P01 · Packing and covering · Classic · Hard

Equal-circle packing in a unit square · n = 273

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 = 273

ObjectiveMaximize common radius

Record comparison

common radius · Higher is better

Record	Value / interval	Author / holder	Source
External best known	[0.0316405345635, 0.0316405345645]	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

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273

0x1

VERIFIED CONSTRUCTIONr = 0.031640534

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": [
    [
      "0.114065032",
      "0.031640535"
    ],
    [
      "0.177346101",
      "0.031640535"
    ],
    [
      "0.24062717",
      "0.031640535"
    ],
    [
      "0.30390824",
      "0.031640535"
    ],
    [
      "0.367189309",
      "0.031640535"
    ],
    [
      "0.430470378",
      "0.031640535"
    ],
    [
      "0.493751447",
      "0.031640535"
    ],
    [
      "0.557032516",
      "0.031640535"
    ],
    [
      "0.620313585",
      "0.031640535"
    ],
    [
      "0.683594654",
      "0.031640535"
    ],
    [
      "0.746875723",
      "0.031640535"
    ],
    [
      "0.810156793",
      "0.031640535"
    ],
    [
      "0.873437862",
      "0.031640535"
    ],
    [
      "0.936718931",
      "0.031640535"
    ],
    [
      "0.039369703",
      "0.032823912"
    ],
    [
      "0.082424498",
      "0.086443548"
    ],
    [
      "0.145705567",
      "0.086443548"
    ],
    [
      "0.208986636",
      "0.086443548"
    ],
    [
      "0.272267705",
      "0.086443548"
    ],
    [
      "0.335548774",
      "0.086443548"
    ],
    [
      "0.398829843",
      "0.086443548"
    ],
    [
      "0.462110912",
      "0.086443548"
    ],
    [
      "0.525391982",
      "0.086443548"
    ],
    [
      "0.588673051",
      "0.086443548"
    ],
    [
      "0.65195412",
      "0.086443548"
    ],
    [
      "0.715235189",
      "0.086443548"
    ],
    [
      "0.778516258",
      "0.086443548"
    ],
    [
      "0.841797327",
      "0.086443548"
    ],
    [
      "0.905078396",
      "0.086443548"
    ],
    [
      "0.968359465",
      "0.086443548"
    ],
    [
      "0.031640535",
      "0.124199115"
    ],
    [
      "0.177346101",
      "0.141246561"
    ],
    [
      "0.24062717",
      "0.141246561"
    ],
    [
      "0.30390824",
      "0.141246561"
    ],
    [
      "0.367189309",
      "0.141246561"
    ],
    [
      "0.430470378",
      "0.141246561"
    ],
    [
      "0.493751447",
      "0.141246561"
    ],
    [
      "0.557032516",
      "0.141246561"
    ],
    [
      "0.620313585",
      "0.141246561"
    ],
    [
      "0.683594654",
      "0.141246561"
    ],
    [
      "0.746875723",
      "0.141246561"
    ],
    [
      "0.810156793",
      "0.141246561"
    ],
    [
      "0.873437862",
      "0.141246561"
    ],
    [
      "0.936718931",
      "0.141246561"
    ],
    [
      "0.0910067",
      "0.150327748"
    ],
    [
      "0.031640535",
      "0.187480184"
    ],
    [
      "0.145705567",
      "0.196049575"
    ],
    [
      "0.208986636",
      "0.196049575"
    ],
    [
      "0.272267705",
      "0.196049575"
    ],
    [
      "0.335548774",
      "0.196049575"
    ],
    [
      "0.398829843",
      "0.196049575"
    ],
    [
      "0.462110912",
      "0.196049575"
    ],
    [
      "0.525391982",
      "0.196049575"
    ],
    [
      "0.588673051",
      "0.196049575"
    ],
    [
      "0.65195412",
      "0.196049575"
    ],
    [
      "0.715235189",
      "0.196049575"
    ],
    [
      "0.778516258",
      "0.196049575"
    ],
    [
      "0.841797327",
      "0.196049575"
    ],
    [
      "0.905078396",
      "0.196049575"
    ],
    [
      "0.968359465",
      "0.196049575"
    ],
    [
      "0.086644183",
