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

Equal-circle packing in a unit circle · n = 244

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 = 244

ObjectiveMaximize common radius

Record comparison

common radius · Higher is better

Record	Value / interval	Author / holder	Source
External best known	[0.0587033382017620243708350657905, 0.0587033382017620243708350657915]	See source attribution	packomania.com ↗
Site record	No 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

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244

0x2

VERIFIED CONSTRUCTIONr = 0.058703337

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

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": [
    [
      "0.995248542",
      "0.226242334"
    ],
    [
      "0.688846955",
      "0.266083662"
    ],
    [
      "1.938313146",
      "0.925114446"
    ],
    [
      "1.59122508",
      "0.425487138"
    ],
    [
      "1.135750563",
      "0.847850858"
    ],
    [
      "0.288040702",
      "1.108477208"
    ],
    [
      "1.940222276",
      "1.044840589"
    ],
    [
      "0.882422965",
      "1.292516298"
    ],
    [
      "1.578488393",
      "0.54220091"
    ],
    [
      "0.666976001",
      "1.385888055"
    ],
    [
      "1.071769706",
      "1.431387182"
    ],
    [
      "1.084565877",
      "1.314679917"
    ],
    [
      "1.38138216",
      "1.406278978"
    ],
    [
      "0.800545766",
      "1.106373592"
    ],
    [
      "1.647505929",
      "0.844906273"
    ],
    [
      "1.821875894",
      "0.541132459"
    ],
    [
      "1.304111297",
      "0.216736422"
    ],
    [
      "0.573597928",
      "0.160840053"
    ],
    [
      "0.663144656",
      "0.499647866"
    ],
    [
      "0.186747145",
      "0.804544144"
    ],
    [
      "1.122954391",
      "0.964558123"
    ],
    [
      "1.363485818",
      "0.636599947"
    ],
    [
      "1.350689646",
      "0.753307212"
    ],
    [
      "1.777937351",
      "0.758285825"
    ],
    [
      "0.42737026",
      "1.605403176"
    ],
    [
      "0.479562598",
      "0.353585476"
    ],
    [
      "1.398840519",
      "0.147377196"
    ],
    [
      "1.189240251",
      "0.241005135"
    ],
    [
      "0.355664304",
      "1.292160791"
    ],
    [
      "1.570728901",
      "1.545149862"
    ],
    [
      "0.535873509",
      "1.560554846"
    ],
    [
      "1.527240216",
      "1.00888536"
    ],
    [
      "0.57250337",
      "0.281847476"
    ],
    [
      "1.872605361",
      "0.647013755"
    ],
    [
      "1.046177364",
      "1.664801712"
    ],
    [
      "0.568229468",
      "0.430543345"
    ],
    [
      "0.117731326",
      "1.328087478"
    ],
    [
      "0.654179829",
      "1.502595319"
    ],
    [
      "0.649079658",
      "0.616209024"
    ],
    [
      "0.692568343",
      "1.152473525"
    ],
    [
      "1.01548485",
      "1.011829946"
    ],
    [
      "1.174139077",
      "0.497729063"
    ],
    [
      "1.664317093",
      "0.728709403"
    ],
    [
      "0.156027414",
      "1.027027822"
    ],
    [
      "1.281608619",
      "0.45045724"
    ],
    [
      "1.458159188",
      "0.706035389"
    ],
    [
      "0.490183614",
      "1.130640827"
    ],
    [
      "0.34291436",
      "1.523846272"
    ],
    [
      "1.552832559",
      "0.775470831"
    ],
    [
      "0.636283487",
      "0.732916289"
    ],
    [
      "0.946403822",
      "0.708979974"
    ],
    [
