P01 · Packing and covering · Classic · Hard

Equal-circle packing in a unit square · n = 285

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 = 285

ObjectiveMaximize common radius

Record comparison

common radius · Higher is better

Record	Value / interval	Author / holder	Source
External best known	[0.0308252867095, 0.0308252867105]	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

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285

0x1

VERIFIED CONSTRUCTIONr = 0.030825286

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": [
    [
      "0.030825287",
      "0.030825287"
    ],
    [
      "0.15411538",
      "0.030825287"
    ],
    [
      "0.272613805",
      "0.030825287"
    ],
    [
      "0.38181523",
      "0.030825287"
    ],
    [
      "0.488656016",
      "0.030825287"
    ],
    [
      "0.595437974",
      "0.030825287"
    ],
    [
      "0.7022199",
      "0.030825287"
    ],
    [
      "0.809001825",
      "0.030825287"
    ],
    [
      "0.915783751",
      "0.030825287"
    ],
    [
      "0.092470333",
      "0.031650776"
    ],
    [
      "0.213364592",
      "0.047864184"
    ],
    [
      "0.327214518",
      "0.059453165"
    ],
    [
      "0.435235671",
      "0.061599626"
    ],
    [
      "0.542046996",
      "0.061650546"
    ],
    [
      "0.969174713",
      "0.061650573"
    ],
    [
      "0.648828937",
      "0.061650573"
    ],
    [
      "0.755610862",
      "0.061650573"
    ],
    [
      "0.862392788",
      "0.061650573"
    ],
    [
      "0.060932916",
      "0.084624208"
    ],
    [
      "0.168983868",
      "0.090656059"
    ],
    [
      "0.27512169",
      "0.09242483"
    ],
    [
      "0.381874136",
      "0.092475832"
    ],
    [
      "0.488656049",
      "0.09247586"
    ],
    [
      "0.595437974",
      "0.09247586"
    ],
    [
      "0.7022199",
      "0.09247586"
    ],
    [
      "0.809001825",
      "0.09247586"
    ],
    [
      "0.915783751",
      "0.09247586"
    ],
    [
      "0.113311596",
      "0.117139851"
    ],
    [
      "0.221530175",
      "0.12290011"
    ],
    [
      "0.328483174",
      "0.123301119"
    ],
    [
      "0.435265084",
      "0.123301144"
    ],
    [
      "0.969174713",
      "0.123301147"
    ],
    [
      "0.542047011",
      "0.123301147"
    ],
    [
      "0.648828937",
      "0.123301147"
    ],
    [
      "0.755610862",
      "0.123301147"
    ],
    [
      "0.862392788",
      "0.123301147"
    ],
    [
      "0.030825287",
      "0.138423128"
    ],
    [
      "0.167332853",
      "0.152284521"
    ],
    [
      "0.275062781",
      "0.154075375"
    ],
    [
      "0.381874122",
      "0.154126431"
    ],
    [
      "0.488656049",
      "0.154126434"
    ],
    [
      "0.595437974",
      "0.154126434"
    ],
    [
      "0.7022199",
      "0.154126434"
    ],
    [
      "0.809001825",
      "0.154126434"
    ],
    [
      "0.915783751",
      "0.154126434"
    ],
    [
      "0.085894996",
      "0.172358718"
    ],
    [
      "0.221471266",
      "0.184550656"
    ],
    [
      "0.328483145",
      "0.184951694"
    ],
    [
      "0.435265084",
      "0.184951718"
    ],
    [
      "0.969174713",
      "0.18495172"
    ],
    [
      "0.542047011",
      "0.18495172"
    ],
    [
      "0.648828937",
      "0.18495172"
    ],
    [
      "0.755610862",
      "0.18495172"
    ],
    [
      "0.862392788",
      "0.18495172"
    ],
    [
      "0.030825287",
      "0.200073702"
    ],
    [
      "0.137435567",
      "0.206200617"
    ],
    [
      "0.275062752",
      "0.215725949"
    ],
    [
      "0.381874121",
      "0.215777004"
    ],
    [
      "0.488656049",
      "0.215777007"
    ],
    [
      "0.595437974",
      "0.215777007"
    ],
    [
      "0.7022199",
      "0.215777007"
    ],
    [
      "0.809001825",
      "0.215777007"
    ],
    [
      "0.915783751",
      "0.215777007"
    ],
    [
      "0.082362021",
      "0.233907977"
