0.057106704",
      "0.952394428"
    ],
    [
      "1.165409722",
      "0.957450512"
    ],
    [
      "1.053810767",
      "0.964339608"
    ],
    [
      "0.942211812",
      "0.971228705"
    ],
    [
      "0.830612856",
      "0.978117801"
    ],
    [
      "0.719013901",
      "0.985006897"
    ],
    [
      "0.607414946",
      "0.991895994"
    ],
    [
      "0.495815991",
      "0.99878509"
    ],
    [
      "0.384217035",
      "1.005674186"
    ],
    [
      "0.272067233",
      "1.012930681"
    ],
    [
      "1.789640925",
      "1.01822121"
    ],
    [
      "0.160429564",
      "1.019161041"
    ],
    [
      "1.673571153",
      "1.023097109"
    ],
    [
      "1.561972198",
      "1.029986205"
    ],
    [
      "1.450373243",
      "1.036875302"
    ],
    [
      "1.338774287",
      "1.043764398"
    ],
    [
      "1.227175332",
      "1.050653494"
    ],
    [
      "1.115576377",
      "1.057542591"
    ],
    [
      "1.942251298",
      "1.058962271"
    ],
    [
      "0.058091178",
      "1.064201482"
    ],
    [
      "1.003977422",
      "1.064431687"
    ],
    [
      "0.892378466",
      "1.071320783"
    ],
    [
      "0.780779511",
      "1.078209879"
    ],
    [
      "0.669180556",
      "1.085098976"
    ],
    [
      "0.557581601",
      "1.091988072"
    ],
    [
      "0.445982645",
      "1.098877168"
    ],
    [
      "0.33438369",
      "1.105766265"
    ],
    [
      "0.217970932",
      "1.115429907"
    ],
    [
      "1.735336763",
      "1.116300091"
    ],
    [
      "1.847138815",
      "1.117744939"
    ],
    [
      "1.623737808",
      "1.123189187"
    ],
    [
      "1.512138853",
      "1.130078284"
    ],
    [
      "1.400539897",
      "1.13696738"
    ],
    [
      "1.288940942",
      "1.143856476"
    ],
    [
      "1.177341987",
      "1.150745573"
    ],
    [
      "1.065743032",
      "1.157634669"
    ],
    [
      "0.954144076",
      "1.164523765"
    ],
    [
      "0.842545121",
      "1.171412862"
    ],
    [
      "0.072287094",
      "1.17510803"
    ],
    [
      "0.730946166",
      "1.178301958"
    ],
    [
      "0.619347211",
      "1.185191054"
    ],
    [
      "0.507748255",
      "1.192080151"
    ],
    [
      "0.3961493",
      "1.198969247"
    ],
    [
      "1.922615202",
      "1.200237979"
    ],
    [
      "0.284550345",
      "1.205858343"
    ],
    [
      "1.68850832",
      "1.217886917"
    ],
    [
      "0.173881566",
      "1.221802243"
    ],
    [
      "1.573904463",
      "1.223281266"
    ],
    [
      "1.813435941",
      "1.224355927"
    ],
    [
      "1.462305507",
      "1.230170362"
    ],
    [
      "1.350706552",
      "1.237059459"
    ],
    [
      "1.239107597",
      "1.243948555"
    ],
    [
      "1.127508642",
      "1.250837651"
    ],
    [
      "1.015909686",
      "1.257726747"
    ],
    [
      "0.904310731",
      "1.264615844"
    ],
    [
      "0.792711776",
      "1.27150494"
    ],
    [
      "0.681112821",
      "1.278394036"
    ],
    [
      "0.569513865",
      "1.285283133"
    ],
    [
      "0.45791491",
      "1.292172229"
    ],
    [
      "0.346315955",
      "1.299061325"
    ],
    [
      "1.890805068",
      "1.309948379"
    ],
    [
      "0.109336898",
      "1.313102694"
    ],
    [
      "1.747466118",
      "1.314631997"
    ],
    [
      "0.235647176",
      "1.315005226"
    ],
    [
      "1.635670073",
      "1.316484248"
    ],
    [
      "1.524071118",
      "1.323373344"
    ],
    [
      "1.412472162",
      "1.330262441"
    ],
    [
      "1.300873207",
      "1.337151537"
    ],
    [
      "1.189274252",
      "1.344040633"
    ],
    [
      "1.077675296",
      "1.35092973"