      "0.218770636"
    ],
    [
      "0.031640535",
      "0.250761253"
    ],
    [
      "0.177346101",
      "0.250852588"
    ],
    [
      "0.24062717",
      "0.250852588"
    ],
    [
      "0.30390824",
      "0.250852588"
    ],
    [
      "0.367189309",
      "0.250852588"
    ],
    [
      "0.430470378",
      "0.250852588"
    ],
    [
      "0.493751447",
      "0.250852588"
    ],
    [
      "0.557032516",
      "0.250852588"
    ],
    [
      "0.620313585",
      "0.250852588"
    ],
    [
      "0.683594654",
      "0.250852588"
    ],
    [
      "0.746875723",
      "0.250852588"
    ],
    [
      "0.810156793",
      "0.250852588"
    ],
    [
      "0.873437862",
      "0.250852588"
    ],
    [
      "0.936718931",
      "0.250852588"
    ],
    [
      "0.086991815",
      "0.28205075"
    ],
    [
      "0.145705567",
      "0.305655602"
    ],
    [
      "0.208986636",
      "0.305655602"
    ],
    [
      "0.272267705",
      "0.305655602"
    ],
    [
      "0.335548774",
      "0.305655602"
    ],
    [
      "0.398829843",
      "0.305655602"
    ],
    [
      "0.462110912",
      "0.305655602"
    ],
    [
      "0.525391982",
      "0.305655602"
    ],
    [
      "0.588673051",
      "0.305655602"
    ],
    [
      "0.65195412",
      "0.305655602"
    ],
    [
      "0.715235189",
      "0.305655602"
    ],
    [
      "0.778516258",
      "0.305655602"
    ],
    [
      "0.841797327",
      "0.305655602"
    ],
    [
      "0.905078396",
      "0.305655602"
    ],
    [
      "0.968359465",
      "0.305655602"
    ],
    [
      "0.032390374",
      "0.314037879"
    ],
    [
      "0.090267376",
      "0.346209373"
    ],
    [
      "0.177346101",
      "0.360458615"
    ],
    [
      "0.24062717",
      "0.360458615"
    ],
    [
      "0.30390824",
      "0.360458615"
    ],
    [
      "0.367189309",
      "0.360458615"
    ],
    [
      "0.430470378",
      "0.360458615"
    ],
    [
      "0.493751447",
      "0.360458615"
    ],
    [
      "0.557032516",
      "0.360458615"
    ],
    [
      "0.620313585",
      "0.360458615"
    ],
    [
      "0.683594654",
      "0.360458615"
    ],
    [
      "0.746875723",
      "0.360458615"
    ],
    [
      "0.810156793",
      "0.360458615"
    ],
    [
      "0.873437862",
      "0.360458615"
    ],
    [
      "0.936718931",
      "0.360458615"
    ],
    [
      "0.031640535",
      "0.377314506"
    ],
    [
      "0.082424789",
      "0.415069681"
    ],
    [
      "0.145705567",
      "0.415261629"
    ],
    [
      "0.208986636",
      "0.415261629"
    ],
    [
      "0.272267705",
      "0.415261629"
    ],
    [
      "0.335548774",
      "0.415261629"
    ],
    [
      "0.398829843",
      "0.415261629"
    ],
    [
      "0.462110912",
      "0.415261629"
    ],
    [
      "0.525391982",
      "0.415261629"
    ],
    [
      "0.588673051",
      "0.415261629"
    ],
    [
      "0.65195412",
      "0.415261629"
    ],
    [
      "0.715235189",
      "0.415261629"
    ],
    [
      "0.778516258",
      "0.415261629"
    ],
    [
      "0.841797327",
      "0.415261629"
    ],
    [
      "0.905078396",
      "0.415261629"
    ],
    [
      "0.968359465",
      "0.415261629"
    ],
    [
      "0.031640535",
      "0.452824856"
    ],
    [
      "0.177346101",
      "0.470064642"
    ],
    [
      "0.24062717",
      "0.470064642"
    ],
    [
      "0.30390824",
      "0.470064642"
    ],
    [
      "0.367189309",
      "0.470064642"
    ],
    [
      "0.430470378",
      "0.470064642"
    ],
    [
      "0.493751447",
      "0.470064642"
    ],
    [
      "0.557032516",
      "0.470064642"
    ],
    [
      "0.620313585",
      "0.470064642"
    ],
    [
      "0.683594654",
      "0.470064642"
    ],
    [
      "0.746875723",
      "0.470064642"