      "1.514444045",
      "1.125592625"
    ],
    [
      "1.432566846",
      "0.939449919"
    ],
    [
      "0.851730451",
      "0.639544532"
    ],
    [
      "0.920811479",
      "0.942394504"
    ],
    [
      "1.758360306",
      "0.442389875"
    ],
    [
      "1.449634163",
      "1.710245379"
    ],
    [
      "1.243220105",
      "0.800579035"
    ],
    [
      "0.844034451",
      "1.642638093"
    ],
    [
      "0.610691144",
      "0.966330818"
    ],
    [
      "1.376281989",
      "0.519892682"
    ],
    [
      "0.515775957",
      "0.897226297"
    ],
    [
      "0.165436416",
      "1.435365398"
    ],
    [
      "0.332400041",
      "0.641136083"
    ],
    [
      "1.583525073",
      "1.428442597"
    ],
    [
      "0.06402677",
      "1.099967586"
    ],
    [
      "0.227857624",
      "0.694570255"
    ],
    [
      "1.261116447",
      "1.570258066"
    ],
    [
      "1.396821014",
      "0.390438283"
    ],
    [
      "0.559506459",
      "1.433159878"
    ],
    [
      "1.406974503",
      "1.172864448"
    ],
    [
      "1.325097304",
      "0.986721741"
    ],
    [
      "1.808278969",
      "1.386528787"
    ],
    [
      "0.57230263",
      "1.316452613"
    ],
    [
      "1.690994617",
      "1.381170771"
    ],
    [
      "0.775294895",
      "0.186641348"
    ],
    [
      "0.923383923",
      "1.938173429"
    ],
    [
      "0.585563536",
      "1.845151953"
    ],
    [
      "1.795482798",
      "1.503236052"
    ],
    [
      "1.204831591",
      "1.150700829"
    ],
    [
      "1.058973535",
      "1.548094447"
    ],
    [
      "1.596321244",
      "1.311735332"
    ],
    [
      "0.762157252",
      "1.456495386"
    ],
    [
      "0.813341937",
      "0.989666327"
    ],
    [
      "1.355789818",
      "1.639693507"
    ],
    [
      "0.83893428",
      "0.756251797"
    ],
    [
      "1.323235072",
      "1.883979908"
    ],
    [
      "0.679772172",
      "1.26918079"
    ],
    [
      "0.69399676",
      "1.890169322"
    ],
    [
      "0.421102586",
      "0.827790856"
    ],
    [
      "0.730956857",
      "0.802351731"
    ],
    [
      "0.637784351",
      "1.618851571"
    ],
    [
      "1.140850734",
      "1.734237153"
    ],
    [
      "1.087256054",
      "0.299173436"
    ],
    [
      "0.891654044",
      "0.170992831"
    ],
    [
      "0.364553551",
      "0.40862765"
    ],
    [
      "0.675566605",
      "0.382801219"
    ],
    [
      "1.407125058",
      "0.273061313"
    ],
    [
      "1.811268086",
      "1.21720932"
    ],
    [
      "1.28670879",
      "1.336843536"
    ],
    [
      "0.80719055",
      "1.921338115"
    ],
    [
      "0.4835778",
      "1.786986351"
    ],
    [
      "0.175752546",
      "1.142765658"
    ],
    [
      "1.166983882",
      "0.073633016"
    ],
    [
      "0.528572128",
      "0.780519033"
    ],
    [
      "0.869626794",
      "1.409223563"
    ],
    [
      "0.236656238",
      "0.548593558"
    ],
    [
      "1.610979686",
      "1.655441303"
    ],
    [
      "0.389626167",
      "1.716577414"
    ],
    [
      "0.977096336",
      "1.36195174"
    ],
    [
      "1.505285177",
      "0.345495509"
    ],
    [
      "1.540036387",
      "0.892178096"
    ],
    [
      "0.379496712",
      "0.292175816"
    ],
    [
      "0.326404183",
      "0.758389558"
    ],
    [
      "1.476055531",
      "1.47571442"
    ],
    [
      "1.053873364",
