P01 · Packing and covering · Classic · Hard

Equal-circle packing in a unit square · n = 271

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 = 271

ObjectiveMaximize common radius

Record comparison

common radius · Higher is better

Record	Value / interval	Author / holder	Source
External best known	[0.0318089292405, 0.0318089292415]	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

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271

0x1

VERIFIED CONSTRUCTIONr = 0.031808928

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": [
    [
      "0.095817522",
      "0.031808929"
    ],
    [
      "0.15943538",
      "0.031808929"
    ],
    [
      "0.223053239",
      "0.031808929"
    ],
    [
      "0.286671097",
      "0.031808929"
    ],
    [
      "0.350288956",
      "0.031808929"
    ],
    [
      "0.413906814",
      "0.031808929"
    ],
    [
      "0.477524673",
      "0.031808929"
    ],
    [
      "0.541142531",
      "0.031808929"
    ],
    [
      "0.604760389",
      "0.031808929"
    ],
    [
      "0.668378248",
      "0.031808929"
    ],
    [
      "0.731996106",
      "0.031808929"
    ],
    [
      "0.795613965",
      "0.031808929"
    ],
    [
      "0.859231823",
      "0.031808929"
    ],
    [
      "0.0318116",
      "0.031814552"
    ],
    [
      "0.967419679",
      "0.03214828"
    ],
    [
      "0.912407353",
      "0.066731628"
    ],
    [
      "0.064008592",
      "0.086903611"
    ],
    [
      "0.127626451",
      "0.086903611"
    ],
    [
      "0.191244309",
      "0.086903611"
    ],
    [
      "0.254862168",
      "0.086903611"
    ],
    [
      "0.318480026",
      "0.086903611"
    ],
    [
      "0.382097885",
      "0.086903611"
    ],
    [
      "0.445715743",
      "0.086903611"
    ],
    [
      "0.509333602",
      "0.086903611"
    ],
    [
      "0.57295146",
      "0.086903611"
    ],
    [
      "0.636569319",
      "0.086903611"
    ],
    [
      "0.700187177",
      "0.086903611"
    ],
    [
      "0.763805036",
      "0.086903611"
    ],
    [
      "0.832824908",
      "0.089866089"
    ],
    [
      "0.968191071",
      "0.097316082"
    ],
    [
      "0.912407353",
      "0.130349487"
    ],
    [
      "0.031808929",
      "0.141770847"
    ],
    [
      "0.095817522",
      "0.141998292"
    ],
    [
      "0.15943538",
      "0.141998292"
    ],
    [
      "0.223053239",
      "0.141998292"
    ],
    [
      "0.286671097",
      "0.141998292"
    ],
    [
      "0.350288956",
      "0.141998292"
    ],
    [
      "0.413906814",
      "0.141998292"
    ],
    [
      "0.477524673",
      "0.141998292"
    ],
    [
      "0.541142531",
      "0.141998292"
    ],
    [
      "0.604760389",
      "0.141998292"
    ],
    [
      "0.668378248",
      "0.141998292"
    ],
    [
      "0.731996106",
      "0.141998292"
    ],
    [
      "0.795613965",
      "0.141998292"
    ],
    [
      "0.856448025",
      "0.160611434"
    ],
    [
      "0.968191071",
      "0.160933941"
    ],
    [
      "0.910635305",
      "0.193942661"
    ],
    [
      "0.063617858",
      "0.196865529"
    ],
    [
      "0.127626451",
      "0.197092974"
    ],
    [
      "0.191244309",
      "0.197092974"
    ],
    [
      "0.254862168",
      "0.197092974"
    ],
    [
      "0.318480026",
      "0.197092974"
    ],
    [
      "0.382097885",
      "0.197092974"
    ],
    [
      "0.445715743",
      "0.197092974"
    ],
    [
      "0.509333602",
      "0.197092974"
    ],
    [
      "0.57295146",
      "0.197092974"
    ],
    [
      "0.636569319",
      "0.197092974"
    ],
    [
      "0.700187177",
      "0.197092974"
    ],
    [
      "0.763805036",
      "0.197092974"
    ],
    [
      "0.852705009",
      "0.224119086"
    ],