    ],
    [
      "0.190379789",
      "0.237787046"
    ],
    [
      "0.328483145",
      "0.246602267"
    ],
    [
      "0.435265084",
      "0.246602291"
    ],
    [
      "0.969174713",
      "0.246602294"
    ],
    [
      "0.542047011",
      "0.246602294"
    ],
    [
      "0.648828937",
      "0.246602294"
    ],
    [
      "0.755610862",
      "0.246602294"
    ],
    [
      "0.862392788",
      "0.246602294"
    ],
    [
      "0.030825287",
      "0.267742253"
    ],
    [
      "0.136553028",
      "0.267844873"
    ],
    [
      "0.24367041",
      "0.268785482"
    ],
    [
      "0.381874122",
      "0.277427578"
    ],
    [
      "0.488656049",
      "0.27742758"
    ],
    [
      "0.595437974",
      "0.27742758"
    ],
    [
      "0.7022199",
      "0.27742758"
    ],
    [
      "0.809001825",
      "0.27742758"
    ],
    [
      "0.915783751",
      "0.27742758"
    ],
    [
      "0.190179667",
      "0.299437295"
    ],
    [
      "0.083658369",
      "0.299514231"
    ],
    [
      "0.297046909",
      "0.299635806"
    ],
    [
      "0.435265084",
      "0.308252865"
    ],
    [
      "0.969174713",
      "0.308252867"
    ],
    [
      "0.542047011",
      "0.308252867"
    ],
    [
      "0.648828937",
      "0.308252867"
    ],
    [
      "0.755610862",
      "0.308252867"
    ],
    [
      "0.862392788",
      "0.308252867"
    ],
    [
      "0.243641496",
      "0.330436051"
    ],
    [
      "0.350437865",
      "0.330461105"
    ],
    [
      "0.136941444",
      "0.330525634"
    ],
    [
      "0.030825287",
      "0.33128621"
    ],
    [
      "0.915783751",
      "0.339078154"
    ],
    [
      "0.488656049",
      "0.339078154"
    ],
    [
      "0.595437974",
      "0.339078154"
    ],
    [
      "0.7022199",
      "0.339078154"
    ],
    [
      "0.809001825",
      "0.339078154"
    ],
    [
      "0.297046895",
      "0.36128638"
    ],
    [
      "0.403828828",
      "0.361286391"
    ],
    [
      "0.19031741",
      "0.361376882"
    ],
    [
      "0.084108362",
      "0.362297613"
    ],
    [
      "0.969174713",
      "0.369903441"
    ],
    [
      "0.542047011",
      "0.369903441"
    ],
    [
      "0.648828937",
      "0.369903441"
    ],
    [
      "0.755610862",
      "0.369903441"
    ],
    [
      "0.862392788",
      "0.369903441"
    ],
    [
      "0.350437865",
      "0.392111678"
    ],
    [
      "0.45721979",
      "0.392111679"
    ],
    [
      "0.24370833",
      "0.392202243"
    ],
    [
      "0.137484328",
      "0.393148861"
    ],
    [
      "0.030825287",
      "0.393309016"
    ],
    [
      "0.915783751",
      "0.400728727"
    ],
    [
      "0.595437974",
      "0.400728727"
    ],
    [
      "0.7022199",
      "0.400728727"
    ],
    [
      "0.809001825",
      "0.400728727"
    ],
    [
      "0.403828827",
      "0.422936966"
    ],
    [
      "0.510610752",
      "0.422936966"
    ],
    [
      "0.297099292",
      "0.42302753"
    ],
    [
      "0.190875247",
      "0.423974222"
    ],
    [
      "0.084201252",
      "0.424160264"
    ],
    [
      "0.969174713",
      "0.431554014"
    ],
    [
      "0.648828937",
      "0.431554014"
    ],
    [
      "0.755610862",
      "0.431554014"
    ],
    [
      "0.862392788",
      "0.431554014"
    ],
    [
      "0.45721979",
      "0.453762253"
    ],
    [
      "0.564001715",
      "0.453762253"
    ],
    [
      "0.350490254",
      "0.453852818"
    ],
    [
      "0.24426621",
      "0.454799508"
    ],
    [
      "0.137592172",
      "0.454985624"
    ],
    [
      "0.030825287",
      "0.455011511"
    ],
    [
      "0.915783751",
      "0.462379301"
    ],
    [
      "0.7022199",
      "0.462379301"
    ],
    [
      "0.809001825",
      "0.462379301"
    ],
    [
      "0.510610752",
      "0.484587539"
    ],
    [
      "0.617392678",
      "0.484587539"
    ],
    [
      "0.403881217",
      "0.484678104"