      "0.661708151"
    ],
    [
      "0.298761899",
      "0.991561069"
    ],
    [
      "1.312301132",
      "1.103429006"
    ],
    [
      "1.891092422",
      "1.303304634"
    ],
    [
      "1.909759497",
      "0.758386542"
    ],
    [
      "0.908015308",
      "1.059101769"
    ],
    [
      "0.783410369",
      "0.335668778"
    ],
    [
      "1.501877586",
      "0.203659436"
    ],
    [
      "0.541368299",
      "0.663811768"
    ],
    [
      "1.683046725",
      "0.352322166"
    ],
    [
      "0.771635098",
      "1.802097669"
    ],
    [
      "1.161342905",
      "0.614436328"
    ],
    [
      "0.450337675",
      "1.361596233"
    ],
    [
      "1.678198445",
      "1.497878036"
    ],
    [
      "1.482760917",
      "0.470429912"
    ],
    [
      "0.313608011",
      "0.875096823"
    ],
    [
      "0.93360765",
      "0.825687239"
    ],
    [
      "1.84377419",
      "0.855496104"
    ],
    [
      "1.419770674",
      "1.056157183"
    ],
    [
      "0.249474223",
      "0.431888687"
    ],
    [
      "0.075413941",
      "0.84192155"
    ],
    [
      "1.273912618",
      "1.453550801"
    ],
    [
      "0.787749595",
      "1.223080856"
    ],
    [
      "0.938707822",
      "1.712073535"
    ],
    [
      "1.097362049",
      "1.197972652"
    ],
    [
      "1.716606112",
      "1.147758343"
    ],
    [
      "1.729383128",
      "1.031048979"
    ],
    [
      "0.433860993",
      "0.711079456"
    ],
    [
      "1.04076923",
      "1.940413353"
    ],
    [
      "0.856830623",
      "1.525930828"
    ],
    [
      "1.837305748",
      "1.102726274"
    ],
    [
      "1.837518085",
      "0.98531979"
    ],
    [
      "1.281004582",
      "0.101626008"
    ],
    [
      "0.059657593",
      "0.958266291"
    ],
    [
      "1.501647873",
      "1.24229989"
    ],
    [
      "0.890879911",
      "0.288396955"
    ],
    [
      "1.755264296",
      "0.643089209"
    ],
    [
      "1.695894384",
      "0.541799816"
    ],
    [
      "1.337893475",
      "0.870014477"
    ],
    [
      "1.148546734",
      "0.731143593"
    ],
    [
      "0.234579391",
      "1.340478219"
    ],
    [
      "0.623487316",
      "0.849623554"
    ],
    [
      "0.460252046",
      "0.476643279"
    ],
    [
      "0.932963318",
      "0.061093461"
    ],
    [
      "1.621913587",
      "1.078320802"
    ],
    [
      "1.192035419",
      "1.267408094"
    ],
    [
      "1.11015822",
      "1.081265387"
    ],
    [
      "1.7421793",
      "0.914341714"
    ],
    [
      "1.166443077",
      "1.500822624"
    ],
    [
      "0.826138109",
      "0.872959062"
    ],
    [
      "0.865287568",
      "0.521811485"
    ],
    [
      "0.959199993",
      "0.592272709"
    ],
    [
      "1.235524104",
      "1.803672595"
    ],
    [
      "1.230423933",
      "0.9172863"
    ],
    [
      "1.294029176",
      "0.333709403"
    ],
    [
      "0.951503993",
      "1.59536627"
    ],
    [
      "0.87808374",
      "0.40510422"
    ],
    [
      "0.757818027",
      "0.569083308"
    ],
    [
      "1.248320276",
      "1.68696533"
    ],
    [
      "0.628539919",
      "1.735893735"
    ],
    [
      "0.351735566",
      "0.525332521"
    ],
    [
      "0.099456038",
      "0.726029239"
    ],
    [
      "0.743753029",
      "0.685644466"
    ],
    [
      "0.477387443",
      "1.247348092"
    ],
    [
      "1.923432143",
      "1.182517074"
    ],
    [