    [
      "0.966419022",
      "0.224527114"
    ],
    [
      "0.031808929",
      "0.25196021"
    ],
    [
      "0.095426788",
      "0.25196021"
    ],
    [
      "0.15943538",
      "0.252187656"
    ],
    [
      "0.223053239",
      "0.252187656"
    ],
    [
      "0.286671097",
      "0.252187656"
    ],
    [
      "0.350288956",
      "0.252187656"
    ],
    [
      "0.413906814",
      "0.252187656"
    ],
    [
      "0.477524673",
      "0.252187656"
    ],
    [
      "0.541142531",
      "0.252187656"
    ],
    [
      "0.604760389",
      "0.252187656"
    ],
    [
      "0.668378248",
      "0.252187656"
    ],
    [
      "0.731996106",
      "0.252187656"
    ],
    [
      "0.795613965",
      "0.252187656"
    ],
    [
      "0.906892288",
      "0.257450312"
    ],
    [
      "0.968191071",
      "0.288120288"
    ],
    [
      "0.846999739",
      "0.289802421"
    ],
    [
      "0.063617858",
      "0.307054892"
    ],
    [
      "0.127235717",
      "0.307054892"
    ],
    [
      "0.191244309",
      "0.307282337"
    ],
    [
      "0.254862168",
      "0.307282337"
    ],
    [
      "0.318480026",
      "0.307282337"
    ],
    [
      "0.382097885",
      "0.307282337"
    ],
    [
      "0.445715743",
      "0.307282337"
    ],
    [
      "0.509333602",
      "0.307282337"
    ],
    [
      "0.57295146",
      "0.307282337"
    ],
    [
      "0.636569319",
      "0.307282337"
    ],
    [
      "0.700187177",
      "0.307282337"
    ],
    [
      "0.763805036",
      "0.307282337"
    ],
    [
      "0.913559302",
      "0.320717862"
    ],
    [
      "0.858464621",
      "0.352526791"
    ],
    [
      "0.968191071",
      "0.353315435"
    ],
    [
      "0.031808929",
      "0.362149573"
    ],
    [
      "0.095426788",
      "0.362149573"
    ],
    [
      "0.159044646",
      "0.362149573"
    ],
    [
      "0.223053239",
      "0.362377019"
    ],
    [
      "0.286671097",
      "0.362377019"
    ],
    [
      "0.350288956",
      "0.362377019"
    ],
    [
      "0.413906814",
      "0.362377019"
    ],
    [
      "0.477524673",
      "0.362377019"
    ],
    [
      "0.541142531",
      "0.362377019"
    ],
    [
      "0.604760389",
      "0.362377019"
    ],
    [
      "0.668378248",
      "0.362377019"
    ],
    [
      "0.731996106",
      "0.362377019"
    ],
    [
      "0.795613965",
      "0.362377019"
    ],
    [
      "0.913096389",
      "0.385124364"
    ],
    [
      "0.968191071",
      "0.416933293"
    ],
    [
      "0.063617858",
      "0.417244255"
    ],
    [
      "0.127235717",
      "0.417244255"
    ],
    [
      "0.190853575",
      "0.417244255"
    ],
    [
      "0.254862168",
      "0.4174717"
    ],
    [
      "0.318480026",
      "0.4174717"
    ],
    [
      "0.382097885",
      "0.4174717"
    ],
    [
      "0.445715743",
      "0.4174717"
    ],
    [
      "0.509333602",
      "0.4174717"
    ],
    [
      "0.57295146",
      "0.4174717"
    ],
    [
      "0.636569319",
      "0.4174717"
    ],
    [
      "0.700187177",
      "0.4174717"
    ],
    [
      "0.763805036",
      "0.4174717"
    ],
    [
      "0.845266839",
      "0.417520099"
    ],
    [
      "0.913096389",
      "0.448742223"
    ],
    [
      "0.031808929",
      "0.472338937"
    ],
    [
      "0.095426788",
      "0.472338937"
    ],
    [
      "0.159044646",
      "0.472338937"
    ],
    [
      "0.222662505",
      "0.472338937"
    ],
    [
      "0.286671097",
      "0.472566382"
    ],
    [
      "0.350288956",
      "0.472566382"
    ],
    [
      "0.413906814",
      "0.472566382"
    ],
    [
      "0.477524673",
      "0.472566382"
    ],
    [
      "0.541142531",
      "0.472566382"
    ],
    [
      "0.604760389",
