P01 · Packing and covering · Classic · Hard

Equal-circle packing in a unit square · n = 236

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 = 236

ObjectiveMaximize common radius

Record comparison

common radius · Higher is better

Record	Value / interval	Author / holder	Source
External best known	[0.0339177352585, 0.0339177352595]	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

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236

0x1

VERIFIED CONSTRUCTIONr = 0.033917734

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": [
    [
      "0.033917735",
      "0.033917735"
    ],
    [
      "0.151412217",
      "0.033917735"
    ],
    [
      "0.268906698",
      "0.033917735"
    ],
    [
      "0.38640118",
      "0.033917735"
    ],
    [
      "0.503895661",
      "0.033917735"
    ],
    [
      "0.621390143",
      "0.033917735"
    ],
    [
      "0.734071146",
      "0.033917735"
    ],
    [
      "0.851565627",
      "0.033917735"
    ],
    [
      "0.96605558",
      "0.033946563"
    ],
    [
      "0.092664976",
      "0.067835471"
    ],
    [
      "0.210159457",
      "0.067835471"
    ],
    [
      "0.327653939",
      "0.067835471"
    ],
    [
      "0.44514842",
      "0.067835471"
    ],
    [
      "0.562642902",
      "0.067835471"
    ],
    [
      "0.792818387",
      "0.067835471"
    ],
    [
      "0.677730644",
      "0.071698669"
    ],
    [
      "0.907713252",
      "0.071984721"
    ],
    [
      "0.033917735",
      "0.101753206"
    ],
    [
      "0.151412217",
      "0.101753206"
    ],
    [
      "0.268906698",
      "0.101753206"
    ],
    [
      "0.38640118",
      "0.101753206"
    ],
    [
      "0.503895661",
      "0.101753206"
    ],
    [
      "0.618983404",
      "0.105616404"
    ],
    [
      "0.736477885",
      "0.105616404"
    ],
    [
      "0.848966011",
      "0.105902456"
    ],
    [
      "0.966082265",
      "0.106549289"
    ],
    [
      "0.092664976",
      "0.135670941"
    ],
    [
      "0.210159457",
      "0.135670941"
    ],
    [
      "0.327653939",
      "0.135670941"
    ],
    [
      "0.44514842",
      "0.135670941"
    ],
    [
      "0.560236163",
      "0.139534139"
    ],
    [
      "0.677730644",
      "0.139534139"
    ],
    [
      "0.907335024",
      "0.140467024"
    ],
    [
      "0.792625509",
      "0.143683389"
    ],
    [
      "0.033917735",
      "0.169588676"
    ],
    [
      "0.151412217",
      "0.169588676"
    ],
    [
      "0.268906698",
      "0.169588676"
    ],
    [
      "0.38640118",
      "0.169588676"
    ],
    [
      "0.501488922",
      "0.173451875"
    ],
    [
      "0.618983404",
      "0.173451875"
    ],
    [
      "0.966082265",
      "0.174384759"
    ],
    [
      "0.733878268",
      "0.177601125"
    ],
    [
      "0.850994522",
      "0.178247957"
    ],
    [
      "0.092664976",
      "0.203506412"
    ],
    [
      "0.210159457",
      "0.203506412"
    ],
    [
      "0.327653939",
      "0.203506412"
    ],
    [
      "0.442741681",
      "0.20736961"
    ],
    [
      "0.560236163",
      "0.20736961"
    ],
    [
      "0.675131028",
      "0.21151886"
    ],
    [
      "0.792247282",
      "0.212165693"
    ],
    [
      "0.909741763",
      "0.212165693"
    ],
    [
      "0.033917735",
      "0.237424147"
    ],
    [
      "0.151412217",
      "0.237424147"
    ],
    [
      "0.268906698",
      "0.237424147"
    ],
    [
      "0.383994441",
      "0.241287345"
    ],
    [
      "0.501488922",
      "0.241287345"
    ],
    [
      "0.616383787",
      "0.245436595"
    ],
    [