    ],
    [
      "0.810156793",
      "0.470064642"
    ],
    [
      "0.873437862",
      "0.470064642"
    ],
    [
      "0.936718931",
      "0.470064642"
    ],
    [
      "0.091461986",
      "0.477903464"
    ],
    [
      "0.031640535",
      "0.516105925"
    ],
    [
      "0.145705567",
      "0.524867656"
    ],
    [
      "0.208986636",
      "0.524867656"
    ],
    [
      "0.272267705",
      "0.524867656"
    ],
    [
      "0.335548774",
      "0.524867656"
    ],
    [
      "0.398829843",
      "0.524867656"
    ],
    [
      "0.462110912",
      "0.524867656"
    ],
    [
      "0.525391982",
      "0.524867656"
    ],
    [
      "0.588673051",
      "0.524867656"
    ],
    [
      "0.65195412",
      "0.524867656"
    ],
    [
      "0.715235189",
      "0.524867656"
    ],
    [
      "0.778516258",
      "0.524867656"
    ],
    [
      "0.841797327",
      "0.524867656"
    ],
    [
      "0.905078396",
      "0.524867656"
    ],
    [
      "0.968359465",
      "0.524867656"
    ],
    [
      "0.086600088",
      "0.547473762"
    ],
    [
      "0.031640535",
      "0.579386994"
    ],
    [
      "0.24062717",
      "0.579670669"
    ],
    [
      "0.30390824",
      "0.579670669"
    ],
    [
      "0.367189309",
      "0.579670669"
    ],
    [
      "0.430470378",
      "0.579670669"
    ],
    [
      "0.493751447",
      "0.579670669"
    ],
    [
      "0.557032516",
      "0.579670669"
    ],
    [
      "0.620313585",
      "0.579670669"
    ],
    [
      "0.683594654",
      "0.579670669"
    ],
    [
      "0.746875723",
      "0.579670669"
    ],
    [
      "0.810156793",
      "0.579670669"
    ],
    [
      "0.873437862",
      "0.579670669"
    ],
    [
      "0.936718931",
      "0.579670669"
    ],
    [
      "0.177343311",
      "0.57967228"
    ],
    [
      "0.087043048",
      "0.610753281"
    ],
    [
      "0.208986636",
      "0.634473682"
    ],
    [
      "0.272267705",
      "0.634473682"
    ],
    [
      "0.335548774",
      "0.634473682"
    ],
    [
      "0.398829843",
      "0.634473682"
    ],
    [
      "0.525391982",
      "0.634473682"
    ],
    [
      "0.588673051",
      "0.634473682"
    ],
    [
      "0.65195412",
      "0.634473682"
    ],
    [
      "0.715235189",
      "0.634473682"
    ],
    [
      "0.778516258",
      "0.634473682"
    ],
    [
      "0.841797327",
      "0.634473682"
    ],
    [
      "0.905078396",
      "0.634473682"
    ],
    [
      "0.968359465",
      "0.634473682"
    ],
    [
      "0.462110912",
      "0.634473682"
    ],
    [
      "0.145705568",
      "0.634485168"
    ],
    [
      "0.032396651",
      "0.642663546"
    ],
    [
      "0.088182897",
      "0.674147118"
    ],
    [
      "0.746875723",
      "0.689276696"
    ],
    [
      "0.810156793",
      "0.689276696"
    ],
    [
      "0.873437862",
      "0.689276696"
    ],
    [
      "0.936718931",
      "0.689276696"
    ],
    [
      "0.493751447",
      "0.689276696"
    ],
    [
      "0.557032516",
      "0.689276696"
    ],
    [
      "0.620313585",
      "0.689276696"
    ],
    [
      "0.177356049",
      "0.689282438"
    ],
    [
      "0.240637118",
      "0.689282438"
    ],
    [
      "0.303918187",
      "0.689282438"
    ],
    [
      "0.367199256",
      "0.689282438"
    ],
    [
      "0.683594697",
      "0.689447687"
    ],
    [
      "0.430475388",
      "0.690072956"
    ],
    [
      "0.031640535",
      "0.705940097"
    ],
    [
      "0.083428128",
      "0.742306825"
    ],
    [
      "0.968359465",
      "0.744079709"
    ],
    [
      "0.715613616",
      "0.744296459"
    ],
    [
      "0.778894685",
      "0.744296459"
    ],
    [
      "0.842175754",
      "0.744296459"
    ],
    [
      "0.462802999",
