P01 · Packing and covering · Classic · Hard

Equal-circle packing in a unit square · n = 257

Also known ascircle packing in a squarepacking equal circles in a unit squarecsq

Place n non-overlapping circles of one common radius inside the unit square, making that radius as large as possible.

Instancen = 257

ObjectiveMaximize common radius

Record comparison

common radius · Higher is better

Record	Value / interval	Author / holder	Source
External best known	[0.0324481124805, 0.0324481124815]	See source attribution	packomania.com ↗
Site record	No player record yet	—	—

Formal definition

ContainerThe unit square: the origin (0, 0) at its lower-left corner, (1, 1) at its upper right
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

1y0

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257

0x1

VERIFIED CONSTRUCTIONr = 0.032448112

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 = 1–30 are proved and make a compact gallery of classic contact structures. For n = 31–300 the public Packomania frontier is imported; optimality remains open except at n = 36. The large instances share one dense table for algorithmic challenges.

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 square of side 1. Its lower-left corner is the origin (0, 0) and its upper-right corner is (1, 1). Coordinates and lengths 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 "0.25".

Starter answer

{
  "centers": [
    [
      "0.144698538",
      "0.032448112"
    ],
    [
      "0.257102094",
      "0.032448112"
    ],
    [
      "0.369505649",
      "0.032448112"
    ],
    [
      "0.48190921",
      "0.032448112"
    ],
    [
      "0.594470393",
      "0.032448112"
    ],
    [
      "0.839497114",
      "0.032448112"
    ],
    [
      "0.904393339",
      "0.032448112"
    ],
    [
      "0.709705362",
      "0.032448113"
    ],
    [
      "0.032448356",
      "0.032448367"
    ],
    [
      "0.774601237",
      "0.032661055"
    ],
    [
      "0.967551888",
      "0.04736514"
    ],
    [
      "0.652087877",
      "0.062310221"
    ],
    [
      "0.538142312",
      "0.064841912"
    ],
    [
      "0.425707429",
      "0.064896223"
    ],
    [
      "0.200900316",
      "0.064896228"
    ],
    [
      "0.313303871",
      "0.064896228"
    ],
    [
      "0.08864989",
      "0.065160023"
    ],
    [
      "0.810652824",
      "0.090581812"
    ],
    [
      "0.875549049",
      "0.090581812"
    ],
    [
      "0.706757964",
      "0.097277372"
    ],
    [
      "0.59431281",
      "0.097344146"
    ],
    [
      "0.481909208",
      "0.097344337"
    ],
    [
      "0.369505652",
      "0.097344339"
    ],
    [
      "0.257102094",
      "0.097344344"
    ],
    [
      "0.032448112",
      "0.097608138"
    ],
    [
      "0.144851668",
      "0.097608139"
    ],
    [
      "0.967551888",
      "0.112261365"
    ],
    [
      "0.650554634",
      "0.129722801"
    ],
    [
      "0.538111063",
      "0.129792319"
    ],
    [
      "0.42570743",
      "0.129792453"
    ],
    [
      "0.313303874",
      "0.129792454"
    ],
    [
      "0.08864989",
      "0.130056253"
    ],
    [
      "0.201053447",
      "0.130056256"
    ],
    [
      "0.761197667",
      "0.132602133"
    ],
    [
      "0.911350108",
      "0.144709478"
    ],
    [
      "0.824712612",
      "0.154289474"
    ],
    [
      "0.594312877",
      "0.162240371"
    ],
    [
      "0.481909359",
      "0.162240562"
    ],
    [
      "0.369505652",
      "0.162240569"
    ],
    [
      "0.257255228",
      "0.162504367"
    ],
    [
      "0.032448112",
      "0.162504369"
    ],
    [
      "0.144851668",
      "0.162504369"
    ],
    [
      "0.704994337",
      "0.165047561"
    ],
    [
      "0.967551888",
      "0.17715759"
    ],
    [
      "0.425707434",