    ],
    [
      "0.966076341",
      "1.357818826"
    ],
    [
      "0.854477386",
      "1.364707922"
    ],
    [
      "0.742878431",
      "1.371597019"
    ],
    [
      "0.631279475",
      "1.378486115"
    ],
    [
      "0.51968052",
      "1.385375211"
    ],
    [
      "0.408081565",
      "1.392264307"
    ],
    [
      "1.846443148",
      "1.415650583"
    ],
    [
      "0.152599669",
      "1.416205162"
    ],
    [
      "1.585836728",
      "1.416576326"
    ],
    [
      "0.264197647",
      "1.423110069"
    ],
    [
      "1.474237772",
      "1.423465423"
    ],
    [
      "1.734325245",
      "1.425668496"
    ],
    [
      "1.362638817",
      "1.430354519"
    ],
    [
      "1.251039862",
      "1.437243615"
    ],
    [
      "1.139440907",
      "1.444132712"
    ],
    [
      "1.027841951",
      "1.451021808"
    ],
    [
      "0.916242996",
      "1.457910904"
    ],
    [
      "0.804644041",
      "1.464800001"
    ],
    [
      "0.693045085",
      "1.471689097"
    ],
    [
      "0.58144613",
      "1.478578193"
    ],
    [
      "0.467048926",
      "1.48732018"
    ],
    [
      "0.353787639",
      "1.490008648"
    ],
    [
      "1.654978939",
      "1.50444635"
    ],
    [
      "1.536003382",
      "1.516668405"
    ],
    [
      "1.424404427",
      "1.523557501"
    ],
    [
      "0.216812709",
      "1.525213764"
    ],
    [
      "1.78414441",
      "1.525767633"
    ],
    [
      "1.312805472",
      "1.530446598"
    ],
    [
      "1.201206517",
      "1.537335694"
    ],
    [
      "1.089607561",
      "1.54422479"
    ],
    [
      "0.978008606",
      "1.551113886"
    ],
    [
      "0.866409651",
      "1.558002983"
    ],
    [
      "0.754810696",
      "1.564892079"
    ],
    [
      "0.64321174",
      "1.571781175"
    ],
    [
      "0.531612785",
      "1.578670272"
    ],
    [
      "0.398984097",
      "1.592278226"
    ],
    [
      "1.605145594",
      "1.604538428"
    ],
    [
      "1.716486438",
      "1.614785526"
    ],
    [
      "0.286172036",
      "1.616486578"
    ],
    [
      "1.490980223",
      "1.619543911"
    ],
    [
      "1.375164682",
      "1.623942928"
    ],
    [
      "1.262972127",
      "1.630538676"
    ],
    [
      "1.151373171",
      "1.637427772"
    ],
    [
      "1.039774216",
      "1.644316869"
    ],
    [
      "0.928175261",
      "1.651205965"
    ],
    [
      "0.816576306",
      "1.658095061"
    ],
    [
      "0.704738285",
      "1.665142145"
    ],
    [
      "0.589398144",
      "1.674740023"
    ],
    [
      "0.474460484",
      "1.674771265"
    ],
    [
      "0.365281223",
      "1.698889213"
    ],
    [
      "1.615504456",
      "1.715868929"
    ],
    [
      "1.436379167",
      "1.717508805"
    ],
    [
      "1.324741498",
      "1.723739166"
    ],
    [
      "1.213142821",
      "1.730632765"
    ],
    [
      "1.101539826",
      "1.737519851"
    ],
    [
      "0.989940871",
      "1.744408947"
    ],
    [
      "0.878421436",
      "1.752667885"
    ],
    [
      "0.766742202",
      "1.758186762"
    ],
    [
      "0.655161242",
      "1.765361421"
    ],
    [
      "1.526554525",
      "1.783616227"
    ],
    [
      "0.477811526",
      "1.786532425"
    ],
    [
      "1.163305436",
      "1.830722833"
    ],
    [
      "1.318519255",
      "1.835377287"
    ],
    [
      "1.430219013",
      "1.840372334"
    ],
    [
      "0.574461184",
      "1.842751906"
    ],
    [
      "0.941359766",
      "1.84511477"
    ],
    [
      "1.053084542",
      "1.849514876"
    ],
    [
      "0.787256066",
      "1.868100219"
    ],
    [
      "0.677079553",
      "1.887150745"
    ],
    [
      "1.238500697",