      "0.472566382"
    ],
    [
      "0.668378248",
      "0.472566382"
    ],
    [
      "0.731996106",
      "0.472566382"
    ],
    [
      "0.795613965",
      "0.472566382"
    ],
    [
      "0.968191071",
      "0.480551152"
    ],
    [
      "0.858593615",
      "0.481555018"
    ],
    [
      "0.913688297",
      "0.513363947"
    ],
    [
      "0.063617858",
      "0.527433618"
    ],
    [
      "0.127235717",
      "0.527433618"
    ],
    [
      "0.190853575",
      "0.527433618"
    ],
    [
      "0.254471434",
      "0.527433618"
    ],
    [
      "0.318480026",
      "0.527661063"
    ],
    [
      "0.382097885",
      "0.527661063"
    ],
    [
      "0.445715743",
      "0.527661063"
    ],
    [
      "0.509333602",
      "0.527661063"
    ],
    [
      "0.57295146",
      "0.527661063"
    ],
    [
      "0.636569319",
      "0.527661063"
    ],
    [
      "0.700187177",
      "0.527661063"
    ],
    [
      "0.763805036",
      "0.527661063"
    ],
    [
      "0.847552782",
      "0.544270301"
    ],
    [
      "0.968191071",
      "0.546176743"
    ],
    [
      "0.910183796",
      "0.576885207"
    ],
    [
      "0.031808929",
      "0.5825283"
    ],
    [
      "0.095426788",
      "0.5825283"
    ],
    [
      "0.159044646",
      "0.5825283"
    ],
    [
      "0.222662505",
      "0.5825283"
    ],
    [
      "0.286280363",
      "0.5825283"
    ],
    [
      "0.796004699",
      "0.5825283"
    ],
    [
      "0.350288956",
      "0.582755745"
    ],
    [
      "0.413906814",
      "0.582755745"
    ],
    [
      "0.477524673",
      "0.582755745"
    ],
    [
      "0.541142531",
      "0.582755745"
    ],
    [
      "0.604760389",
      "0.582755745"
    ],
    [
      "0.668378248",
      "0.582755745"
    ],
    [
      "0.731996106",
      "0.582755745"
    ],
    [
      "0.854472927",
      "0.607602155"
    ],
    [
      "0.968191071",
      "0.609794601"
    ],
    [
      "0.063617858",
      "0.637622981"
    ],
    [
      "0.127235717",
      "0.637622981"
    ],
    [
      "0.190853575",
      "0.637622981"
    ],
    [
      "0.254471434",
      "0.637622981"
    ],
    [
      "0.318089292",
      "0.637622981"
    ],
    [
      "0.76419577",
      "0.637622981"
    ],
    [
      "0.382097885",
      "0.637850427"
    ],
    [
      "0.445715743",
      "0.637850427"
    ],
    [
      "0.509333602",
      "0.637850427"
    ],
    [
      "0.57295146",
      "0.637850427"
    ],
    [
      "0.636569319",
      "0.637850427"
    ],
    [
      "0.700187177",
      "0.637850427"
    ],
    [
      "0.911585583",
      "0.640487619"
    ],
    [
      "0.855874714",
      "0.671204568"
    ],
    [
      "0.966042676",
      "0.673376173"
    ],
    [
      "0.031808929",
      "0.692717663"
    ],
    [
      "0.095426788",
      "0.692717663"
    ],
    [
      "0.159044646",
      "0.692717663"
    ],
    [
      "0.222662505",
      "0.692717663"
    ],
    [
      "0.286280363",
      "0.692717663"
    ],
    [
      "0.349898222",
      "0.692717663"
    ],
    [
      "0.73238684",
      "0.692717663"
    ],
    [
      "0.796004699",
      "0.692717663"
    ],
    [
      "0.413906814",
      "0.692945108"
    ],
    [
      "0.477524673",
      "0.692945108"
    ],
    [
      "0.541142531",
      "0.692945108"
    ],
    [
      "0.604760389",
      "0.692945108"
    ],
    [
      "0.668378248",
      "0.692945108"
    ],
    [
      "0.910331806",
      "0.704093122"
    ],
    [
      "0.968191071",
      "0.736957745"
    ],
    [
      "0.829895109",
      "0.746595539"
    ],
    [
      "0.063617858",
      "0.747812344"
    ],
    [
      "0.127235717",
      "0.747812344"
    ],
    [
      "0.190853575",
      "0.747812344"
    ],
    [