    ],
    [
      "0.297657172",
      "0.485624796"
    ],
    [
      "0.190983135",
      "0.485810911"
    ],
    [
      "0.084216207",
      "0.485836872"
    ],
    [
      "0.969174713",
      "0.493204587"
    ],
    [
      "0.755610862",
      "0.493204587"
    ],
    [
      "0.862392788",
      "0.493204587"
    ],
    [
      "0.564001715",
      "0.515412826"
    ],
    [
      "0.670783641",
      "0.515412826"
    ],
    [
      "0.45727218",
      "0.515503391"
    ],
    [
      "0.351048135",
      "0.516450083"
    ],
    [
      "0.244374097",
      "0.516636199"
    ],
    [
      "0.137607169",
      "0.516662159"
    ],
    [
      "0.030825287",
      "0.516662233"
    ],
    [
      "0.915783751",
      "0.524029874"
    ],
    [
      "0.809001825",
      "0.524029874"
    ],
    [
      "0.617392678",
      "0.546238113"
    ],
    [
      "0.724174603",
      "0.546238113"
    ],
    [
      "0.510663143",
      "0.546328678"
    ],
    [
      "0.404439098",
      "0.54727537"
    ],
    [
      "0.29776506",
      "0.547461486"
    ],
    [
      "0.190998131",
      "0.547487447"
    ],
    [
      "0.084216249",
      "0.54748752"
    ],
    [
      "0.969174713",
      "0.554855161"
    ],
    [
      "0.862392788",
      "0.554855161"
    ],
    [
      "0.670783641",
      "0.5770634"
    ],
    [
      "0.777565566",
      "0.5770634"
    ],
    [
      "0.564054105",
      "0.577153964"
    ],
    [
      "0.45783006",
      "0.578100656"
    ],
    [
      "0.351156022",
      "0.578286773"
    ],
    [
      "0.244389094",
      "0.578312734"
    ],
    [
      "0.030825287",
      "0.578312807"
    ],
    [
      "0.137607211",
      "0.578312808"
    ],
    [
      "0.915783751",
      "0.585680447"
    ],
    [
      "0.830956529",
      "0.607888686"
    ],
    [
      "0.724174603",
      "0.607888686"
    ],
    [
      "0.617445068",
      "0.607979251"
    ],
    [
      "0.511221023",
      "0.608925943"
    ],
    [
      "0.404546985",
      "0.609112059"
    ],
    [
      "0.297780057",
      "0.60913802"
    ],
    [
      "0.190998174",
      "0.609138095"
    ],
    [
      "0.084216249",
      "0.609138095"
    ],
    [
      "0.969174713",
      "0.616505734"
    ],
    [
      "0.884347492",
      "0.638713973"
    ],
    [
      "0.777565566",
      "0.638713973"
    ],
    [
      "0.670836031",
      "0.638804538"
    ],
    [
      "0.564611986",
      "0.63975123"
    ],
    [
      "0.457937948",
      "0.639937346"
    ],
    [
      "0.35117102",
      "0.639963307"
    ],
    [
      "0.244389137",
      "0.639963381"
    ],
    [
      "0.137607211",
      "0.639963381"
    ],
    [
      "0.030825287",
      "0.639963383"
    ],
    [
      "0.937738454",
      "0.66953926"
    ],
    [
      "0.830956529",
      "0.66953926"
    ],
    [
      "0.724226993",
      "0.669629825"
    ],
    [
      "0.618002949",
      "0.670576517"
    ],
    [
      "0.511328911",
      "0.670762633"
    ],
    [
      "0.404561982",
      "0.670788594"
    ],
    [
      "0.2977801",
      "0.670788668"
    ],
    [
      "0.190998174",
      "0.670788668"
    ],
    [
      "0.084216249",
      "0.670788669"
    ],
    [
      "0.884347492",
      "0.700364546"
    ],
    [
      "0.777617956",
      "0.700455111"
    ],
    [
      "0.671393911",
      "0.701401803"
    ],
    [
      "0.564719873",
      "0.701587919"
    ],
    [
      "0.457952945",
      "0.701613881"
    ],
    [
      "0.351171062",
      "0.701613955"
    ],
    [
      "0.244389137",
      "0.701613955"
    ],
    [
      "0.030825287",
      "0.701613956"
    ],
    [
      "0.137607212",
      "0.701613956"
    ],
    [
      "0.969174713",
      "0.722572785"
    ],
    [
      "0.831008919",
      "0.731280398"
    ],
    [
      "0.724784874",
      "0.73222709"
    ],
    [
      "0.618110836",
      "0.732413206"
    ],
    [
      "0.511343908",