      "1.634709758",
      "0.961613537"
    ],
    [
      "0.886427688",
      "1.826734816"
    ],
    [
      "0.382714072",
      "1.17791265"
    ],
    [
      "0.226125011",
      "1.535870234"
    ],
    [
      "0.502979785",
      "1.013933562"
    ],
    [
      "0.083751902",
      "1.215705422"
    ],
    [
      "0.585098802",
      "1.199745348"
    ],
    [
      "0.705364515",
      "1.03576626"
    ],
    [
      "0.140566517",
      "0.61605535"
    ],
    [
      "0.816604169",
      "0.076741978"
    ],
    [
      "1.002688678",
      "1.12853721"
    ],
    [
      "0.736619618",
      "1.690034098"
    ],
    [
      "1.597106823",
      "0.272330537"
    ],
    [
      "1.113800236",
      "1.848485122"
    ],
    [
      "1.066669535",
      "0.545000886"
    ],
    [
      "1.208473607",
      "1.917920563"
    ],
    [
      "1.609117415",
      "1.195028067"
    ],
    [
      "0.446694929",
      "0.594376326"
    ],
    [
      "1.718449227",
      "1.608169478"
    ],
    [
      "1.55628744",
      "1.75933108"
    ],
    [
      "1.153646905",
      "1.617529889"
    ],
    [
      "0.526504958",
      "1.677691143"
    ],
    [
      "1.080226652",
      "0.427267839"
    ],
    [
      "1.299504961",
      "1.220136271"
    ],
    [
      "0.770614198",
      "0.452376043"
    ],
    [
      "1.448377752",
      "1.827645333"
    ],
    [
      "1.488851702",
      "1.359007155"
    ],
    [
      "0.718160686",
      "0.919058995"
    ],
    [
      "0.205323959",
      "0.920471835"
    ],
    [
      "0.597894973",
      "1.083038083"
    ],
    [
      "0.964300164",
      "1.478659005"
    ],
    [
      "1.179239248",
      "1.384115359"
    ],
    [
      "1.463808543",
      "1.59365135"
    ],
    [
      "1.028281021",
      "0.895122681"
    ],
    [
      "1.050365373",
      "0.060051738"
    ],
    [
      "1.445363017",
      "0.822742654"
    ],
    [
      "0.395510243",
      "1.061205385"
    ],
    [
      "1.256016276",
      "0.68387177"
    ],
    [
      "1.368585989",
      "1.522986243"
    ],
    [
      "0.472437485",
      "0.220437817"
    ],
    [
      "0.681404423",
      "0.114287683"
    ],
    [
      "1.181929424",
      "0.368608877"
    ],
    [
      "0.74856638",
      "1.573119919"
    ],
    [
      "1.09723274",
      "0.168074034"
    ],
    [
      "1.217627762",
      "1.033993564"
    ],
    [
      "1.394178332",
      "1.289571713"
    ],
    [
      "1.041077192",
      "0.778415416"
    ],
    [
      "0.985553281",
      "0.357832397"
    ],
    [
      "1.703790788",
      "1.264463506"
    ],
    [
      "1.002706958",
      "1.810503399"
    ],
    [
      "0.989892507",
      "1.245244475"
    ],
    [
      "1.47095536",
      "0.589328124"
    ],
    [
      "0.331312454",
      "1.407014241"
    ],
    [
      "1.347334615",
      "1.767857273"
    ],
    [
      "0.408306415",
      "0.94449812"
    ],
    [
      "0.774953423",
      "1.339788121"
    ],
    [
      "0.451417609",
      "1.478997942"
    ],
    [
      "1.268812447",
      "0.567164505"
    ],
    [
      "0.554164471",
      "0.547104503"
    ],
    [
      "0.258931242",
      "1.225624769"
    ],
    [
      "0.97275711",
      "0.474539662"
    ],
    [
      "0.305170267",
      "1.63502051"
    ],
    [
      "1.569643723",
      "0.659273961"
    ],
    [
      "0.895219137",
      "1.175809033"
    ]
  ],
  "radius": "0.058703337"
}