      "1.913472209"
    ],
    [
      "1.124239228",
      "1.935804233"
    ],
    [
      "0.876139941",
      "1.935934156"
    ],
    [
      "0.99341155",
      "1.944071317"
    ]
  ],
  "radius": "0.055905693"
}
Submission format and technical detailsOpen this when you are ready to prepare a JSON answer+

Instance parameters

{
  "n": 270
}

Starter answer

{
  "centers": [
    [
      "1.063255922",
      "0.058027205"
    ],
    [
      "0.936744078",
      "0.059137337"
    ],
    [
      "1.174176665",
      "0.07211178"
    ],
    [
      "0.823019376",
      "0.073562459"
    ],
    [
      "0.712103576",
      "0.100872808"
    ],
    [
      "1.312208451",
      "0.109023041"
    ],
    [
      "1.001477108",
      "0.151221436"
    ],
    [
      "1.415354297",
      "0.152182291"
    ],
    [
      "0.579937176",
      "0.154505303"
    ],
    [
      "1.220972839",
      "0.173659328"
    ],
    [
      "1.109373884",
      "0.180548425"
    ],
    [
      "0.787579962",
      "0.183365847"
    ],
    [
      "0.898746244",
      "0.195359355"
    ],
    [
      "1.512674283",
      "0.207233238"
    ],
    [
      "0.678400701",
      "0.207483796"
    ],
    [
      "0.482924848",
      "0.210096622"
    ],
    [
      "1.403191269",
      "0.263330153"
    ],
    [
      "1.291050064",
      "0.265027787"
    ],
    [
      "0.393165142",
      "0.276767317"
    ],
    [
      "1.179446273",
      "0.277473252"
    ],
    [
      "1.067847318",
      "0.284362348"
    ],
    [
      "0.956248362",
      "0.291251445"
    ],
    [
      "0.844442755",
      "0.294792903"
    ],
    [
      "0.733050452",
      "0.305029637"
    ],
    [
      "1.564198325",
      "0.30646559"
    ],
    [
      "0.620958038",
      "0.307037265"
    ],
    [
      "0.509596945",
      "0.318680165"
    ],
    [
      "1.67183979",
      "0.336716233"
    ],
    [
      "1.464405754",
      "0.35689603"
    ],
    [
      "1.352768085",
      "0.363126391"
    ],
    [
      "1.241211883",
      "0.370676234"
    ],
    [
      "1.129612928",
      "0.37756533"
    ],
    [
      "0.354575125",
      "0.381708239"
    ],
    [
      "1.018013972",
      "0.384454427"
    ],
    [
      "0.906415017",
      "0.391343523"
    ],
    [
      "0.794816062",
      "0.398232619"
    ],
    [
      "0.683217107",
      "0.405121716"
    ],
    [
      "0.571600862",
      "0.411724782"
    ],
    [
      "0.460019902",
      "0.41889944"
    ],
    [
      "1.748313144",
      "0.424502187"
    ],
    [
      "0.251387274",
      "0.424766965"
    ],
    [
      "1.637774359",
      "0.443211927"
    ],
    [
      "1.526175125",
      "0.45009652"
    ],
    [
      "1.414576448",
      "0.45699012"
    ],
    [
      "1.302977493",
      "0.463879216"
    ],
    [
      "1.191378538",
      "0.470768312"
    ],
    [
      "1.079779582",
      "0.477657409"
    ],
    [
      "0.968180627",
      "0.484546505"
    ],
    [
      "0.856581672",
      "0.491435601"
    ],
    [
      "0.744982717",
      "0.498324698"
    ],
    [
      "0.633383761",
      "0.505213794"
    ],
    [
      "0.521784806",
      "0.51210289"
    ],
    [
      "0.408960411",
      "0.518376686"
    ],
    [
      "0.185704481",
      "0.522258577"
    ],
    [
      "0.297429257",
      "0.526658683"
    ],
    [
      "1.709159192",
      "0.52927"
    ],
    [
      "1.820883968",
      "0.533670106"
    ],
    [
      "1.587941013",
      "0.543304006"
    ],
    [
      "1.476342058",
      "0.550193102"
    ],
    [
      "1.364743103",
      "0.557082198"
    ],
    [
      "1.253144148",
      "0.563971295"
    ],
    [
      "1.141545192",
      "0.570860391"
    ],
    [
      "1.029946237",