      "0.732439167"
    ],
    [
      "0.404562025",
      "0.732439241"
    ],
    [
      "0.2977801",
      "0.732439241"
    ],
    [
      "0.084216249",
      "0.732439243"
    ],
    [
      "0.190998175",
      "0.732439243"
    ],
    [
      "0.915783751",
      "0.753398072"
    ],
    [
      "0.778175837",
      "0.763052377"
    ],
    [
      "0.671501799",
      "0.763238493"
    ],
    [
      "0.564734871",
      "0.763264454"
    ],
    [
      "0.457952988",
      "0.763264528"
    ],
    [
      "0.351171062",
      "0.763264528"
    ],
    [
      "0.030825287",
      "0.763264529"
    ],
    [
      "0.137607212",
      "0.763264529"
    ],
    [
      "0.244389138",
      "0.763264529"
    ],
    [
      "0.969174713",
      "0.784223359"
    ],
    [
      "0.862286958",
      "0.784407392"
    ],
    [
      "0.724892762",
      "0.794063779"
    ],
    [
      "0.618125833",
      "0.794089741"
    ],
    [
      "0.511343951",
      "0.794089815"
    ],
    [
      "0.404562025",
      "0.794089815"
    ],
    [
      "0.084216249",
      "0.794089816"
    ],
    [
      "0.190998175",
      "0.794089816"
    ],
    [
      "0.2977801",
      "0.794089816"
    ],
    [
      "0.915783751",
      "0.815048645"
    ],
    [
      "0.80787129",
      "0.8170799"
    ],
    [
      "0.564734913",
      "0.824915102"
    ],
    [
      "0.457952988",
      "0.824915102"
    ],
    [
      "0.030825287",
      "0.824915103"
    ],
    [
      "0.137607212",
      "0.824915103"
    ],
    [
      "0.351171063",
      "0.824915103"
    ],
    [
      "0.244389138",
      "0.824915103"
    ],
    [
      "0.671543983",
      "0.824962016"
    ],
    [
      "0.969174713",
      "0.845873932"
    ],
    [
      "0.862286958",
      "0.846057965"
    ],
    [
      "0.754584089",
      "0.84809357"
    ],
    [
      "0.618125919",
      "0.855740314"
    ],
    [
      "0.511343951",
      "0.855740388"
    ],
    [
      "0.404562026",
      "0.85574039"
    ],
    [
      "0.084216249",
      "0.85574039"
    ],
    [
      "0.190998175",
      "0.85574039"
    ],
    [
      "0.2977801",
      "0.85574039"
    ],
    [
      "0.915783751",
      "0.876699219"
    ],
    [
      "0.808083582",
      "0.878730108"
    ],
    [
      "0.701302319",
      "0.879107215"
    ],
    [
      "0.030825287",
      "0.886565676"
    ],
    [
      "0.145031843",
      "0.899824342"
    ],
    [
      "0.969174713",
      "0.907524505"
    ],
    [
      "0.86249925",
      "0.907708173"
    ],
    [
      "0.332175911",
      "0.90921944"
    ],
    [
      "0.583803046",
      "0.90938525"
    ],
    [
      "0.754801816",
      "0.909743759"
    ],
    [
      "0.647817762",
      "0.909769821"
    ],
    [
      "0.27000148",
      "0.910778026"
    ],
    [
      "0.459149689",
      "0.911864987"
    ],
    [
      "0.208486101",
      "0.914858624"
    ],
    [
      "0.522368287",
      "0.916397269"
    ],
    [
      "0.396279731",
      "0.916832098"
    ],
    [
      "0.084216249",
      "0.917390963"
    ],
    [
      "0.913350835",
      "0.942563726"
    ],
    [
      "0.798073659",
      "0.953656636"
    ],
    [
      "0.61549505",
      "0.962267778"
    ],
    [
      "0.302339226",
      "0.963266725"
    ],
    [
      "0.030857593",
      "0.965583325"
    ],
    [
      "0.11767124",
      "0.969174713"
    ],
    [
      "0.179321814",
      "0.969174713"
    ],
    [
      "0.240972387",
      "0.969174713"
    ],
    [
      "0.363706064",
      "0.969174713"
    ],
    [
      "0.428853398",
      "0.969174713"
    ],
    [
      "0.490503972",
      "0.969174713"
    ],
    [
      "0.554232603",
      "0.969174713"
    ],
    [
      "0.676757497",
      "0.969174713"
    ],
    [
      "0.738408071",
      "0.969174713"
    ],
    [
      "0.857739248",
      "0.969174713"
    ],
    [
      "0.968962421",
      "0.969174713"
    ]
  ],
  "radius": "0.030825286"
}