      "0.744473501"
    ],
    [
      "0.526084068",
      "0.744473501"
    ],
    [
      "0.589365137",
      "0.744473501"
    ],
    [
      "0.146666768",
      "0.744623758"
    ],
    [
      "0.209947837",
      "0.744623758"
    ],
    [
      "0.273228906",
      "0.744623758"
    ],
    [
      "0.336509975",
      "0.744623758"
    ],
    [
      "0.399661393",
      "0.748672472"
    ],
    [
      "0.652495619",
      "0.748836525"
    ],
    [
      "0.905276007",
      "0.749076809"
    ],
    [
      "0.031640535",
      "0.778673552"
    ],
    [
      "0.747214845",
      "0.799122147"
    ],
    [
      "0.810495914",
      "0.799122147"
    ],
    [
      "0.494404228",
      "0.799299188"
    ],
    [
      "0.557685297",
      "0.799299188"
    ],
    [
      "0.178267997",
      "0.799449446"
    ],
    [
      "0.241549066",
      "0.799449446"
    ],
    [
      "0.304830135",
      "0.799449446"
    ],
    [
      "0.941145351",
      "0.801210137"
    ],
    [
      "0.367981553",
      "0.80349816"
    ],
    [
      "0.431262622",
      "0.80349816"
    ],
    [
      "0.620815779",
      "0.803662212"
    ],
    [
      "0.684096848",
      "0.803662212"
    ],
    [
      "0.873599447",
      "0.803859007"
    ],
    [
      "0.09485246",
      "0.804683994"
    ],
    [
      "0.031640535",
      "0.841954621"
    ],
    [
      "0.778695024",
      "0.854017429"
    ],
    [
      "0.525884407",
      "0.854194471"
    ],
    [
      "0.146711491",
      "0.854300887"
    ],
    [
      "0.273029245",
      "0.854344728"
    ],
    [
      "0.209869004",
      "0.858253388"
    ],
    [
      "0.968359465",
      "0.858340564"
    ],
    [
      "0.336180663",
      "0.858393442"
    ],
    [
      "0.399461732",
      "0.858393442"
    ],
    [
      "0.462742802",
      "0.858393442"
    ],
    [
      "0.589014889",
      "0.858557495"
    ],
    [
      "0.652295958",
      "0.858557495"
    ],
    [
      "0.715577027",
      "0.858557495"
    ],
    [
      "0.841798679",
      "0.858752658"
    ],
    [
      "0.905079748",
      "0.858754219"
    ],
    [
      "0.086443548",
      "0.873595156"
    ],
    [
      "0.031640535",
      "0.90523569"
    ],
    [
      "0.177075468",
      "0.913105739"
    ],
    [
      "0.303908371",
      "0.913236142"
    ],
    [
      "0.557032959",
      "0.913244044"
    ],
    [
      "0.937005677",
      "0.913391467"
    ],
    [
      "0.810156793",
      "0.913554892"
    ],
    [
      "0.24062717",
      "0.913556452"
    ],
    [
      "0.367189309",
      "0.913556452"
    ],
    [
      "0.430470378",
      "0.913556452"
    ],
    [
      "0.493751447",
      "0.913556452"
    ],
    [
      "0.620313585",
      "0.913556452"
    ],
    [
      "0.683594654",
      "0.913556452"
    ],
    [
      "0.746875723",
      "0.913556452"
    ],
    [
      "0.873437862",
      "0.913556452"
    ],
    [
      "0.090902553",
      "0.936718931"
    ],
    [
      "0.968359465",
      "0.968359038"
    ],
    [
      "0.03609954",
      "0.968359465"
    ],
    [
      "0.145705567",
      "0.968359465"
    ],
    [
      "0.208986636",
      "0.968359465"
    ],
    [
      "0.272267705",
      "0.968359465"
    ],
    [
      "0.335548774",
      "0.968359465"
    ],
    [
      "0.398829843",
      "0.968359465"
    ],
    [
      "0.462110912",
      "0.968359465"
    ],
    [
      "0.525391982",
      "0.968359465"
    ],
    [
      "0.588673051",
      "0.968359465"
    ],
    [
      "0.65195412",
      "0.968359465"
    ],
    [
      "0.715235189",
      "0.968359465"
    ],
    [
      "0.778516258",
      "0.968359465"
    ],
    [
      "0.841797327",
      "0.968359465"
    ],
    [
      "0.905078396",
      "0.968359465"
    ]
  ],
  "radius": "0.031640534"
}