      "0.194688678"
    ],
    [
      "0.538262661",
      "0.194949895"
    ],
    [
      "0.201053447",
      "0.194952481"
    ],
    [
      "0.313457006",
      "0.194952481"
    ],
    [
      "0.08864989",
      "0.194952485"
    ],
    [
      "0.873602869",
      "0.197498358"
    ],
    [
      "0.76119931",
      "0.197498358"
    ],
    [
      "0.64879493",
      "0.197499781"
    ],
    [
      "0.481909215",
      "0.227136787"
    ],
    [
      "0.369658787",
      "0.227400591"
    ],
    [
      "0.257255227",
      "0.227400594"
    ],
    [
      "0.144851669",
      "0.227400597"
    ],
    [
      "0.032448112",
      "0.2274006"
    ],
    [
      "0.817401089",
      "0.229946471"
    ],
    [
      "0.929804648",
      "0.229946471"
    ],
    [
      "0.70499753",
      "0.229946471"
    ],
    [
      "0.592745514",
      "0.230210375"
    ],
    [
      "0.42586057",
      "0.259848702"
    ],
    [
      "0.313457009",
      "0.259848706"
    ],
    [
      "0.201053449",
      "0.259848709"
    ],
    [
      "0.088649892",
      "0.259848713"
    ],
    [
      "0.873602869",
      "0.262394583"
    ],
    [
      "0.76119931",
      "0.262394583"
    ],
    [
      "0.536392249",
      "0.262394681"
    ],
    [
      "0.648948944",
      "0.262658487"
    ],
    [
      "0.967551888",
      "0.282735351"
    ],
    [
      "0.369658791",
      "0.292296816"
    ],
    [
      "0.25725523",
      "0.292296819"
    ],
    [
      "0.032448112",
      "0.292296825"
    ],
    [
      "0.144851671",
      "0.292296825"
    ],
    [
      "0.817401089",
      "0.294842696"
    ],
    [
      "0.705150723",
      "0.2951066"
    ],
    [
      "0.592747165",
      "0.2951066"
    ],
    [
      "0.480343606",
      "0.2951066"
    ],
    [
      "0.911350108",
      "0.315183464"
    ],
    [
      "0.313457013",
      "0.324744931"
    ],
    [
      "0.201053452",
      "0.324744935"
    ],
    [
      "0.088649892",
      "0.324744938"
    ],
    [
      "0.424141825",
      "0.32755471"
    ],
    [
      "0.536545385",
      "0.327554712"
    ],
    [
      "0.648948944",
      "0.327554712"
    ],
    [
      "0.761352503",
      "0.327554712"
    ],
    [
      "0.855148329",
      "0.347631576"
    ],
    [
      "0.967551888",
      "0.347631576"
    ],
    [
      "0.257255234",
      "0.357193044"
    ],
    [
      "0.032448112",
      "0.35719305"
    ],
    [
      "0.144851671",
      "0.35719305"
    ],
    [
      "0.705150724",
      "0.360002825"
    ],
    [
      "0.592747165",
      "0.360002825"
    ],
    [
      "0.480343606",
      "0.360002825"
    ],
    [
      "0.367940047",
      "0.360002825"
    ],
    [
      "0.911350108",
      "0.380079689"
    ],
    [
      "0.799099743",
      "0.380343593"
    ],
    [
      "0.201053452",
      "0.38964116"
    ],
    [
      "0.088649892",
      "0.389641163"
    ],
    [
      "0.648948944",
      "0.392450937"
    ],
    [
      "0.536545385",
      "0.392450937"
    ],
    [
      "0.424141826",
      "0.392450937"
    ],
    [
      "0.311738268",
      "0.392450937"
    ],
    [
      "0.967551888",
      "0.412527801"
    ],
    [
      "0.742897963",
      "0.412791705"
    ],
    [
      "0.855301522",
      "0.412791705"
    ],
    [
      "0.032448112",
      "0.422089275"
    ],
    [
      "0.144851671",
      "0.422089275"
    ],
    [
      "0.592747165",
      "0.42489905"
    ],
    [
      "0.480343606",
      "0.42489905"
    ],
    [
      "0.367940047",
      "0.42489905"
    ],
    [
      "0.255536488",
      "0.42489905"
    ],
    [
      "0.686696184",
      "0.445239818"
    ],
    [
      "0.799099743",
      "0.445239818"
    ],
    [
      "0.911503302",
      "0.445239818"
    ],
    [
      "0.088649892",