      "0.254471434",
      "0.747812344"
    ],
    [
      "0.318089292",
      "0.747812344"
    ],
    [
      "0.381707151",
      "0.747812344"
    ],
    [
      "0.700577911",
      "0.747812344"
    ],
    [
      "0.76419577",
      "0.747812344"
    ],
    [
      "0.445715743",
      "0.74803979"
    ],
    [
      "0.509333602",
      "0.74803979"
    ],
    [
      "0.57295146",
      "0.74803979"
    ],
    [
      "0.636569319",
      "0.74803979"
    ],
    [
      "0.912480201",
      "0.767674694"
    ],
    [
      "0.966937294",
      "0.800563248"
    ],
    [
      "0.031808929",
      "0.802907026"
    ],
    [
      "0.095426788",
      "0.802907026"
    ],
    [
      "0.159044646",
      "0.802907026"
    ],
    [
      "0.222662505",
      "0.802907026"
    ],
    [
      "0.286280363",
      "0.802907026"
    ],
    [
      "0.349898222",
      "0.802907026"
    ],
    [
      "0.41351608",
      "0.802907026"
    ],
    [
      "0.668768982",
      "0.802907026"
    ],
    [
      "0.73238684",
      "0.802907026"
    ],
    [
      "0.796004699",
      "0.802907026"
    ],
    [
      "0.859622332",
      "0.803076355"
    ],
    [
      "0.477524673",
      "0.803134471"
    ],
    [
      "0.541142531",
      "0.803134471"
    ],
    [
      "0.604760389",
      "0.803134471"
    ],
    [
      "0.899133338",
      "0.852938954"
    ],
    [
      "0.063617858",
      "0.858001708"
    ],
    [
      "0.127235717",
      "0.858001708"
    ],
    [
      "0.190853575",
      "0.858001708"
    ],
    [
      "0.254471434",
      "0.858001708"
    ],
    [
      "0.318089292",
      "0.858001708"
    ],
    [
      "0.381707151",
      "0.858001708"
    ],
    [
      "0.445325009",
      "0.858001708"
    ],
    [
      "0.636960053",
      "0.858001708"
    ],
    [
      "0.700577911",
      "0.858001708"
    ],
    [
      "0.76419577",
      "0.858001708"
    ],
    [
      "0.509333602",
      "0.858229153"
    ],
    [
      "0.57295146",
      "0.858229153"
    ],
    [
      "0.830457651",
      "0.859615308"
    ],
    [
      "0.968191071",
      "0.86416875"
    ],
    [
      "0.925809031",
      "0.911613398"
    ],
    [
      "0.031808929",
      "0.913096389"
    ],
    [
      "0.095426788",
      "0.913096389"
    ],
    [
      "0.159044646",
      "0.913096389"
    ],
    [
      "0.222662505",
      "0.913096389"
    ],
    [
      "0.286280363",
      "0.913096389"
    ],
    [
      "0.349898222",
      "0.913096389"
    ],
    [
      "0.41351608",
      "0.913096389"
    ],
    [
      "0.477133939",
      "0.913096389"
    ],
    [
      "0.605151123",
      "0.913096389"
    ],
    [
      "0.668768982",
      "0.913096389"
    ],
    [
      "0.73238684",
      "0.913096389"
    ],
    [
      "0.796004699",
      "0.913096389"
    ],
    [
      "0.541142531",
      "0.913323835"
    ],
    [
      "0.86226658",
      "0.91470999"
    ],
    [
      "0.96606494",
      "0.961573024"
    ],
    [
      "0.063617858",
      "0.968191071"
    ],
    [
      "0.127235717",
      "0.968191071"
    ],
    [
      "0.190853575",
      "0.968191071"
    ],
    [
      "0.254471434",
      "0.968191071"
    ],
    [
      "0.318089292",
      "0.968191071"
    ],
    [
      "0.381707151",
      "0.968191071"
    ],
    [
      "0.445325009",
      "0.968191071"
    ],
    [
      "0.508942868",
      "0.968191071"
    ],
    [
      "0.573342194",
      "0.968191071"
    ],
    [
      "0.636960053",
      "0.968191071"
    ],
    [
      "0.700577911",
      "0.968191071"
    ],
    [
      "0.76419577",
      "0.968191071"
    ],
    [
      "0.827813628",
      "0.968191071"
    ],
    [
      "0.896719533",
      "0.968191071"
    ]
  ],
  "radius": "0.031808928"
}