Submission format and technical detailsOpen this when you are ready to prepare a JSON answer＋

Instance parameters

{
  "n": 244
}

Starter answer

{
  "centers": [
    [
      "0.995248542",
      "0.226242334"
    ],
    [
      "0.688846955",
      "0.266083662"
    ],
    [
      "1.938313146",
      "0.925114446"
    ],
    [
      "1.59122508",
      "0.425487138"
    ],
    [
      "1.135750563",
      "0.847850858"
    ],
    [
      "0.288040702",
      "1.108477208"
    ],
    [
      "1.940222276",
      "1.044840589"
    ],
    [
      "0.882422965",
      "1.292516298"
    ],
    [
      "1.578488393",
      "0.54220091"
    ],
    [
      "0.666976001",
      "1.385888055"
    ],
    [
      "1.071769706",
      "1.431387182"
    ],
    [
      "1.084565877",
      "1.314679917"
    ],
    [
      "1.38138216",
      "1.406278978"
    ],
    [
      "0.800545766",
      "1.106373592"
    ],
    [
      "1.647505929",
      "0.844906273"
    ],
    [
      "1.821875894",
      "0.541132459"
    ],
    [
      "1.304111297",
      "0.216736422"
    ],
    [
      "0.573597928",
      "0.160840053"
    ],
    [
      "0.663144656",
      "0.499647866"
    ],
    [
      "0.186747145",
      "0.804544144"
    ],
    [
      "1.122954391",
      "0.964558123"
    ],
    [
      "1.363485818",
      "0.636599947"
    ],
    [
      "1.350689646",
      "0.753307212"
    ],
    [
      "1.777937351",
      "0.758285825"
    ],
    [
      "0.42737026",
      "1.605403176"
    ],
    [
      "0.479562598",
      "0.353585476"
    ],
    [
      "1.398840519",
      "0.147377196"
    ],
    [
      "1.189240251",
      "0.241005135"
    ],
    [
      "0.355664304",
      "1.292160791"
    ],
    [
      "1.570728901",
      "1.545149862"
    ],
    [
      "0.535873509",
      "1.560554846"
    ],
    [
      "1.527240216",
      "1.00888536"
    ],
    [
      "0.57250337",
      "0.281847476"
    ],
    [
      "1.872605361",
      "0.647013755"
    ],
    [
      "1.046177364",
      "1.664801712"
    ],
    [
      "0.568229468",
      "0.430543345"
    ],
    [
      "0.117731326",
      "1.328087478"
    ],
    [
      "0.654179829",
      "1.502595319"
    ],
    [
      "0.649079658",
      "0.616209024"
    ],
    [
      "0.692568343",
      "1.152473525"
    ],
    [
      "1.01548485",
      "1.011829946"
    ],
    [
      "1.174139077",
      "0.497729063"
    ],
    [
      "1.664317093",
      "0.728709403"
    ],
    [
      "0.156027414",
      "1.027027822"
    ],
    [
      "1.281608619",
      "0.45045724"
    ],
    [
      "1.458159188",
      "0.706035389"
    ],
    [
      "0.490183614",
      "1.130640827"
    ],
    [
      "0.34291436",
      "1.523846272"
    ],
    [
      "1.552832559",
      "0.775470831"
    ],
    [
      "0.636283487",
      "0.732916289"
    ],
    [
      "0.946403822",
      "0.708979974"
    ],
    [
      "1.514444045",
      "1.125592625"
    ],
    [
      "1.432566846",
      "0.939449919"
    ],
    [
      "0.851730451",
      "0.639544532"
    ],
    [
      "0.920811479",
      "0.942394504"
    ],
    [
      "1.758360306",
      "0.442389875"
    ],
    [
      "1.449634163",
      "1.710245379"
    ],
    [
      "1.243220105",
      "0.800579035"
    ],
    [
      "0.844034451",
      "1.642638093"
    ],