      "0.454537388"
    ],
    [
      "0.536545385",
      "0.457347162"
    ],
    [
      "0.424141826",
      "0.457347162"
    ],
    [
      "0.311738268",
      "0.457347162"
    ],
    [
      "0.199334709",
      "0.457347163"
    ],
    [
      "0.630494404",
      "0.47768793"
    ],
    [
      "0.742897963",
      "0.47768793"
    ],
    [
      "0.855301522",
      "0.47768793"
    ],
    [
      "0.967551888",
      "0.477951834"
    ],
    [
      "0.032448112",
      "0.4869855"
    ],
    [
      "0.480343606",
      "0.489795275"
    ],
    [
      "0.367940047",
      "0.489795275"
    ],
    [
      "0.14313293",
      "0.489795275"
    ],
    [
      "0.255536488",
      "0.489795275"
    ],
    [
      "0.574292625",
      "0.510136043"
    ],
    [
      "0.686696184",
      "0.510136043"
    ],
    [
      "0.799099743",
      "0.510136043"
    ],
    [
      "0.911350108",
      "0.510399947"
    ],
    [
      "0.424141827",
      "0.522243387"
    ],
    [
      "0.311738268",
      "0.522243388"
    ],
    [
      "0.08693115",
      "0.522243388"
    ],
    [
      "0.199334709",
      "0.522243388"
    ],
    [
      "0.742897963",
      "0.542584155"
    ],
    [
      "0.518090846",
      "0.542584155"
    ],
    [
      "0.630494404",
      "0.542584155"
    ],
    [
      "0.855148329",
      "0.542848059"
    ],
    [
      "0.967551888",
      "0.542848059"
    ],
    [
      "0.367940047",
      "0.5546915"
    ],
    [
      "0.14313293",
      "0.5546915"
    ],
    [
      "0.255536488",
      "0.5546915"
    ],
    [
      "0.032448112",
      "0.557501275"
    ],
    [
      "0.686696184",
      "0.575032268"
    ],
    [
      "0.574292625",
      "0.575032268"
    ],
    [
      "0.461889066",
      "0.575032268"
    ],
    [
      "0.798946549",
      "0.575296172"
    ],
    [
      "0.911350108",
      "0.575296172"
    ],
    [
      "0.199334709",
      "0.587139613"
    ],
    [
      "0.313363016",
      "0.589857272"
    ],
    [
      "0.088649892",
      "0.589949388"
    ],
    [
      "0.630494404",
      "0.60748038"
    ],
    [
      "0.518090846",
      "0.60748038"
    ],
    [
      "0.405687287",
      "0.607480381"
    ],
    [
      "0.74274477",
      "0.607744284"
    ],
    [
      "0.855148329",
      "0.607744284"
    ],
    [
      "0.967551888",
      "0.607744284"
    ],
    [
      "0.255536488",
      "0.619587725"
    ],
    [
      "0.032448112",
      "0.6223975"
    ],
    [
      "0.144851671",
      "0.6223975"
    ],
    [
      "0.574292625",
      "0.639928493"
    ],
    [
      "0.461889066",
      "0.639928493"
    ],
    [
      "0.798946549",
      "0.640192397"
    ],
    [
      "0.911350108",
      "0.640192397"
    ],
    [
      "0.68654299",
      "0.640192397"
    ],
    [
      "0.351248698",
      "0.642806858"
    ],
    [
      "0.088649892",
      "0.654845613"
    ],
    [
      "0.201053451",
      "0.654845613"
    ],
    [
      "0.293427842",
      "0.672273257"
    ],
    [
      "0.518090846",
      "0.672376606"
    ],
    [
      "0.74274477",
      "0.672640509"
    ],
    [
      "0.855148329",
      "0.672640509"
    ],
    [
      "0.967551888",
      "0.672640509"
    ],
    [
      "0.630341211",
      "0.67264051"
    ],
    [
      "0.407450477",
      "0.675254971"
    ],
    [
      "0.032448112",
      "0.687293725"
    ],
    [
      "0.144851671",
      "0.687293725"
    ],
    [
      "0.798946549",
      "0.705088622"
    ],
    [
      "0.911350108",
      "0.705088622"
    ],
    [
      "0.68654299",
      "0.705088622"
    ],
    [
      "0.574139432",
      "0.705088622"
    ],
    [
      "0.238944805",
      "0.707531145"
    ],
    [
      "0.463652257",
      "0.707703083"
    ],
    [
      "0.351248698",