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

Instance parameters

{
  "n": 285
}

Starter answer

{
  "centers": [
    [
      "0.030825287",
      "0.030825287"
    ],
    [
      "0.15411538",
      "0.030825287"
    ],
    [
      "0.272613805",
      "0.030825287"
    ],
    [
      "0.38181523",
      "0.030825287"
    ],
    [
      "0.488656016",
      "0.030825287"
    ],
    [
      "0.595437974",
      "0.030825287"
    ],
    [
      "0.7022199",
      "0.030825287"
    ],
    [
      "0.809001825",
      "0.030825287"
    ],
    [
      "0.915783751",
      "0.030825287"
    ],
    [
      "0.092470333",
      "0.031650776"
    ],
    [
      "0.213364592",
      "0.047864184"
    ],
    [
      "0.327214518",
      "0.059453165"
    ],
    [
      "0.435235671",
      "0.061599626"
    ],
    [
      "0.542046996",
      "0.061650546"
    ],
    [
      "0.969174713",
      "0.061650573"
    ],
    [
      "0.648828937",
      "0.061650573"
    ],
    [
      "0.755610862",
      "0.061650573"
    ],
    [
      "0.862392788",
      "0.061650573"
    ],
    [
      "0.060932916",
      "0.084624208"
    ],
    [
      "0.168983868",
      "0.090656059"
    ],
    [
      "0.27512169",
      "0.09242483"
    ],
    [
      "0.381874136",
      "0.092475832"
    ],
    [
      "0.488656049",
      "0.09247586"
    ],
    [
      "0.595437974",
      "0.09247586"
    ],
    [
      "0.7022199",
      "0.09247586"
    ],
    [
      "0.809001825",
      "0.09247586"
    ],
    [
      "0.915783751",
      "0.09247586"
    ],
    [
      "0.113311596",
      "0.117139851"
    ],
    [
      "0.221530175",
      "0.12290011"
    ],
    [
      "0.328483174",
      "0.123301119"
    ],
    [
      "0.435265084",
      "0.123301144"
    ],
    [
      "0.969174713",
      "0.123301147"
    ],
    [
      "0.542047011",
      "0.123301147"
    ],
    [
      "0.648828937",
      "0.123301147"
    ],
    [
      "0.755610862",
      "0.123301147"
    ],
    [
      "0.862392788",
      "0.123301147"
    ],
    [
      "0.030825287",
      "0.138423128"
    ],
    [
      "0.167332853",
      "0.152284521"
    ],
    [
      "0.275062781",
      "0.154075375"
    ],
    [
      "0.381874122",
      "0.154126431"
    ],
    [
      "0.488656049",
      "0.154126434"
    ],
    [
      "0.595437974",
      "0.154126434"
    ],
    [
      "0.7022199",
      "0.154126434"
    ],
    [
      "0.809001825",
      "0.154126434"
    ],
    [
      "0.915783751",
      "0.154126434"
    ],
    [
      "0.085894996",
      "0.172358718"
    ],
    [
      "0.221471266",
      "0.184550656"
    ],
    [
      "0.328483145",
      "0.184951694"
    ],
    [
      "0.435265084",
      "0.184951718"
    ],
    [
      "0.969174713",
      "0.18495172"
    ],
    [
      "0.542047011",
      "0.18495172"
    ],
    [
      "0.648828937",
      "0.18495172"
    ],
    [
      "0.755610862",
      "0.18495172"
    ],
    [
      "0.862392788",
      "0.18495172"
    ],
    [
      "0.030825287",
      "0.200073702"
    ],
    [
      "0.137435567",
      "0.206200617"
    ],
    [
      "0.275062752",
      "0.215725949"
    ],
    [
      "0.381874121",
      "0.215777004"
    ],
    [
      "0.488656049",
      "0.215777007"
    ],
    [
      "0.595437974",
      "0.215777007"
    ],
    [
      "0.7022199",
      "0.215777007"
    ],
    [
      "0.809001825",
      "0.215777007"
    ],
    [
      "0.915783751",
      "0.215777007"
    ],
    [
      "0.082362021",
      "0.233907977"
    ],
    [
      "0.190379789",
      "0.237787046"
    ],
    [
      "0.328483145",
      "0.246602267"
    ],
    [
      "0.435265084",
      "0.246602291"
    ],
    [
      "0.969174713",
      "0.246602294"
    ],
    [
      "0.542047011",
      "0.246602294"
    ],
    [
      "0.648828937",
      "0.246602294"
    ],