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

Instance parameters

{
  "n": 273
}

Starter answer

{
  "centers": [
    [
      "0.114065032",
      "0.031640535"
    ],
    [
      "0.177346101",
      "0.031640535"
    ],
    [
      "0.24062717",
      "0.031640535"
    ],
    [
      "0.30390824",
      "0.031640535"
    ],
    [
      "0.367189309",
      "0.031640535"
    ],
    [
      "0.430470378",
      "0.031640535"
    ],
    [
      "0.493751447",
      "0.031640535"
    ],
    [
      "0.557032516",
      "0.031640535"
    ],
    [
      "0.620313585",
      "0.031640535"
    ],
    [
      "0.683594654",
      "0.031640535"
    ],
    [
      "0.746875723",
      "0.031640535"
    ],
    [
      "0.810156793",
      "0.031640535"
    ],
    [
      "0.873437862",
      "0.031640535"
    ],
    [
      "0.936718931",
      "0.031640535"
    ],
    [
      "0.039369703",
      "0.032823912"
    ],
    [
      "0.082424498",
      "0.086443548"
    ],
    [
      "0.145705567",
      "0.086443548"
    ],
    [
      "0.208986636",
      "0.086443548"
    ],
    [
      "0.272267705",
      "0.086443548"
    ],
    [
      "0.335548774",
      "0.086443548"
    ],
    [
      "0.398829843",
      "0.086443548"
    ],
    [
      "0.462110912",
      "0.086443548"
    ],
    [
      "0.525391982",
      "0.086443548"
    ],
    [
      "0.588673051",
      "0.086443548"
    ],
    [
      "0.65195412",
      "0.086443548"
    ],
    [
      "0.715235189",
      "0.086443548"
    ],
    [
      "0.778516258",
      "0.086443548"
    ],
    [
      "0.841797327",
      "0.086443548"
    ],
    [
      "0.905078396",
      "0.086443548"
    ],
    [
      "0.968359465",
      "0.086443548"
    ],
    [
      "0.031640535",
      "0.124199115"
    ],
    [
      "0.177346101",
      "0.141246561"
    ],
    [
      "0.24062717",
      "0.141246561"
    ],
    [
      "0.30390824",
      "0.141246561"
    ],
    [
      "0.367189309",
      "0.141246561"
    ],
    [
      "0.430470378",
      "0.141246561"
    ],
    [
      "0.493751447",
      "0.141246561"
    ],
    [
      "0.557032516",
      "0.141246561"
    ],
    [
      "0.620313585",
      "0.141246561"
    ],
    [
      "0.683594654",
      "0.141246561"
    ],
    [
      "0.746875723",
      "0.141246561"
    ],
    [
      "0.810156793",
      "0.141246561"
    ],
    [
      "0.873437862",
      "0.141246561"
    ],
    [
      "0.936718931",
      "0.141246561"
    ],
    [
      "0.0910067",
      "0.150327748"
    ],
    [
      "0.031640535",
      "0.187480184"
    ],
    [
      "0.145705567",
      "0.196049575"
    ],
    [
      "0.208986636",
      "0.196049575"
    ],
    [
      "0.272267705",
      "0.196049575"
    ],
    [
      "0.335548774",
      "0.196049575"
    ],
    [
      "0.398829843",
      "0.196049575"
    ],
    [
      "0.462110912",
      "0.196049575"
    ],
    [
      "0.525391982",
      "0.196049575"
    ],
    [
      "0.588673051",
      "0.196049575"
    ],
    [
      "0.65195412",
      "0.196049575"
    ],
    [
      "0.715235189",
      "0.196049575"
    ],
    [
      "0.778516258",
      "0.196049575"
    ],
    [
      "0.841797327",
      "0.196049575"
    ],
    [
      "0.905078396",
      "0.196049575"
    ],
    [
      "0.968359465",
      "0.196049575"
    ],
    [
      "0.086644183",
      "0.218770636"
    ],
    [
      "0.031640535",
      "0.250761253"
    ],
    [
      "0.177346101",
      "0.250852588"
    ],
    [
      "0.24062717",
      "0.250852588"
    ],
    [
      "0.30390824",
      "0.250852588"
    ],
    [
      "0.367189309",
      "0.250852588"
    ],
    [
      "0.430470378",
      "0.250852588"
    ],