    [
      "0.610691144",
      "0.966330818"
    ],
    [
      "1.376281989",
      "0.519892682"
    ],
    [
      "0.515775957",
      "0.897226297"
    ],
    [
      "0.165436416",
      "1.435365398"
    ],
    [
      "0.332400041",
      "0.641136083"
    ],
    [
      "1.583525073",
      "1.428442597"
    ],
    [
      "0.06402677",
      "1.099967586"
    ],
    [
      "0.227857624",
      "0.694570255"
    ],
    [
      "1.261116447",
      "1.570258066"
    ],
    [
      "1.396821014",
      "0.390438283"
    ],
    [
      "0.559506459",
      "1.433159878"
    ],
    [
      "1.406974503",
      "1.172864448"
    ],
    [
      "1.325097304",
      "0.986721741"
    ],
    [
      "1.808278969",
      "1.386528787"
    ],
    [
      "0.57230263",
      "1.316452613"
    ],
    [
      "1.690994617",
      "1.381170771"
    ],
    [
      "0.775294895",
      "0.186641348"
    ],
    [
      "0.923383923",
      "1.938173429"
    ],
    [
      "0.585563536",
      "1.845151953"
    ],
    [
      "1.795482798",
      "1.503236052"
    ],
    [
      "1.204831591",
      "1.150700829"
    ],
    [
      "1.058973535",
      "1.548094447"
    ],
    [
      "1.596321244",
      "1.311735332"
    ],
    [
      "0.762157252",
      "1.456495386"
    ],
    [
      "0.813341937",
      "0.989666327"
    ],
    [
      "1.355789818",
      "1.639693507"
    ],
    [
      "0.83893428",
      "0.756251797"
    ],
    [
      "1.323235072",
      "1.883979908"
    ],
    [
      "0.679772172",
      "1.26918079"
    ],
    [
      "0.69399676",
      "1.890169322"
    ],
    [
      "0.421102586",
      "0.827790856"
    ],
    [
      "0.730956857",
      "0.802351731"
    ],
    [
      "0.637784351",
      "1.618851571"
    ],
    [
      "1.140850734",
      "1.734237153"
    ],
    [
      "1.087256054",
      "0.299173436"
    ],
    [
      "0.891654044",
      "0.170992831"
    ],
    [
      "0.364553551",
      "0.40862765"
    ],
    [
      "0.675566605",
      "0.382801219"
    ],
    [
      "1.407125058",
      "0.273061313"
    ],
    [
      "1.811268086",
      "1.21720932"
    ],
    [
      "1.28670879",
      "1.336843536"
    ],
    [
      "0.80719055",
      "1.921338115"
    ],
    [
      "0.4835778",
      "1.786986351"
    ],
    [
      "0.175752546",
      "1.142765658"
    ],
    [
      "1.166983882",
      "0.073633016"
    ],
    [
      "0.528572128",
      "0.780519033"
    ],
    [
      "0.869626794",
      "1.409223563"
    ],
    [
      "0.236656238",
      "0.548593558"
    ],
    [
      "1.610979686",
      "1.655441303"
    ],
    [
      "0.389626167",
      "1.716577414"
    ],
    [
      "0.977096336",
      "1.36195174"
    ],
    [
      "1.505285177",
      "0.345495509"
    ],
    [
      "1.540036387",
      "0.892178096"
    ],
    [
      "0.379496712",
      "0.292175816"
    ],
    [
      "0.326404183",
      "0.758389558"
    ],
    [
      "1.476055531",
      "1.47571442"
    ],
    [
      "1.053873364",
      "0.661708151"
    ],
    [
      "0.298761899",
      "0.991561069"
    ],
    [
      "1.312301132",
      "1.103429006"
    ],
    [
      "1.891092422",
      "1.303304634"
    ],
    [
      "1.909759497",
      "0.758386542"
    ],
    [
      "0.908015308",
      "1.059101769"
    ],
    [