    [
      "0.755610862",
      "0.246602294"
    ],
    [
      "0.862392788",
      "0.246602294"
    ],
    [
      "0.030825287",
      "0.267742253"
    ],
    [
      "0.136553028",
      "0.267844873"
    ],
    [
      "0.24367041",
      "0.268785482"
    ],
    [
      "0.381874122",
      "0.277427578"
    ],
    [
      "0.488656049",
      "0.27742758"
    ],
    [
      "0.595437974",
      "0.27742758"
    ],
    [
      "0.7022199",
      "0.27742758"
    ],
    [
      "0.809001825",
      "0.27742758"
    ],
    [
      "0.915783751",
      "0.27742758"
    ],
    [
      "0.190179667",
      "0.299437295"
    ],
    [
      "0.083658369",
      "0.299514231"
    ],
    [
      "0.297046909",
      "0.299635806"
    ],
    [
      "0.435265084",
      "0.308252865"
    ],
    [
      "0.969174713",
      "0.308252867"
    ],
    [
      "0.542047011",
      "0.308252867"
    ],
    [
      "0.648828937",
      "0.308252867"
    ],
    [
      "0.755610862",
      "0.308252867"
    ],
    [
      "0.862392788",
      "0.308252867"
    ],
    [
      "0.243641496",
      "0.330436051"
    ],
    [
      "0.350437865",
      "0.330461105"
    ],
    [
      "0.136941444",
      "0.330525634"
    ],
    [
      "0.030825287",
      "0.33128621"
    ],
    [
      "0.915783751",
      "0.339078154"
    ],
    [
      "0.488656049",
      "0.339078154"
    ],
    [
      "0.595437974",
      "0.339078154"
    ],
    [
      "0.7022199",
      "0.339078154"
    ],
    [
      "0.809001825",
      "0.339078154"
    ],
    [
      "0.297046895",
      "0.36128638"
    ],
    [
      "0.403828828",
      "0.361286391"
    ],
    [
      "0.19031741",
      "0.361376882"
    ],
    [
      "0.084108362",
      "0.362297613"
    ],
    [
      "0.969174713",
      "0.369903441"
    ],
    [
      "0.542047011",
      "0.369903441"
    ],
    [
      "0.648828937",
      "0.369903441"
    ],
    [
      "0.755610862",
      "0.369903441"
    ],
    [
      "0.862392788",
      "0.369903441"
    ],
    [
      "0.350437865",
      "0.392111678"
    ],
    [
      "0.45721979",
      "0.392111679"
    ],
    [
      "0.24370833",
      "0.392202243"
    ],
    [
      "0.137484328",
      "0.393148861"
    ],
    [
      "0.030825287",
      "0.393309016"
    ],
    [
      "0.915783751",
      "0.400728727"
    ],
    [
      "0.595437974",
      "0.400728727"
    ],
    [
      "0.7022199",
      "0.400728727"
    ],
    [
      "0.809001825",
      "0.400728727"
    ],
    [
      "0.403828827",
      "0.422936966"
    ],
    [
      "0.510610752",
      "0.422936966"
    ],
    [
      "0.297099292",
      "0.42302753"
    ],
    [
      "0.190875247",
      "0.423974222"
    ],
    [
      "0.084201252",
      "0.424160264"
    ],
    [
      "0.969174713",
      "0.431554014"
    ],
    [
      "0.648828937",
      "0.431554014"
    ],
    [
      "0.755610862",
      "0.431554014"
    ],
    [
      "0.862392788",
      "0.431554014"
    ],
    [
      "0.45721979",
      "0.453762253"
    ],
    [
      "0.564001715",
      "0.453762253"
    ],
    [
      "0.350490254",
      "0.453852818"
    ],
    [
      "0.24426621",
      "0.454799508"
    ],
    [
      "0.137592172",
      "0.454985624"
    ],
    [
      "0.030825287",
      "0.455011511"
    ],
    [
      "0.915783751",
      "0.462379301"
    ],
    [
      "0.7022199",
      "0.462379301"
    ],
    [
      "0.809001825",
      "0.462379301"
    ],
    [
      "0.510610752",
      "0.484587539"
    ],
    [
      "0.617392678",
      "0.484587539"
    ],
    [
      "0.403881217",
      "0.484678104"
    ],
    [
      "0.297657172",
      "0.485624796"
    ],
    [
      "0.190983135",
      "0.485810911"
    ],
    [
      "0.084216207",
      "0.485836872"
    ],
    [
      "0.969174713",
      "0.493204587"
    ],
    [