    [
      "0.493751447",
      "0.250852588"
    ],
    [
      "0.557032516",
      "0.250852588"
    ],
    [
      "0.620313585",
      "0.250852588"
    ],
    [
      "0.683594654",
      "0.250852588"
    ],
    [
      "0.746875723",
      "0.250852588"
    ],
    [
      "0.810156793",
      "0.250852588"
    ],
    [
      "0.873437862",
      "0.250852588"
    ],
    [
      "0.936718931",
      "0.250852588"
    ],
    [
      "0.086991815",
      "0.28205075"
    ],
    [
      "0.145705567",
      "0.305655602"
    ],
    [
      "0.208986636",
      "0.305655602"
    ],
    [
      "0.272267705",
      "0.305655602"
    ],
    [
      "0.335548774",
      "0.305655602"
    ],
    [
      "0.398829843",
      "0.305655602"
    ],
    [
      "0.462110912",
      "0.305655602"
    ],
    [
      "0.525391982",
      "0.305655602"
    ],
    [
      "0.588673051",
      "0.305655602"
    ],
    [
      "0.65195412",
      "0.305655602"
    ],
    [
      "0.715235189",
      "0.305655602"
    ],
    [
      "0.778516258",
      "0.305655602"
    ],
    [
      "0.841797327",
      "0.305655602"
    ],
    [
      "0.905078396",
      "0.305655602"
    ],
    [
      "0.968359465",
      "0.305655602"
    ],
    [
      "0.032390374",
      "0.314037879"
    ],
    [
      "0.090267376",
      "0.346209373"
    ],
    [
      "0.177346101",
      "0.360458615"
    ],
    [
      "0.24062717",
      "0.360458615"
    ],
    [
      "0.30390824",
      "0.360458615"
    ],
    [
      "0.367189309",
      "0.360458615"
    ],
    [
      "0.430470378",
      "0.360458615"
    ],
    [
      "0.493751447",
      "0.360458615"
    ],
    [
      "0.557032516",
      "0.360458615"
    ],
    [
      "0.620313585",
      "0.360458615"
    ],
    [
      "0.683594654",
      "0.360458615"
    ],
    [
      "0.746875723",
      "0.360458615"
    ],
    [
      "0.810156793",
      "0.360458615"
    ],
    [
      "0.873437862",
      "0.360458615"
    ],
    [
      "0.936718931",
      "0.360458615"
    ],
    [
      "0.031640535",
      "0.377314506"
    ],
    [
      "0.082424789",
      "0.415069681"
    ],
    [
      "0.145705567",
      "0.415261629"
    ],
    [
      "0.208986636",
      "0.415261629"
    ],
    [
      "0.272267705",
      "0.415261629"
    ],
    [
      "0.335548774",
      "0.415261629"
    ],
    [
      "0.398829843",
      "0.415261629"
    ],
    [
      "0.462110912",
      "0.415261629"
    ],
    [
      "0.525391982",
      "0.415261629"
    ],
    [
      "0.588673051",
      "0.415261629"
    ],
    [
      "0.65195412",
      "0.415261629"
    ],
    [
      "0.715235189",
      "0.415261629"
    ],
    [
      "0.778516258",
      "0.415261629"
    ],
    [
      "0.841797327",
      "0.415261629"
    ],
    [
      "0.905078396",
      "0.415261629"
    ],
    [
      "0.968359465",
      "0.415261629"
    ],
    [
      "0.031640535",
      "0.452824856"
    ],
    [
      "0.177346101",
      "0.470064642"
    ],
    [
      "0.24062717",
      "0.470064642"
    ],
    [
      "0.30390824",
      "0.470064642"
    ],
    [
      "0.367189309",
      "0.470064642"
    ],
    [
      "0.430470378",
      "0.470064642"
    ],
    [
      "0.493751447",
      "0.470064642"
    ],
    [
      "0.557032516",
      "0.470064642"
    ],
    [
      "0.620313585",
      "0.470064642"
    ],
    [
      "0.683594654",
      "0.470064642"
    ],
    [
      "0.746875723",
      "0.470064642"
    ],
    [
      "0.810156793",
      "0.470064642"
    ],
    [
      "0.873437862",
      "0.470064642"
    ],
    [
      "0.936718931",
      "0.470064642"
    ],
    [
      "0.091461986",
      "0.477903464"
    ],
    [