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

Instance parameters

{
  "n": 271
}

Starter answer

{
  "centers": [
    [
      "0.095817522",
      "0.031808929"
    ],
    [
      "0.15943538",
      "0.031808929"
    ],
    [
      "0.223053239",
      "0.031808929"
    ],
    [
      "0.286671097",
      "0.031808929"
    ],
    [
      "0.350288956",
      "0.031808929"
    ],
    [
      "0.413906814",
      "0.031808929"
    ],
    [
      "0.477524673",
      "0.031808929"
    ],
    [
      "0.541142531",
      "0.031808929"
    ],
    [
      "0.604760389",
      "0.031808929"
    ],
    [
      "0.668378248",
      "0.031808929"
    ],
    [
      "0.731996106",
      "0.031808929"
    ],
    [
      "0.795613965",
      "0.031808929"
    ],
    [
      "0.859231823",
      "0.031808929"
    ],
    [
      "0.0318116",
      "0.031814552"
    ],
    [
      "0.967419679",
      "0.03214828"
    ],
    [
      "0.912407353",
      "0.066731628"
    ],
    [
      "0.064008592",
      "0.086903611"
    ],
    [
      "0.127626451",
      "0.086903611"
    ],
    [
      "0.191244309",
      "0.086903611"
    ],
    [
      "0.254862168",
      "0.086903611"
    ],
    [
      "0.318480026",
      "0.086903611"
    ],
    [
      "0.382097885",
      "0.086903611"
    ],
    [
      "0.445715743",
      "0.086903611"
    ],
    [
      "0.509333602",
      "0.086903611"
    ],
    [
      "0.57295146",
      "0.086903611"
    ],
    [
      "0.636569319",
      "0.086903611"
    ],
    [
      "0.700187177",
      "0.086903611"
    ],
    [
      "0.763805036",
      "0.086903611"
    ],
    [
      "0.832824908",
      "0.089866089"
    ],
    [
      "0.968191071",
      "0.097316082"
    ],
    [
      "0.912407353",
      "0.130349487"
    ],
    [
      "0.031808929",
      "0.141770847"
    ],
    [
      "0.095817522",
      "0.141998292"
    ],
    [
      "0.15943538",
      "0.141998292"
    ],
    [
      "0.223053239",
      "0.141998292"
    ],
    [
      "0.286671097",
      "0.141998292"
    ],
    [
      "0.350288956",
      "0.141998292"
    ],
    [
      "0.413906814",
      "0.141998292"
    ],
    [
      "0.477524673",
      "0.141998292"
    ],
    [
      "0.541142531",
      "0.141998292"
    ],
    [
      "0.604760389",
      "0.141998292"
    ],
    [
      "0.668378248",
      "0.141998292"
    ],
    [
      "0.731996106",
      "0.141998292"
    ],
    [
      "0.795613965",
      "0.141998292"
    ],
    [
      "0.856448025",
      "0.160611434"
    ],
    [
      "0.968191071",
      "0.160933941"
    ],
    [
      "0.910635305",
      "0.193942661"
    ],
    [
      "0.063617858",
      "0.196865529"
    ],
    [
      "0.127626451",
      "0.197092974"
    ],
    [
      "0.191244309",
      "0.197092974"
    ],
    [
      "0.254862168",
      "0.197092974"
    ],
    [
      "0.318480026",
      "0.197092974"
    ],
    [
      "0.382097885",
      "0.197092974"
    ],
    [
      "0.445715743",
      "0.197092974"
    ],
    [
      "0.509333602",
      "0.197092974"
    ],
    [
      "0.57295146",
      "0.197092974"
    ],
    [
      "0.636569319",
      "0.197092974"
    ],
    [
      "0.700187177",
      "0.197092974"
    ],
    [
      "0.763805036",
      "0.197092974"
    ],
    [
      "0.852705009",
      "0.224119086"
    ],
    [
      "0.966419022",
      "0.224527114"
    ],
    [
      "0.031808929",
      "0.25196021"
    ],
    [
      "0.095426788",
      "0.25196021"
    ],
    [
      "0.15943538",
      "0.252187656"
    ],
    [
      "0.223053239",
      "0.252187656"
    ],
    [
      "0.286671097",
      "0.252187656"
    ],
    [