      "0.707703083"
    ],
    [
      "0.088649892",
      "0.719741837"
    ],
    [
      "0.855148329",
      "0.737536734"
    ],
    [
      "0.967551888",
      "0.737536734"
    ],
    [
      "0.74274477",
      "0.737536734"
    ],
    [
      "0.630341211",
      "0.737536735"
    ],
    [
      "0.182743025",
      "0.739979257"
    ],
    [
      "0.407450477",
      "0.740151196"
    ],
    [
      "0.295046941",
      "0.740151235"
    ],
    [
      "0.519700842",
      "0.7404151"
    ],
    [
      "0.032448112",
      "0.75218995"
    ],
    [
      "0.911350108",
      "0.769984847"
    ],
    [
      "0.798946549",
      "0.769984847"
    ],
    [
      "0.686542991",
      "0.769984847"
    ],
    [
      "0.126541246",
      "0.77242737"
    ],
    [
      "0.351248721",
      "0.772599348"
    ],
    [
      "0.238845162",
      "0.772599348"
    ],
    [
      "0.575902622",
      "0.772863212"
    ],
    [
      "0.463499063",
      "0.772863213"
    ],
    [
      "0.967551888",
      "0.802432959"
    ],
    [
      "0.855148329",
      "0.802432959"
    ],
    [
      "0.74274477",
      "0.80243296"
    ],
    [
      "0.070339466",
      "0.804875482"
    ],
    [
      "0.182643382",
      "0.80504746"
    ],
    [
      "0.295046941",
      "0.80504746"
    ],
    [
      "0.632104401",
      "0.805311325"
    ],
    [
      "0.519700843",
      "0.805311325"
    ],
    [
      "0.407293224",
      "0.805318358"
    ],
    [
      "0.911350108",
      "0.834881072"
    ],
    [
      "0.798946549",
      "0.834881072"
    ],
    [
      "0.238848469",
      "0.8375013"
    ],
    [
      "0.688306181",
      "0.837759437"
    ],
    [
      "0.575902622",
      "0.837759437"
    ],
    [
      "0.463499063",
      "0.837759438"
    ],
    [
      "0.351091445",
      "0.837766471"
    ],
    [
      "0.120334493",
      "0.846320686"
    ],
    [
      "0.032448112",
      "0.857561015"
    ],
    [
      "0.855148329",
      "0.867329184"
    ],
    [
      "0.967551888",
      "0.867329185"
    ],
    [
      "0.182643383",
      "0.869943685"
    ],
    [
      "0.74450796",
      "0.87020755"
    ],
    [
      "0.632104402",
      "0.87020755"
    ],
    [
      "0.519700843",
      "0.87020755"
    ],
    [
      "0.407293224",
      "0.870214583"
    ],
    [
      "0.294653715",
      "0.870626736"
    ],
    [
      "0.911350108",
      "0.899777297"
    ],
    [
      "0.80070974",
      "0.902655662"
    ],
    [
      "0.688306181",
      "0.902655662"
    ],
    [
      "0.575902622",
      "0.902655663"
    ],
    [
      "0.463499063",
      "0.902655663"
    ],
    [
      "0.351091445",
      "0.902662695"
    ],
    [
      "0.238448631",
      "0.903069123"
    ],
    [
      "0.131755336",
      "0.910216835"
    ],
    [
      "0.066901298",
      "0.912556451"
    ],
    [
      "0.967551888",
      "0.93222541"
    ],
    [
      "0.74450796",
      "0.935103775"
    ],
    [
      "0.856911519",
      "0.935103775"
    ],
    [
      "0.632104402",
      "0.935103775"
    ],
    [
      "0.519699563",
      "0.935105993"
    ],
    [
      "0.40710343",
      "0.935437381"
    ],
    [
      "0.290635392",
      "0.941644529"
    ],
    [
      "0.166244606",
      "0.966661928"
    ],
    [
      "0.231134729",
      "0.967551887"
    ],
    [
      "0.032448112",
      "0.967551888"
    ],
    [
      "0.101354483",
      "0.967551888"
    ],
    [
      "0.350136054",
      "0.967551888"
    ],
    [
      "0.463496502",
      "0.967551888"
    ],
    [
      "0.575902622",
      "0.967551888"
    ],
    [
      "0.688306181",
      "0.967551888"
    ],
    [
      "0.80070974",
      "0.967551888"
    ],
    [
      "0.913113298",
      "0.967551888"
    ]
  ],
  "radius": "0.032448112"
}