      "0.577749487"
    ],
    [
      "0.918347282",
      "0.584638584"
    ],
    [
      "0.806748327",
      "0.59152768"
    ],
    [
      "0.695149371",
      "0.598416776"
    ],
    [
      "0.583550416",
      "0.605305872"
    ],
    [
      "0.471951461",
      "0.612194969"
    ],
    [
      "0.360352506",
      "0.619084065"
    ],
    [
      "0.237756266",
      "0.621215124"
    ],
    [
      "1.761210977",
      "0.628226547"
    ],
    [
      "1.649706624",
      "0.636506988"
    ],
    [
      "1.872472785",
      "0.639298879"
    ],
    [
      "0.127449164",
      "0.639691245"
    ],
    [
      "1.538107668",
      "0.643396084"
    ],
    [
      "1.426508713",
      "0.65028518"
    ],
    [
      "1.314909758",
      "0.657174277"
    ],
    [
      "1.203310802",
      "0.664063373"
    ],
    [
      "1.091711847",
      "0.670952469"
    ],
    [
      "0.980112892",
      "0.677841566"
    ],
    [
      "0.868513937",
      "0.684730662"
    ],
    [
      "0.756914981",
      "0.691619758"
    ],
    [
      "0.645316026",
      "0.698508855"
    ],
    [
      "0.533717071",
      "0.705397951"
    ],
    [
      "0.422118116",
      "0.712287047"
    ],
    [
      "0.31051916",
      "0.719176144"
    ],
    [
      "0.198920205",
      "0.72606524"
    ],
    [
      "1.712618814",
      "0.728957069"
    ],
    [
      "1.599873278",
      "0.736599066"
    ],
    [
      "1.488274323",
      "0.743488163"
    ],
    [
      "0.089659513",
      "0.749811558"
    ],
    [
      "1.85816881",
      "0.750191542"
    ],
    [
      "1.376675368",
      "0.750377259"
    ],
    [
      "1.265076413",
      "0.757266355"
    ],
    [
      "1.153477457",
      "0.764155452"
    ],
    [
      "1.041878502",
      "0.771044548"
    ],
    [
      "0.930279547",
      "0.777933644"
    ],
    [
      "0.818680591",
      "0.78482274"
    ],
    [
      "0.707081636",
      "0.791711837"
    ],
    [
      "0.595482681",
      "0.798600933"
    ],
    [
      "0.483883726",
      "0.805490029"
    ],
    [
      "0.37228477",
      "0.812379126"
    ],
    [
      "0.260682054",
      "0.819270715"
    ],
    [
      "1.773237896",
      "0.822913797"
    ],
    [
      "1.661638888",
      "0.829802048"
    ],
    [
      "1.929755305",
      "0.836081938"
    ],
    [
      "1.550039933",
      "0.836691145"
    ],
    [
      "1.438440978",
      "0.843580241"
    ],
    [
      "1.326842023",
      "0.850469337"
    ],
    [
      "1.215243067",
      "0.857358434"
    ],
    [
      "0.11728242",
      "0.858157123"
    ],
    [
      "1.103644112",
      "0.86424753"
    ],
    [
      "0.992045157",
      "0.871136626"
    ],
    [
      "0.880446202",
      "0.878025723"
    ],
    [
      "0.768847246",
      "0.884914819"
    ],
    [
      "0.657248291",
      "0.891803915"
    ],
    [
      "0.545649336",
      "0.898693012"
    ],
    [
      "0.43405038",
      "0.905582108"
    ],
    [
      "0.322451425",
      "0.912471204"
    ],
    [
      "1.835241813",
      "0.915958414"
    ],
    [
      "0.210852748",
      "0.919364804"
    ],
    [
      "1.723660852",
      "0.923133073"
    ],
    [
      "1.611805543",
      "0.929894127"
    ],
    [
      "1.500206588",
      "0.936783223"
    ],
    [
      "1.388607633",
      "0.943672319"
    ],
    [
      "1.942613968",
      "0.947151472"
    ],
    [
      "1.277008677",
      "0.950561416"
    ],
    [
      "0.057106704",
      "0.952394428"
    ],
    [
      "1.165409722",
      "0.957450512"
    ],
    [
      "1.053810767",
      "0.964339608"
    ],
    [
      "0.942211812",
      "0.971228705"
    ],
    [
      "0.830612856",
      "0.978117801"
    ],
    [