      "0.350288956",
      "0.252187656"
    ],
    [
      "0.413906814",
      "0.252187656"
    ],
    [
      "0.477524673",
      "0.252187656"
    ],
    [
      "0.541142531",
      "0.252187656"
    ],
    [
      "0.604760389",
      "0.252187656"
    ],
    [
      "0.668378248",
      "0.252187656"
    ],
    [
      "0.731996106",
      "0.252187656"
    ],
    [
      "0.795613965",
      "0.252187656"
    ],
    [
      "0.906892288",
      "0.257450312"
    ],
    [
      "0.968191071",
      "0.288120288"
    ],
    [
      "0.846999739",
      "0.289802421"
    ],
    [
      "0.063617858",
      "0.307054892"
    ],
    [
      "0.127235717",
      "0.307054892"
    ],
    [
      "0.191244309",
      "0.307282337"
    ],
    [
      "0.254862168",
      "0.307282337"
    ],
    [
      "0.318480026",
      "0.307282337"
    ],
    [
      "0.382097885",
      "0.307282337"
    ],
    [
      "0.445715743",
      "0.307282337"
    ],
    [
      "0.509333602",
      "0.307282337"
    ],
    [
      "0.57295146",
      "0.307282337"
    ],
    [
      "0.636569319",
      "0.307282337"
    ],
    [
      "0.700187177",
      "0.307282337"
    ],
    [
      "0.763805036",
      "0.307282337"
    ],
    [
      "0.913559302",
      "0.320717862"
    ],
    [
      "0.858464621",
      "0.352526791"
    ],
    [
      "0.968191071",
      "0.353315435"
    ],
    [
      "0.031808929",
      "0.362149573"
    ],
    [
      "0.095426788",
      "0.362149573"
    ],
    [
      "0.159044646",
      "0.362149573"
    ],
    [
      "0.223053239",
      "0.362377019"
    ],
    [
      "0.286671097",
      "0.362377019"
    ],
    [
      "0.350288956",
      "0.362377019"
    ],
    [
      "0.413906814",
      "0.362377019"
    ],
    [
      "0.477524673",
      "0.362377019"
    ],
    [
      "0.541142531",
      "0.362377019"
    ],
    [
      "0.604760389",
      "0.362377019"
    ],
    [
      "0.668378248",
      "0.362377019"
    ],
    [
      "0.731996106",
      "0.362377019"
    ],
    [
      "0.795613965",
      "0.362377019"
    ],
    [
      "0.913096389",
      "0.385124364"
    ],
    [
      "0.968191071",
      "0.416933293"
    ],
    [
      "0.063617858",
      "0.417244255"
    ],
    [
      "0.127235717",
      "0.417244255"
    ],
    [
      "0.190853575",
      "0.417244255"
    ],
    [
      "0.254862168",
      "0.4174717"
    ],
    [
      "0.318480026",
      "0.4174717"
    ],
    [
      "0.382097885",
      "0.4174717"
    ],
    [
      "0.445715743",
      "0.4174717"
    ],
    [
      "0.509333602",
      "0.4174717"
    ],
    [
      "0.57295146",
      "0.4174717"
    ],
    [
      "0.636569319",
      "0.4174717"
    ],
    [
      "0.700187177",
      "0.4174717"
    ],
    [
      "0.763805036",
      "0.4174717"
    ],
    [
      "0.845266839",
      "0.417520099"
    ],
    [
      "0.913096389",
      "0.448742223"
    ],
    [
      "0.031808929",
      "0.472338937"
    ],
    [
      "0.095426788",
      "0.472338937"
    ],
    [
      "0.159044646",
      "0.472338937"
    ],
    [
      "0.222662505",
      "0.472338937"
    ],
    [
      "0.286671097",
      "0.472566382"
    ],
    [
      "0.350288956",
      "0.472566382"
    ],
    [
      "0.413906814",
      "0.472566382"
    ],
    [
      "0.477524673",
      "0.472566382"
    ],
    [
      "0.541142531",
      "0.472566382"
    ],
    [
      "0.604760389",
      "0.472566382"
    ],
    [
      "0.668378248",
      "0.472566382"
    ],
    [
      "0.731996106",
      "0.472566382"
    ],
    [
      "0.795613965",
      "0.472566382"
    ],
    [
      "0.968191071",
      "0.480551152"
    ],
    [