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

Instance parameters

{
  "n": 257
}

Starter answer

{
  "centers": [
    [
      "0.144698538",
      "0.032448112"
    ],
    [
      "0.257102094",
      "0.032448112"
    ],
    [
      "0.369505649",
      "0.032448112"
    ],
    [
      "0.48190921",
      "0.032448112"
    ],
    [
      "0.594470393",
      "0.032448112"
    ],
    [
      "0.839497114",
      "0.032448112"
    ],
    [
      "0.904393339",
      "0.032448112"
    ],
    [
      "0.709705362",
      "0.032448113"
    ],
    [
      "0.032448356",
      "0.032448367"
    ],
    [
      "0.774601237",
      "0.032661055"
    ],
    [
      "0.967551888",
      "0.04736514"
    ],
    [
      "0.652087877",
      "0.062310221"
    ],
    [
      "0.538142312",
      "0.064841912"
    ],
    [
      "0.425707429",
      "0.064896223"
    ],
    [
      "0.200900316",
      "0.064896228"
    ],
    [
      "0.313303871",
      "0.064896228"
    ],
    [
      "0.08864989",
      "0.065160023"
    ],
    [
      "0.810652824",
      "0.090581812"
    ],
    [
      "0.875549049",
      "0.090581812"
    ],
    [
      "0.706757964",
      "0.097277372"
    ],
    [
      "0.59431281",
      "0.097344146"
    ],
    [
      "0.481909208",
      "0.097344337"
    ],
    [
      "0.369505652",
      "0.097344339"
    ],
    [
      "0.257102094",
      "0.097344344"
    ],
    [
      "0.032448112",
      "0.097608138"
    ],
    [
      "0.144851668",
      "0.097608139"
    ],
    [
      "0.967551888",
      "0.112261365"
    ],
    [
      "0.650554634",
      "0.129722801"
    ],
    [
      "0.538111063",
      "0.129792319"
    ],
    [
      "0.42570743",
      "0.129792453"
    ],
    [
      "0.313303874",
      "0.129792454"
    ],
    [
      "0.08864989",
      "0.130056253"
    ],
    [
      "0.201053447",
      "0.130056256"
    ],
    [
      "0.761197667",
      "0.132602133"
    ],
    [
      "0.911350108",
      "0.144709478"
    ],
    [
      "0.824712612",
      "0.154289474"
    ],
    [
      "0.594312877",
      "0.162240371"
    ],
    [
      "0.481909359",
      "0.162240562"
    ],
    [
      "0.369505652",
      "0.162240569"
    ],
    [
      "0.257255228",
      "0.162504367"
    ],
    [
      "0.032448112",
      "0.162504369"
    ],
    [
      "0.144851668",
      "0.162504369"
    ],
    [
      "0.704994337",
      "0.165047561"
    ],
    [
      "0.967551888",
      "0.17715759"
    ],
    [
      "0.425707434",
      "0.194688678"
    ],
    [
      "0.538262661",
      "0.194949895"
    ],
    [
      "0.201053447",
      "0.194952481"
    ],
    [
      "0.313457006",
      "0.194952481"
    ],
    [
      "0.08864989",
      "0.194952485"
    ],
    [
      "0.873602869",
      "0.197498358"
    ],
    [
      "0.76119931",
      "0.197498358"
    ],
    [
      "0.64879493",
      "0.197499781"
    ],
    [
      "0.481909215",
      "0.227136787"
    ],
    [
      "0.369658787",
      "0.227400591"
    ],
    [
      "0.257255227",
      "0.227400594"
    ],
    [
      "0.144851669",
      "0.227400597"
    ],
    [
      "0.032448112",
      "0.2274006"
    ],
    [
      "0.817401089",
      "0.229946471"
    ],
    [
      "0.929804648",
      "0.229946471"
    ],
    [
      "0.70499753",
      "0.229946471"
    ],
    [
      "0.592745514",
      "0.230210375"
    ],
    [
      "0.42586057",
      "0.259848702"
    ],
    [
      "0.313457009",
      "0.259848706"
    ],
    [
      "0.201053449",