      "0.755610862",
      "0.493204587"
    ],
    [
      "0.862392788",
      "0.493204587"
    ],
    [
      "0.564001715",
      "0.515412826"
    ],
    [
      "0.670783641",
      "0.515412826"
    ],
    [
      "0.45727218",
      "0.515503391"
    ],
    [
      "0.351048135",
      "0.516450083"
    ],
    [
      "0.244374097",
      "0.516636199"
    ],
    [
      "0.137607169",
      "0.516662159"
    ],
    [
      "0.030825287",
      "0.516662233"
    ],
    [
      "0.915783751",
      "0.524029874"
    ],
    [
      "0.809001825",
      "0.524029874"
    ],
    [
      "0.617392678",
      "0.546238113"
    ],
    [
      "0.724174603",
      "0.546238113"
    ],
    [
      "0.510663143",
      "0.546328678"
    ],
    [
      "0.404439098",
      "0.54727537"
    ],
    [
      "0.29776506",
      "0.547461486"
    ],
    [
      "0.190998131",
      "0.547487447"
    ],
    [
      "0.084216249",
      "0.54748752"
    ],
    [
      "0.969174713",
      "0.554855161"
    ],
    [
      "0.862392788",
      "0.554855161"
    ],
    [
      "0.670783641",
      "0.5770634"
    ],
    [
      "0.777565566",
      "0.5770634"
    ],
    [
      "0.564054105",
      "0.577153964"
    ],
    [
      "0.45783006",
      "0.578100656"
    ],
    [
      "0.351156022",
      "0.578286773"
    ],
    [
      "0.244389094",
      "0.578312734"
    ],
    [
      "0.030825287",
      "0.578312807"
    ],
    [
      "0.137607211",
      "0.578312808"
    ],
    [
      "0.915783751",
      "0.585680447"
    ],
    [
      "0.830956529",
      "0.607888686"
    ],
    [
      "0.724174603",
      "0.607888686"
    ],
    [
      "0.617445068",
      "0.607979251"
    ],
    [
      "0.511221023",
      "0.608925943"
    ],
    [
      "0.404546985",
      "0.609112059"
    ],
    [
      "0.297780057",
      "0.60913802"
    ],
    [
      "0.190998174",
      "0.609138095"
    ],
    [
      "0.084216249",
      "0.609138095"
    ],
    [
      "0.969174713",
      "0.616505734"
    ],
    [
      "0.884347492",
      "0.638713973"
    ],
    [
      "0.777565566",
      "0.638713973"
    ],
    [
      "0.670836031",
      "0.638804538"
    ],
    [
      "0.564611986",
      "0.63975123"
    ],
    [
      "0.457937948",
      "0.639937346"
    ],
    [
      "0.35117102",
      "0.639963307"
    ],
    [
      "0.244389137",
      "0.639963381"
    ],
    [
      "0.137607211",
      "0.639963381"
    ],
    [
      "0.030825287",
      "0.639963383"
    ],
    [
      "0.937738454",
      "0.66953926"
    ],
    [
      "0.830956529",
      "0.66953926"
    ],
    [
      "0.724226993",
      "0.669629825"
    ],
    [
      "0.618002949",
      "0.670576517"
    ],
    [
      "0.511328911",
      "0.670762633"
    ],
    [
      "0.404561982",
      "0.670788594"
    ],
    [
      "0.2977801",
      "0.670788668"
    ],
    [
      "0.190998174",
      "0.670788668"
    ],
    [
      "0.084216249",
      "0.670788669"
    ],
    [
      "0.884347492",
      "0.700364546"
    ],
    [
      "0.777617956",
      "0.700455111"
    ],
    [
      "0.671393911",
      "0.701401803"
    ],
    [
      "0.564719873",
      "0.701587919"
    ],
    [
      "0.457952945",
      "0.701613881"
    ],
    [
      "0.351171062",
      "0.701613955"
    ],
    [
      "0.244389137",
      "0.701613955"
    ],
    [
      "0.030825287",
      "0.701613956"
    ],
    [
      "0.137607212",
      "0.701613956"
    ],
    [
      "0.969174713",
      "0.722572785"
    ],
    [
      "0.831008919",
      "0.731280398"
    ],
    [
      "0.724784874",
      "0.73222709"
    ],
    [
      "0.618110836",
      "0.732413206"
    ],
    [
      "0.511343908",
      "0.732439167"
    ],
    [
      "0.404562025",
      "0.732439241"
    ],
    [
      "0.2977801",
      "0.732439241"
    ],
    [
      "0.084216249",