      "0.031640535",
      "0.516105925"
    ],
    [
      "0.145705567",
      "0.524867656"
    ],
    [
      "0.208986636",
      "0.524867656"
    ],
    [
      "0.272267705",
      "0.524867656"
    ],
    [
      "0.335548774",
      "0.524867656"
    ],
    [
      "0.398829843",
      "0.524867656"
    ],
    [
      "0.462110912",
      "0.524867656"
    ],
    [
      "0.525391982",
      "0.524867656"
    ],
    [
      "0.588673051",
      "0.524867656"
    ],
    [
      "0.65195412",
      "0.524867656"
    ],
    [
      "0.715235189",
      "0.524867656"
    ],
    [
      "0.778516258",
      "0.524867656"
    ],
    [
      "0.841797327",
      "0.524867656"
    ],
    [
      "0.905078396",
      "0.524867656"
    ],
    [
      "0.968359465",
      "0.524867656"
    ],
    [
      "0.086600088",
      "0.547473762"
    ],
    [
      "0.031640535",
      "0.579386994"
    ],
    [
      "0.24062717",
      "0.579670669"
    ],
    [
      "0.30390824",
      "0.579670669"
    ],
    [
      "0.367189309",
      "0.579670669"
    ],
    [
      "0.430470378",
      "0.579670669"
    ],
    [
      "0.493751447",
      "0.579670669"
    ],
    [
      "0.557032516",
      "0.579670669"
    ],
    [
      "0.620313585",
      "0.579670669"
    ],
    [
      "0.683594654",
      "0.579670669"
    ],
    [
      "0.746875723",
      "0.579670669"
    ],
    [
      "0.810156793",
      "0.579670669"
    ],
    [
      "0.873437862",
      "0.579670669"
    ],
    [
      "0.936718931",
      "0.579670669"
    ],
    [
      "0.177343311",
      "0.57967228"
    ],
    [
      "0.087043048",
      "0.610753281"
    ],
    [
      "0.208986636",
      "0.634473682"
    ],
    [
      "0.272267705",
      "0.634473682"
    ],
    [
      "0.335548774",
      "0.634473682"
    ],
    [
      "0.398829843",
      "0.634473682"
    ],
    [
      "0.525391982",
      "0.634473682"
    ],
    [
      "0.588673051",
      "0.634473682"
    ],
    [
      "0.65195412",
      "0.634473682"
    ],
    [
      "0.715235189",
      "0.634473682"
    ],
    [
      "0.778516258",
      "0.634473682"
    ],
    [
      "0.841797327",
      "0.634473682"
    ],
    [
      "0.905078396",
      "0.634473682"
    ],
    [
      "0.968359465",
      "0.634473682"
    ],
    [
      "0.462110912",
      "0.634473682"
    ],
    [
      "0.145705568",
      "0.634485168"
    ],
    [
      "0.032396651",
      "0.642663546"
    ],
    [
      "0.088182897",
      "0.674147118"
    ],
    [
      "0.746875723",
      "0.689276696"
    ],
    [
      "0.810156793",
      "0.689276696"
    ],
    [
      "0.873437862",
      "0.689276696"
    ],
    [
      "0.936718931",
      "0.689276696"
    ],
    [
      "0.493751447",
      "0.689276696"
    ],
    [
      "0.557032516",
      "0.689276696"
    ],
    [
      "0.620313585",
      "0.689276696"
    ],
    [
      "0.177356049",
      "0.689282438"
    ],
    [
      "0.240637118",
      "0.689282438"
    ],
    [
      "0.303918187",
      "0.689282438"
    ],
    [
      "0.367199256",
      "0.689282438"
    ],
    [
      "0.683594697",
      "0.689447687"
    ],
    [
      "0.430475388",
      "0.690072956"
    ],
    [
      "0.031640535",
      "0.705940097"
    ],
    [
      "0.083428128",
      "0.742306825"
    ],
    [
      "0.968359465",
      "0.744079709"
    ],
    [
      "0.715613616",
      "0.744296459"
    ],
    [
      "0.778894685",
      "0.744296459"
    ],
    [
      "0.842175754",
      "0.744296459"
    ],
    [
      "0.462802999",
      "0.744473501"
    ],
    [
      "0.526084068",
      "0.744473501"
    ],
    [
      "0.589365137",
      "0.744473501"
    ],
    [
      "0.146666768",