      "0.858593615",
      "0.481555018"
    ],
    [
      "0.913688297",
      "0.513363947"
    ],
    [
      "0.063617858",
      "0.527433618"
    ],
    [
      "0.127235717",
      "0.527433618"
    ],
    [
      "0.190853575",
      "0.527433618"
    ],
    [
      "0.254471434",
      "0.527433618"
    ],
    [
      "0.318480026",
      "0.527661063"
    ],
    [
      "0.382097885",
      "0.527661063"
    ],
    [
      "0.445715743",
      "0.527661063"
    ],
    [
      "0.509333602",
      "0.527661063"
    ],
    [
      "0.57295146",
      "0.527661063"
    ],
    [
      "0.636569319",
      "0.527661063"
    ],
    [
      "0.700187177",
      "0.527661063"
    ],
    [
      "0.763805036",
      "0.527661063"
    ],
    [
      "0.847552782",
      "0.544270301"
    ],
    [
      "0.968191071",
      "0.546176743"
    ],
    [
      "0.910183796",
      "0.576885207"
    ],
    [
      "0.031808929",
      "0.5825283"
    ],
    [
      "0.095426788",
      "0.5825283"
    ],
    [
      "0.159044646",
      "0.5825283"
    ],
    [
      "0.222662505",
      "0.5825283"
    ],
    [
      "0.286280363",
      "0.5825283"
    ],
    [
      "0.796004699",
      "0.5825283"
    ],
    [
      "0.350288956",
      "0.582755745"
    ],
    [
      "0.413906814",
      "0.582755745"
    ],
    [
      "0.477524673",
      "0.582755745"
    ],
    [
      "0.541142531",
      "0.582755745"
    ],
    [
      "0.604760389",
      "0.582755745"
    ],
    [
      "0.668378248",
      "0.582755745"
    ],
    [
      "0.731996106",
      "0.582755745"
    ],
    [
      "0.854472927",
      "0.607602155"
    ],
    [
      "0.968191071",
      "0.609794601"
    ],
    [
      "0.063617858",
      "0.637622981"
    ],
    [
      "0.127235717",
      "0.637622981"
    ],
    [
      "0.190853575",
      "0.637622981"
    ],
    [
      "0.254471434",
      "0.637622981"
    ],
    [
      "0.318089292",
      "0.637622981"
    ],
    [
      "0.76419577",
      "0.637622981"
    ],
    [
      "0.382097885",
      "0.637850427"
    ],
    [
      "0.445715743",
      "0.637850427"
    ],
    [
      "0.509333602",
      "0.637850427"
    ],
    [
      "0.57295146",
      "0.637850427"
    ],
    [
      "0.636569319",
      "0.637850427"
    ],
    [
      "0.700187177",
      "0.637850427"
    ],
    [
      "0.911585583",
      "0.640487619"
    ],
    [
      "0.855874714",
      "0.671204568"
    ],
    [
      "0.966042676",
      "0.673376173"
    ],
    [
      "0.031808929",
      "0.692717663"
    ],
    [
      "0.095426788",
      "0.692717663"
    ],
    [
      "0.159044646",
      "0.692717663"
    ],
    [
      "0.222662505",
      "0.692717663"
    ],
    [
      "0.286280363",
      "0.692717663"
    ],
    [
      "0.349898222",
      "0.692717663"
    ],
    [
      "0.73238684",
      "0.692717663"
    ],
    [
      "0.796004699",
      "0.692717663"
    ],
    [
      "0.413906814",
      "0.692945108"
    ],
    [
      "0.477524673",
      "0.692945108"
    ],
    [
      "0.541142531",
      "0.692945108"
    ],
    [
      "0.604760389",
      "0.692945108"
    ],
    [
      "0.668378248",
      "0.692945108"
    ],
    [
      "0.910331806",
      "0.704093122"
    ],
    [
      "0.968191071",
      "0.736957745"
    ],
    [
      "0.829895109",
      "0.746595539"
    ],
    [
      "0.063617858",
      "0.747812344"
    ],
    [
      "0.127235717",
      "0.747812344"
    ],
    [
      "0.190853575",
      "0.747812344"
    ],
    [
      "0.254471434",
      "0.747812344"
    ],
    [
      "0.318089292",
      "0.747812344"
    ],
    [
      "0.381707151",
      "0.747812344"