      "0.783410369",
      "0.335668778"
    ],
    [
      "1.501877586",
      "0.203659436"
    ],
    [
      "0.541368299",
      "0.663811768"
    ],
    [
      "1.683046725",
      "0.352322166"
    ],
    [
      "0.771635098",
      "1.802097669"
    ],
    [
      "1.161342905",
      "0.614436328"
    ],
    [
      "0.450337675",
      "1.361596233"
    ],
    [
      "1.678198445",
      "1.497878036"
    ],
    [
      "1.482760917",
      "0.470429912"
    ],
    [
      "0.313608011",
      "0.875096823"
    ],
    [
      "0.93360765",
      "0.825687239"
    ],
    [
      "1.84377419",
      "0.855496104"
    ],
    [
      "1.419770674",
      "1.056157183"
    ],
    [
      "0.249474223",
      "0.431888687"
    ],
    [
      "0.075413941",
      "0.84192155"
    ],
    [
      "1.273912618",
      "1.453550801"
    ],
    [
      "0.787749595",
      "1.223080856"
    ],
    [
      "0.938707822",
      "1.712073535"
    ],
    [
      "1.097362049",
      "1.197972652"
    ],
    [
      "1.716606112",
      "1.147758343"
    ],
    [
      "1.729383128",
      "1.031048979"
    ],
    [
      "0.433860993",
      "0.711079456"
    ],
    [
      "1.04076923",
      "1.940413353"
    ],
    [
      "0.856830623",
      "1.525930828"
    ],
    [
      "1.837305748",
      "1.102726274"
    ],
    [
      "1.837518085",
      "0.98531979"
    ],
    [
      "1.281004582",
      "0.101626008"
    ],
    [
      "0.059657593",
      "0.958266291"
    ],
    [
      "1.501647873",
      "1.24229989"
    ],
    [
      "0.890879911",
      "0.288396955"
    ],
    [
      "1.755264296",
      "0.643089209"
    ],
    [
      "1.695894384",
      "0.541799816"
    ],
    [
      "1.337893475",
      "0.870014477"
    ],
    [
      "1.148546734",
      "0.731143593"
    ],
    [
      "0.234579391",
      "1.340478219"
    ],
    [
      "0.623487316",
      "0.849623554"
    ],
    [
      "0.460252046",
      "0.476643279"
    ],
    [
      "0.932963318",
      "0.061093461"
    ],
    [
      "1.621913587",
      "1.078320802"
    ],
    [
      "1.192035419",
      "1.267408094"
    ],
    [
      "1.11015822",
      "1.081265387"
    ],
    [
      "1.7421793",
      "0.914341714"
    ],
    [
      "1.166443077",
      "1.500822624"
    ],
    [
      "0.826138109",
      "0.872959062"
    ],
    [
      "0.865287568",
      "0.521811485"
    ],
    [
      "0.959199993",
      "0.592272709"
    ],
    [
      "1.235524104",
      "1.803672595"
    ],
    [
      "1.230423933",
      "0.9172863"
    ],
    [
      "1.294029176",
      "0.333709403"
    ],
    [
      "0.951503993",
      "1.59536627"
    ],
    [
      "0.87808374",
      "0.40510422"
    ],
    [
      "0.757818027",
      "0.569083308"
    ],
    [
      "1.248320276",
      "1.68696533"
    ],
    [
      "0.628539919",
      "1.735893735"
    ],
    [
      "0.351735566",
      "0.525332521"
    ],
    [
      "0.099456038",
      "0.726029239"
    ],
    [
      "0.743753029",
      "0.685644466"
    ],
    [
      "0.477387443",
      "1.247348092"
    ],
    [
      "1.923432143",
      "1.182517074"
    ],
    [
      "1.634709758",
      "0.961613537"
    ],
    [
      "0.886427688",
      "1.826734816"
    ],
    [
      "0.382714072",
      "1.17791265"
    ],
    [
      "0.226125011",