      "0.744623758"
    ],
    [
      "0.209947837",
      "0.744623758"
    ],
    [
      "0.273228906",
      "0.744623758"
    ],
    [
      "0.336509975",
      "0.744623758"
    ],
    [
      "0.399661393",
      "0.748672472"
    ],
    [
      "0.652495619",
      "0.748836525"
    ],
    [
      "0.905276007",
      "0.749076809"
    ],
    [
      "0.031640535",
      "0.778673552"
    ],
    [
      "0.747214845",
      "0.799122147"
    ],
    [
      "0.810495914",
      "0.799122147"
    ],
    [
      "0.494404228",
      "0.799299188"
    ],
    [
      "0.557685297",
      "0.799299188"
    ],
    [
      "0.178267997",
      "0.799449446"
    ],
    [
      "0.241549066",
      "0.799449446"
    ],
    [
      "0.304830135",
      "0.799449446"
    ],
    [
      "0.941145351",
      "0.801210137"
    ],
    [
      "0.367981553",
      "0.80349816"
    ],
    [
      "0.431262622",
      "0.80349816"
    ],
    [
      "0.620815779",
      "0.803662212"
    ],
    [
      "0.684096848",
      "0.803662212"
    ],
    [
      "0.873599447",
      "0.803859007"
    ],
    [
      "0.09485246",
      "0.804683994"
    ],
    [
      "0.031640535",
      "0.841954621"
    ],
    [
      "0.778695024",
      "0.854017429"
    ],
    [
      "0.525884407",
      "0.854194471"
    ],
    [
      "0.146711491",
      "0.854300887"
    ],
    [
      "0.273029245",
      "0.854344728"
    ],
    [
      "0.209869004",
      "0.858253388"
    ],
    [
      "0.968359465",
      "0.858340564"
    ],
    [
      "0.336180663",
      "0.858393442"
    ],
    [
      "0.399461732",
      "0.858393442"
    ],
    [
      "0.462742802",
      "0.858393442"
    ],
    [
      "0.589014889",
      "0.858557495"
    ],
    [
      "0.652295958",
      "0.858557495"
    ],
    [
      "0.715577027",
      "0.858557495"
    ],
    [
      "0.841798679",
      "0.858752658"
    ],
    [
      "0.905079748",
      "0.858754219"
    ],
    [
      "0.086443548",
      "0.873595156"
    ],
    [
      "0.031640535",
      "0.90523569"
    ],
    [
      "0.177075468",
      "0.913105739"
    ],
    [
      "0.303908371",
      "0.913236142"
    ],
    [
      "0.557032959",
      "0.913244044"
    ],
    [
      "0.937005677",
      "0.913391467"
    ],
    [
      "0.810156793",
      "0.913554892"
    ],
    [
      "0.24062717",
      "0.913556452"
    ],
    [
      "0.367189309",
      "0.913556452"
    ],
    [
      "0.430470378",
      "0.913556452"
    ],
    [
      "0.493751447",
      "0.913556452"
    ],
    [
      "0.620313585",
      "0.913556452"
    ],
    [
      "0.683594654",
      "0.913556452"
    ],
    [
      "0.746875723",
      "0.913556452"
    ],
    [
      "0.873437862",
      "0.913556452"
    ],
    [
      "0.090902553",
      "0.936718931"
    ],
    [
      "0.968359465",
      "0.968359038"
    ],
    [
      "0.03609954",
      "0.968359465"
    ],
    [
      "0.145705567",
      "0.968359465"
    ],
    [
      "0.208986636",
      "0.968359465"
    ],
    [
      "0.272267705",
      "0.968359465"
    ],
    [
      "0.335548774",
      "0.968359465"
    ],
    [
      "0.398829843",
      "0.968359465"
    ],
    [
      "0.462110912",
      "0.968359465"
    ],
    [
      "0.525391982",
      "0.968359465"
    ],
    [
      "0.588673051",
      "0.968359465"
    ],
    [
      "0.65195412",
      "0.968359465"
    ],
    [
      "0.715235189",
      "0.968359465"
    ],
    [
      "0.778516258",
      "0.968359465"
    ],
    [
      "0.841797327",
      "0.968359465"
    ],
    [
      "0.905078396",
      "0.968359465"
    ]
  ],
  "radius": "0.031640534"
}

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