      "0.259848709"
    ],
    [
      "0.088649892",
      "0.259848713"
    ],
    [
      "0.873602869",
      "0.262394583"
    ],
    [
      "0.76119931",
      "0.262394583"
    ],
    [
      "0.536392249",
      "0.262394681"
    ],
    [
      "0.648948944",
      "0.262658487"
    ],
    [
      "0.967551888",
      "0.282735351"
    ],
    [
      "0.369658791",
      "0.292296816"
    ],
    [
      "0.25725523",
      "0.292296819"
    ],
    [
      "0.032448112",
      "0.292296825"
    ],
    [
      "0.144851671",
      "0.292296825"
    ],
    [
      "0.817401089",
      "0.294842696"
    ],
    [
      "0.705150723",
      "0.2951066"
    ],
    [
      "0.592747165",
      "0.2951066"
    ],
    [
      "0.480343606",
      "0.2951066"
    ],
    [
      "0.911350108",
      "0.315183464"
    ],
    [
      "0.313457013",
      "0.324744931"
    ],
    [
      "0.201053452",
      "0.324744935"
    ],
    [
      "0.088649892",
      "0.324744938"
    ],
    [
      "0.424141825",
      "0.32755471"
    ],
    [
      "0.536545385",
      "0.327554712"
    ],
    [
      "0.648948944",
      "0.327554712"
    ],
    [
      "0.761352503",
      "0.327554712"
    ],
    [
      "0.855148329",
      "0.347631576"
    ],
    [
      "0.967551888",
      "0.347631576"
    ],
    [
      "0.257255234",
      "0.357193044"
    ],
    [
      "0.032448112",
      "0.35719305"
    ],
    [
      "0.144851671",
      "0.35719305"
    ],
    [
      "0.705150724",
      "0.360002825"
    ],
    [
      "0.592747165",
      "0.360002825"
    ],
    [
      "0.480343606",
      "0.360002825"
    ],
    [
      "0.367940047",
      "0.360002825"
    ],
    [
      "0.911350108",
      "0.380079689"
    ],
    [
      "0.799099743",
      "0.380343593"
    ],
    [
      "0.201053452",
      "0.38964116"
    ],
    [
      "0.088649892",
      "0.389641163"
    ],
    [
      "0.648948944",
      "0.392450937"
    ],
    [
      "0.536545385",
      "0.392450937"
    ],
    [
      "0.424141826",
      "0.392450937"
    ],
    [
      "0.311738268",
      "0.392450937"
    ],
    [
      "0.967551888",
      "0.412527801"
    ],
    [
      "0.742897963",
      "0.412791705"
    ],
    [
      "0.855301522",
      "0.412791705"
    ],
    [
      "0.032448112",
      "0.422089275"
    ],
    [
      "0.144851671",
      "0.422089275"
    ],
    [
      "0.592747165",
      "0.42489905"
    ],
    [
      "0.480343606",
      "0.42489905"
    ],
    [
      "0.367940047",
      "0.42489905"
    ],
    [
      "0.255536488",
      "0.42489905"
    ],
    [
      "0.686696184",
      "0.445239818"
    ],
    [
      "0.799099743",
      "0.445239818"
    ],
    [
      "0.911503302",
      "0.445239818"
    ],
    [
      "0.088649892",
      "0.454537388"
    ],
    [
      "0.536545385",
      "0.457347162"
    ],
    [
      "0.424141826",
      "0.457347162"
    ],
    [
      "0.311738268",
      "0.457347162"
    ],
    [
      "0.199334709",
      "0.457347163"
    ],
    [
      "0.630494404",
      "0.47768793"
    ],
    [
      "0.742897963",
      "0.47768793"
    ],
    [
      "0.855301522",
      "0.47768793"
    ],
    [
      "0.967551888",
      "0.477951834"
    ],
    [
      "0.032448112",
      "0.4869855"
    ],
    [
      "0.480343606",
      "0.489795275"
    ],
    [
      "0.367940047",
      "0.489795275"
    ],
    [
      "0.14313293",
      "0.489795275"
    ],
    [
      "0.255536488",
      "0.489795275"
    ],
    [
      "0.574292625",