      "0.732439243"
    ],
    [
      "0.190998175",
      "0.732439243"
    ],
    [
      "0.915783751",
      "0.753398072"
    ],
    [
      "0.778175837",
      "0.763052377"
    ],
    [
      "0.671501799",
      "0.763238493"
    ],
    [
      "0.564734871",
      "0.763264454"
    ],
    [
      "0.457952988",
      "0.763264528"
    ],
    [
      "0.351171062",
      "0.763264528"
    ],
    [
      "0.030825287",
      "0.763264529"
    ],
    [
      "0.137607212",
      "0.763264529"
    ],
    [
      "0.244389138",
      "0.763264529"
    ],
    [
      "0.969174713",
      "0.784223359"
    ],
    [
      "0.862286958",
      "0.784407392"
    ],
    [
      "0.724892762",
      "0.794063779"
    ],
    [
      "0.618125833",
      "0.794089741"
    ],
    [
      "0.511343951",
      "0.794089815"
    ],
    [
      "0.404562025",
      "0.794089815"
    ],
    [
      "0.084216249",
      "0.794089816"
    ],
    [
      "0.190998175",
      "0.794089816"
    ],
    [
      "0.2977801",
      "0.794089816"
    ],
    [
      "0.915783751",
      "0.815048645"
    ],
    [
      "0.80787129",
      "0.8170799"
    ],
    [
      "0.564734913",
      "0.824915102"
    ],
    [
      "0.457952988",
      "0.824915102"
    ],
    [
      "0.030825287",
      "0.824915103"
    ],
    [
      "0.137607212",
      "0.824915103"
    ],
    [
      "0.351171063",
      "0.824915103"
    ],
    [
      "0.244389138",
      "0.824915103"
    ],
    [
      "0.671543983",
      "0.824962016"
    ],
    [
      "0.969174713",
      "0.845873932"
    ],
    [
      "0.862286958",
      "0.846057965"
    ],
    [
      "0.754584089",
      "0.84809357"
    ],
    [
      "0.618125919",
      "0.855740314"
    ],
    [
      "0.511343951",
      "0.855740388"
    ],
    [
      "0.404562026",
      "0.85574039"
    ],
    [
      "0.084216249",
      "0.85574039"
    ],
    [
      "0.190998175",
      "0.85574039"
    ],
    [
      "0.2977801",
      "0.85574039"
    ],
    [
      "0.915783751",
      "0.876699219"
    ],
    [
      "0.808083582",
      "0.878730108"
    ],
    [
      "0.701302319",
      "0.879107215"
    ],
    [
      "0.030825287",
      "0.886565676"
    ],
    [
      "0.145031843",
      "0.899824342"
    ],
    [
      "0.969174713",
      "0.907524505"
    ],
    [
      "0.86249925",
      "0.907708173"
    ],
    [
      "0.332175911",
      "0.90921944"
    ],
    [
      "0.583803046",
      "0.90938525"
    ],
    [
      "0.754801816",
      "0.909743759"
    ],
    [
      "0.647817762",
      "0.909769821"
    ],
    [
      "0.27000148",
      "0.910778026"
    ],
    [
      "0.459149689",
      "0.911864987"
    ],
    [
      "0.208486101",
      "0.914858624"
    ],
    [
      "0.522368287",
      "0.916397269"
    ],
    [
      "0.396279731",
      "0.916832098"
    ],
    [
      "0.084216249",
      "0.917390963"
    ],
    [
      "0.913350835",
      "0.942563726"
    ],
    [
      "0.798073659",
      "0.953656636"
    ],
    [
      "0.61549505",
      "0.962267778"
    ],
    [
      "0.302339226",
      "0.963266725"
    ],
    [
      "0.030857593",
      "0.965583325"
    ],
    [
      "0.11767124",
      "0.969174713"
    ],
    [
      "0.179321814",
      "0.969174713"
    ],
    [
      "0.240972387",
      "0.969174713"
    ],
    [
      "0.363706064",
      "0.969174713"
    ],
    [
      "0.428853398",
      "0.969174713"
    ],
    [
      "0.490503972",
      "0.969174713"
    ],
    [
      "0.554232603",
      "0.969174713"
    ],
    [
      "0.676757497",
      "0.969174713"
    ],
    [
      "0.738408071",
      "0.969174713"
    ],
    [
      "0.857739248",
      "0.969174713"
    ],
    [
      "0.968962421",
      "0.969174713"
    ]
  ],
  "radius": "0.030825286"
}

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