    ],
    [
      "0.700577911",
      "0.747812344"
    ],
    [
      "0.76419577",
      "0.747812344"
    ],
    [
      "0.445715743",
      "0.74803979"
    ],
    [
      "0.509333602",
      "0.74803979"
    ],
    [
      "0.57295146",
      "0.74803979"
    ],
    [
      "0.636569319",
      "0.74803979"
    ],
    [
      "0.912480201",
      "0.767674694"
    ],
    [
      "0.966937294",
      "0.800563248"
    ],
    [
      "0.031808929",
      "0.802907026"
    ],
    [
      "0.095426788",
      "0.802907026"
    ],
    [
      "0.159044646",
      "0.802907026"
    ],
    [
      "0.222662505",
      "0.802907026"
    ],
    [
      "0.286280363",
      "0.802907026"
    ],
    [
      "0.349898222",
      "0.802907026"
    ],
    [
      "0.41351608",
      "0.802907026"
    ],
    [
      "0.668768982",
      "0.802907026"
    ],
    [
      "0.73238684",
      "0.802907026"
    ],
    [
      "0.796004699",
      "0.802907026"
    ],
    [
      "0.859622332",
      "0.803076355"
    ],
    [
      "0.477524673",
      "0.803134471"
    ],
    [
      "0.541142531",
      "0.803134471"
    ],
    [
      "0.604760389",
      "0.803134471"
    ],
    [
      "0.899133338",
      "0.852938954"
    ],
    [
      "0.063617858",
      "0.858001708"
    ],
    [
      "0.127235717",
      "0.858001708"
    ],
    [
      "0.190853575",
      "0.858001708"
    ],
    [
      "0.254471434",
      "0.858001708"
    ],
    [
      "0.318089292",
      "0.858001708"
    ],
    [
      "0.381707151",
      "0.858001708"
    ],
    [
      "0.445325009",
      "0.858001708"
    ],
    [
      "0.636960053",
      "0.858001708"
    ],
    [
      "0.700577911",
      "0.858001708"
    ],
    [
      "0.76419577",
      "0.858001708"
    ],
    [
      "0.509333602",
      "0.858229153"
    ],
    [
      "0.57295146",
      "0.858229153"
    ],
    [
      "0.830457651",
      "0.859615308"
    ],
    [
      "0.968191071",
      "0.86416875"
    ],
    [
      "0.925809031",
      "0.911613398"
    ],
    [
      "0.031808929",
      "0.913096389"
    ],
    [
      "0.095426788",
      "0.913096389"
    ],
    [
      "0.159044646",
      "0.913096389"
    ],
    [
      "0.222662505",
      "0.913096389"
    ],
    [
      "0.286280363",
      "0.913096389"
    ],
    [
      "0.349898222",
      "0.913096389"
    ],
    [
      "0.41351608",
      "0.913096389"
    ],
    [
      "0.477133939",
      "0.913096389"
    ],
    [
      "0.605151123",
      "0.913096389"
    ],
    [
      "0.668768982",
      "0.913096389"
    ],
    [
      "0.73238684",
      "0.913096389"
    ],
    [
      "0.796004699",
      "0.913096389"
    ],
    [
      "0.541142531",
      "0.913323835"
    ],
    [
      "0.86226658",
      "0.91470999"
    ],
    [
      "0.96606494",
      "0.961573024"
    ],
    [
      "0.063617858",
      "0.968191071"
    ],
    [
      "0.127235717",
      "0.968191071"
    ],
    [
      "0.190853575",
      "0.968191071"
    ],
    [
      "0.254471434",
      "0.968191071"
    ],
    [
      "0.318089292",
      "0.968191071"
    ],
    [
      "0.381707151",
      "0.968191071"
    ],
    [
      "0.445325009",
      "0.968191071"
    ],
    [
      "0.508942868",
      "0.968191071"
    ],
    [
      "0.573342194",
      "0.968191071"
    ],
    [
      "0.636960053",
      "0.968191071"
    ],
    [
      "0.700577911",
      "0.968191071"
    ],
    [
      "0.76419577",
      "0.968191071"
    ],
    [
      "0.827813628",
      "0.968191071"
    ],
    [
      "0.896719533",
      "0.968191071"
    ]
  ],
  "radius": "0.031808928"
}

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