      "0.510136043"
    ],
    [
      "0.686696184",
      "0.510136043"
    ],
    [
      "0.799099743",
      "0.510136043"
    ],
    [
      "0.911350108",
      "0.510399947"
    ],
    [
      "0.424141827",
      "0.522243387"
    ],
    [
      "0.311738268",
      "0.522243388"
    ],
    [
      "0.08693115",
      "0.522243388"
    ],
    [
      "0.199334709",
      "0.522243388"
    ],
    [
      "0.742897963",
      "0.542584155"
    ],
    [
      "0.518090846",
      "0.542584155"
    ],
    [
      "0.630494404",
      "0.542584155"
    ],
    [
      "0.855148329",
      "0.542848059"
    ],
    [
      "0.967551888",
      "0.542848059"
    ],
    [
      "0.367940047",
      "0.5546915"
    ],
    [
      "0.14313293",
      "0.5546915"
    ],
    [
      "0.255536488",
      "0.5546915"
    ],
    [
      "0.032448112",
      "0.557501275"
    ],
    [
      "0.686696184",
      "0.575032268"
    ],
    [
      "0.574292625",
      "0.575032268"
    ],
    [
      "0.461889066",
      "0.575032268"
    ],
    [
      "0.798946549",
      "0.575296172"
    ],
    [
      "0.911350108",
      "0.575296172"
    ],
    [
      "0.199334709",
      "0.587139613"
    ],
    [
      "0.313363016",
      "0.589857272"
    ],
    [
      "0.088649892",
      "0.589949388"
    ],
    [
      "0.630494404",
      "0.60748038"
    ],
    [
      "0.518090846",
      "0.60748038"
    ],
    [
      "0.405687287",
      "0.607480381"
    ],
    [
      "0.74274477",
      "0.607744284"
    ],
    [
      "0.855148329",
      "0.607744284"
    ],
    [
      "0.967551888",
      "0.607744284"
    ],
    [
      "0.255536488",
      "0.619587725"
    ],
    [
      "0.032448112",
      "0.6223975"
    ],
    [
      "0.144851671",
      "0.6223975"
    ],
    [
      "0.574292625",
      "0.639928493"
    ],
    [
      "0.461889066",
      "0.639928493"
    ],
    [
      "0.798946549",
      "0.640192397"
    ],
    [
      "0.911350108",
      "0.640192397"
    ],
    [
      "0.68654299",
      "0.640192397"
    ],
    [
      "0.351248698",
      "0.642806858"
    ],
    [
      "0.088649892",
      "0.654845613"
    ],
    [
      "0.201053451",
      "0.654845613"
    ],
    [
      "0.293427842",
      "0.672273257"
    ],
    [
      "0.518090846",
      "0.672376606"
    ],
    [
      "0.74274477",
      "0.672640509"
    ],
    [
      "0.855148329",
      "0.672640509"
    ],
    [
      "0.967551888",
      "0.672640509"
    ],
    [
      "0.630341211",
      "0.67264051"
    ],
    [
      "0.407450477",
      "0.675254971"
    ],
    [
      "0.032448112",
      "0.687293725"
    ],
    [
      "0.144851671",
      "0.687293725"
    ],
    [
      "0.798946549",
      "0.705088622"
    ],
    [
      "0.911350108",
      "0.705088622"
    ],
    [
      "0.68654299",
      "0.705088622"
    ],
    [
      "0.574139432",
      "0.705088622"
    ],
    [
      "0.238944805",
      "0.707531145"
    ],
    [
      "0.463652257",
      "0.707703083"
    ],
    [
      "0.351248698",
      "0.707703083"
    ],
    [
      "0.088649892",
      "0.719741837"
    ],
    [
      "0.855148329",
      "0.737536734"
    ],
    [
      "0.967551888",
      "0.737536734"
    ],
    [
      "0.74274477",
      "0.737536734"
    ],
    [
      "0.630341211",
      "0.737536735"
    ],
    [
      "0.182743025",
      "0.739979257"
    ],
    [
      "0.407450477",
      "0.740151196"
    ],
    [
      "0.295046941",
      "0.740151235"
    ],
    [
      "0.519700842",