      "0.719013901",
      "0.985006897"
    ],
    [
      "0.607414946",
      "0.991895994"
    ],
    [
      "0.495815991",
      "0.99878509"
    ],
    [
      "0.384217035",
      "1.005674186"
    ],
    [
      "0.272067233",
      "1.012930681"
    ],
    [
      "1.789640925",
      "1.01822121"
    ],
    [
      "0.160429564",
      "1.019161041"
    ],
    [
      "1.673571153",
      "1.023097109"
    ],
    [
      "1.561972198",
      "1.029986205"
    ],
    [
      "1.450373243",
      "1.036875302"
    ],
    [
      "1.338774287",
      "1.043764398"
    ],
    [
      "1.227175332",
      "1.050653494"
    ],
    [
      "1.115576377",
      "1.057542591"
    ],
    [
      "1.942251298",
      "1.058962271"
    ],
    [
      "0.058091178",
      "1.064201482"
    ],
    [
      "1.003977422",
      "1.064431687"
    ],
    [
      "0.892378466",
      "1.071320783"
    ],
    [
      "0.780779511",
      "1.078209879"
    ],
    [
      "0.669180556",
      "1.085098976"
    ],
    [
      "0.557581601",
      "1.091988072"
    ],
    [
      "0.445982645",
      "1.098877168"
    ],
    [
      "0.33438369",
      "1.105766265"
    ],
    [
      "0.217970932",
      "1.115429907"
    ],
    [
      "1.735336763",
      "1.116300091"
    ],
    [
      "1.847138815",
      "1.117744939"
    ],
    [
      "1.623737808",
      "1.123189187"
    ],
    [
      "1.512138853",
      "1.130078284"
    ],
    [
      "1.400539897",
      "1.13696738"
    ],
    [
      "1.288940942",
      "1.143856476"
    ],
    [
      "1.177341987",
      "1.150745573"
    ],
    [
      "1.065743032",
      "1.157634669"
    ],
    [
      "0.954144076",
      "1.164523765"
    ],
    [
      "0.842545121",
      "1.171412862"
    ],
    [
      "0.072287094",
      "1.17510803"
    ],
    [
      "0.730946166",
      "1.178301958"
    ],
    [
      "0.619347211",
      "1.185191054"
    ],
    [
      "0.507748255",
      "1.192080151"
    ],
    [
      "0.3961493",
      "1.198969247"
    ],
    [
      "1.922615202",
      "1.200237979"
    ],
    [
      "0.284550345",
      "1.205858343"
    ],
    [
      "1.68850832",
      "1.217886917"
    ],
    [
      "0.173881566",
      "1.221802243"
    ],
    [
      "1.573904463",
      "1.223281266"
    ],
    [
      "1.813435941",
      "1.224355927"
    ],
    [
      "1.462305507",
      "1.230170362"
    ],
    [
      "1.350706552",
      "1.237059459"
    ],
    [
      "1.239107597",
      "1.243948555"
    ],
    [
      "1.127508642",
      "1.250837651"
    ],
    [
      "1.015909686",
      "1.257726747"
    ],
    [
      "0.904310731",
      "1.264615844"
    ],
    [
      "0.792711776",
      "1.27150494"
    ],
    [
      "0.681112821",
      "1.278394036"
    ],
    [
      "0.569513865",
      "1.285283133"
    ],
    [
      "0.45791491",
      "1.292172229"
    ],
    [
      "0.346315955",
      "1.299061325"
    ],
    [
      "1.890805068",
      "1.309948379"
    ],
    [
      "0.109336898",
      "1.313102694"
    ],
    [
      "1.747466118",
      "1.314631997"
    ],
    [
      "0.235647176",
      "1.315005226"
    ],
    [
      "1.635670073",
      "1.316484248"
    ],
    [
      "1.524071118",
      "1.323373344"
    ],
    [
      "1.412472162",
      "1.330262441"
    ],
    [
      "1.300873207",
      "1.337151537"
    ],
    [
      "1.189274252",
      "1.344040633"
    ],
    [
      "1.077675296",
      "1.35092973"
    ],
    [
      "0.966076341",
      "1.357818826"
    ],
    [
      "0.854477386",
      "1.364707922"
    ],
    [
      "0.742878431",
      "1.371597019"
    ],
    [
      "0.631279475",
      "1.378486115"
    ],
    [
      "0.51968052",
      "1.385375211"
    ],