      "1.535870234"
    ],
    [
      "0.502979785",
      "1.013933562"
    ],
    [
      "0.083751902",
      "1.215705422"
    ],
    [
      "0.585098802",
      "1.199745348"
    ],
    [
      "0.705364515",
      "1.03576626"
    ],
    [
      "0.140566517",
      "0.61605535"
    ],
    [
      "0.816604169",
      "0.076741978"
    ],
    [
      "1.002688678",
      "1.12853721"
    ],
    [
      "0.736619618",
      "1.690034098"
    ],
    [
      "1.597106823",
      "0.272330537"
    ],
    [
      "1.113800236",
      "1.848485122"
    ],
    [
      "1.066669535",
      "0.545000886"
    ],
    [
      "1.208473607",
      "1.917920563"
    ],
    [
      "1.609117415",
      "1.195028067"
    ],
    [
      "0.446694929",
      "0.594376326"
    ],
    [
      "1.718449227",
      "1.608169478"
    ],
    [
      "1.55628744",
      "1.75933108"
    ],
    [
      "1.153646905",
      "1.617529889"
    ],
    [
      "0.526504958",
      "1.677691143"
    ],
    [
      "1.080226652",
      "0.427267839"
    ],
    [
      "1.299504961",
      "1.220136271"
    ],
    [
      "0.770614198",
      "0.452376043"
    ],
    [
      "1.448377752",
      "1.827645333"
    ],
    [
      "1.488851702",
      "1.359007155"
    ],
    [
      "0.718160686",
      "0.919058995"
    ],
    [
      "0.205323959",
      "0.920471835"
    ],
    [
      "0.597894973",
      "1.083038083"
    ],
    [
      "0.964300164",
      "1.478659005"
    ],
    [
      "1.179239248",
      "1.384115359"
    ],
    [
      "1.463808543",
      "1.59365135"
    ],
    [
      "1.028281021",
      "0.895122681"
    ],
    [
      "1.050365373",
      "0.060051738"
    ],
    [
      "1.445363017",
      "0.822742654"
    ],
    [
      "0.395510243",
      "1.061205385"
    ],
    [
      "1.256016276",
      "0.68387177"
    ],
    [
      "1.368585989",
      "1.522986243"
    ],
    [
      "0.472437485",
      "0.220437817"
    ],
    [
      "0.681404423",
      "0.114287683"
    ],
    [
      "1.181929424",
      "0.368608877"
    ],
    [
      "0.74856638",
      "1.573119919"
    ],
    [
      "1.09723274",
      "0.168074034"
    ],
    [
      "1.217627762",
      "1.033993564"
    ],
    [
      "1.394178332",
      "1.289571713"
    ],
    [
      "1.041077192",
      "0.778415416"
    ],
    [
      "0.985553281",
      "0.357832397"
    ],
    [
      "1.703790788",
      "1.264463506"
    ],
    [
      "1.002706958",
      "1.810503399"
    ],
    [
      "0.989892507",
      "1.245244475"
    ],
    [
      "1.47095536",
      "0.589328124"
    ],
    [
      "0.331312454",
      "1.407014241"
    ],
    [
      "1.347334615",
      "1.767857273"
    ],
    [
      "0.408306415",
      "0.94449812"
    ],
    [
      "0.774953423",
      "1.339788121"
    ],
    [
      "0.451417609",
      "1.478997942"
    ],
    [
      "1.268812447",
      "0.567164505"
    ],
    [
      "0.554164471",
      "0.547104503"
    ],
    [
      "0.258931242",
      "1.225624769"
    ],
    [
      "0.97275711",
      "0.474539662"
    ],
    [
      "0.305170267",
      "1.63502051"
    ],
    [
      "1.569643723",
      "0.659273961"
    ],
    [
      "0.895219137",
      "1.175809033"
    ]
  ],
  "radius": "0.058703337"
}

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?