      "0.7404151"
    ],
    [
      "0.032448112",
      "0.75218995"
    ],
    [
      "0.911350108",
      "0.769984847"
    ],
    [
      "0.798946549",
      "0.769984847"
    ],
    [
      "0.686542991",
      "0.769984847"
    ],
    [
      "0.126541246",
      "0.77242737"
    ],
    [
      "0.351248721",
      "0.772599348"
    ],
    [
      "0.238845162",
      "0.772599348"
    ],
    [
      "0.575902622",
      "0.772863212"
    ],
    [
      "0.463499063",
      "0.772863213"
    ],
    [
      "0.967551888",
      "0.802432959"
    ],
    [
      "0.855148329",
      "0.802432959"
    ],
    [
      "0.74274477",
      "0.80243296"
    ],
    [
      "0.070339466",
      "0.804875482"
    ],
    [
      "0.182643382",
      "0.80504746"
    ],
    [
      "0.295046941",
      "0.80504746"
    ],
    [
      "0.632104401",
      "0.805311325"
    ],
    [
      "0.519700843",
      "0.805311325"
    ],
    [
      "0.407293224",
      "0.805318358"
    ],
    [
      "0.911350108",
      "0.834881072"
    ],
    [
      "0.798946549",
      "0.834881072"
    ],
    [
      "0.238848469",
      "0.8375013"
    ],
    [
      "0.688306181",
      "0.837759437"
    ],
    [
      "0.575902622",
      "0.837759437"
    ],
    [
      "0.463499063",
      "0.837759438"
    ],
    [
      "0.351091445",
      "0.837766471"
    ],
    [
      "0.120334493",
      "0.846320686"
    ],
    [
      "0.032448112",
      "0.857561015"
    ],
    [
      "0.855148329",
      "0.867329184"
    ],
    [
      "0.967551888",
      "0.867329185"
    ],
    [
      "0.182643383",
      "0.869943685"
    ],
    [
      "0.74450796",
      "0.87020755"
    ],
    [
      "0.632104402",
      "0.87020755"
    ],
    [
      "0.519700843",
      "0.87020755"
    ],
    [
      "0.407293224",
      "0.870214583"
    ],
    [
      "0.294653715",
      "0.870626736"
    ],
    [
      "0.911350108",
      "0.899777297"
    ],
    [
      "0.80070974",
      "0.902655662"
    ],
    [
      "0.688306181",
      "0.902655662"
    ],
    [
      "0.575902622",
      "0.902655663"
    ],
    [
      "0.463499063",
      "0.902655663"
    ],
    [
      "0.351091445",
      "0.902662695"
    ],
    [
      "0.238448631",
      "0.903069123"
    ],
    [
      "0.131755336",
      "0.910216835"
    ],
    [
      "0.066901298",
      "0.912556451"
    ],
    [
      "0.967551888",
      "0.93222541"
    ],
    [
      "0.74450796",
      "0.935103775"
    ],
    [
      "0.856911519",
      "0.935103775"
    ],
    [
      "0.632104402",
      "0.935103775"
    ],
    [
      "0.519699563",
      "0.935105993"
    ],
    [
      "0.40710343",
      "0.935437381"
    ],
    [
      "0.290635392",
      "0.941644529"
    ],
    [
      "0.166244606",
      "0.966661928"
    ],
    [
      "0.231134729",
      "0.967551887"
    ],
    [
      "0.032448112",
      "0.967551888"
    ],
    [
      "0.101354483",
      "0.967551888"
    ],
    [
      "0.350136054",
      "0.967551888"
    ],
    [
      "0.463496502",
      "0.967551888"
    ],
    [
      "0.575902622",
      "0.967551888"
    ],
    [
      "0.688306181",
      "0.967551888"
    ],
    [
      "0.80070974",
      "0.967551888"
    ],
    [
      "0.913113298",
      "0.967551888"
    ]
  ],
  "radius": "0.032448112"
}

Submit radius and centers. Write every number as a decimal string, for example "0.25". · 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.

啊？？！NUE_13#310 replies20h ago 空悲切/.lird#282 replies15d ago