    [
      "0.408081565",
      "1.392264307"
    ],
    [
      "1.846443148",
      "1.415650583"
    ],
    [
      "0.152599669",
      "1.416205162"
    ],
    [
      "1.585836728",
      "1.416576326"
    ],
    [
      "0.264197647",
      "1.423110069"
    ],
    [
      "1.474237772",
      "1.423465423"
    ],
    [
      "1.734325245",
      "1.425668496"
    ],
    [
      "1.362638817",
      "1.430354519"
    ],
    [
      "1.251039862",
      "1.437243615"
    ],
    [
      "1.139440907",
      "1.444132712"
    ],
    [
      "1.027841951",
      "1.451021808"
    ],
    [
      "0.916242996",
      "1.457910904"
    ],
    [
      "0.804644041",
      "1.464800001"
    ],
    [
      "0.693045085",
      "1.471689097"
    ],
    [
      "0.58144613",
      "1.478578193"
    ],
    [
      "0.467048926",
      "1.48732018"
    ],
    [
      "0.353787639",
      "1.490008648"
    ],
    [
      "1.654978939",
      "1.50444635"
    ],
    [
      "1.536003382",
      "1.516668405"
    ],
    [
      "1.424404427",
      "1.523557501"
    ],
    [
      "0.216812709",
      "1.525213764"
    ],
    [
      "1.78414441",
      "1.525767633"
    ],
    [
      "1.312805472",
      "1.530446598"
    ],
    [
      "1.201206517",
      "1.537335694"
    ],
    [
      "1.089607561",
      "1.54422479"
    ],
    [
      "0.978008606",
      "1.551113886"
    ],
    [
      "0.866409651",
      "1.558002983"
    ],
    [
      "0.754810696",
      "1.564892079"
    ],
    [
      "0.64321174",
      "1.571781175"
    ],
    [
      "0.531612785",
      "1.578670272"
    ],
    [
      "0.398984097",
      "1.592278226"
    ],
    [
      "1.605145594",
      "1.604538428"
    ],
    [
      "1.716486438",
      "1.614785526"
    ],
    [
      "0.286172036",
      "1.616486578"
    ],
    [
      "1.490980223",
      "1.619543911"
    ],
    [
      "1.375164682",
      "1.623942928"
    ],
    [
      "1.262972127",
      "1.630538676"
    ],
    [
      "1.151373171",
      "1.637427772"
    ],
    [
      "1.039774216",
      "1.644316869"
    ],
    [
      "0.928175261",
      "1.651205965"
    ],
    [
      "0.816576306",
      "1.658095061"
    ],
    [
      "0.704738285",
      "1.665142145"
    ],
    [
      "0.589398144",
      "1.674740023"
    ],
    [
      "0.474460484",
      "1.674771265"
    ],
    [
      "0.365281223",
      "1.698889213"
    ],
    [
      "1.615504456",
      "1.715868929"
    ],
    [
      "1.436379167",
      "1.717508805"
    ],
    [
      "1.324741498",
      "1.723739166"
    ],
    [
      "1.213142821",
      "1.730632765"
    ],
    [
      "1.101539826",
      "1.737519851"
    ],
    [
      "0.989940871",
      "1.744408947"
    ],
    [
      "0.878421436",
      "1.752667885"
    ],
    [
      "0.766742202",
      "1.758186762"
    ],
    [
      "0.655161242",
      "1.765361421"
    ],
    [
      "1.526554525",
      "1.783616227"
    ],
    [
      "0.477811526",
      "1.786532425"
    ],
    [
      "1.163305436",
      "1.830722833"
    ],
    [
      "1.318519255",
      "1.835377287"
    ],
    [
      "1.430219013",
      "1.840372334"
    ],
    [
      "0.574461184",
      "1.842751906"
    ],
    [
      "0.941359766",
      "1.84511477"
    ],
    [
      "1.053084542",
      "1.849514876"
    ],
    [
      "0.787256066",
      "1.868100219"
    ],
    [
      "0.677079553",
      "1.887150745"
    ],
    [
      "1.238500697",
      "1.913472209"
    ],
    [
      "1.124239228",
      "1.935804233"
    ],
    [
      "0.876139941",
      "1.935934156"
    ],
    [
      "0.99341155",
      "1.944071317"
    ]
  ],
  "radius": "0.055905693"
}

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?