      "0.733500041",
      "0.246083428"
    ],
    [
      "0.850994522",
      "0.246083428"
    ],
    [
      "0.966082265",
      "0.249946626"
    ],
    [
      "0.092664976",
      "0.271341882"
    ],
    [
      "0.210159457",
      "0.271341882"
    ],
    [
      "0.3252472",
      "0.27520508"
    ],
    [
      "0.442741681",
      "0.27520508"
    ],
    [
      "0.557636546",
      "0.27935433"
    ],
    [
      "0.6747528",
      "0.280001163"
    ],
    [
      "0.792247282",
      "0.280001163"
    ],
    [
      "0.907335024",
      "0.283864361"
    ],
    [
      "0.033917735",
      "0.305259617"
    ],
    [
      "0.151412217",
      "0.305259617"
    ],
    [
      "0.266499959",
      "0.309122816"
    ],
    [
      "0.383994441",
      "0.309122816"
    ],
    [
      "0.498889305",
      "0.313272066"
    ],
    [
      "0.616005559",
      "0.313918898"
    ],
    [
      "0.733500041",
      "0.313918898"
    ],
    [
      "0.848587783",
      "0.317782097"
    ],
    [
      "0.966082265",
      "0.317782097"
    ],
    [
      "0.092664976",
      "0.339177353"
    ],
    [
      "0.207752718",
      "0.343040551"
    ],
    [
      "0.3252472",
      "0.343040551"
    ],
    [
      "0.440142065",
      "0.347189801"
    ],
    [
      "0.557258319",
      "0.347836634"
    ],
    [
      "0.6747528",
      "0.347836634"
    ],
    [
      "0.789840543",
      "0.351699832"
    ],
    [
      "0.907335024",
      "0.351699832"
    ],
    [
      "0.033917735",
      "0.373095088"
    ],
    [
      "0.149005478",
      "0.376958286"
    ],
    [
      "0.266499959",
      "0.376958286"
    ],
    [
      "0.381394824",
      "0.381107536"
    ],
    [
      "0.498511078",
      "0.381754369"
    ],
    [
      "0.616005559",
      "0.381754369"
    ],
    [
      "0.731093302",
      "0.385617567"
    ],
    [
      "0.848587783",
      "0.385617567"
    ],
    [
      "0.966082265",
      "0.385617567"
    ],
    [
      "0.090258237",
      "0.410876021"
    ],
    [
      "0.207752718",
      "0.410876021"
    ],
    [
      "0.322647583",
      "0.415025271"
    ],
    [
      "0.439763837",
      "0.415672104"
    ],
    [
      "0.557258319",
      "0.415672104"
    ],
    [
      "0.672346061",
      "0.419535302"
    ],
    [
      "0.789840543",
      "0.419535302"
    ],
    [
      "0.907335024",
      "0.419535302"
    ],
    [
      "0.149005478",
      "0.444793757"
    ],
    [
      "0.033917735",
      "0.448656955"
    ],
    [
      "0.263900342",
      "0.448943007"
    ],
    [
      "0.381016596",
      "0.449589839"
    ],
    [
      "0.498511078",
      "0.449589839"
    ],
    [
      "0.61359882",
      "0.453453038"
    ],
    [
      "0.731093302",
      "0.453453038"
    ],
    [
      "0.848587783",
      "0.453453038"
    ],
    [
      "0.966082265",
      "0.453453038"
    ],
    [
      "0.092664976",
      "0.48257469"
    ],
    [
      "0.205153102",
      "0.482860742"
    ],
    [
      "0.322269356",
      "0.483507575"
    ],
    [
      "0.439763837",
      "0.483507575"
    ],
    [
      "0.55485158",
      "0.487370773"
    ],
    [
      "0.672346061",
      "0.487370773"
    ],
    [
      "0.789840543",
      "0.487370773"
    ],
    [
      "0.907335024",
      "0.487370773"
    ],
    [
      "0.033917735",
      "0.516492425"
    ],
    [
      "0.263522115",
      "0.51742531"
    ],
    [
      "0.381016596",
      "0.51742531"
    ],
    [
      "0.1488126",
      "0.520641675"
    ],
    [
      "0.496104339",
      "0.521288508"
    ],
    [
      "0.61359882",
      "0.521288508"
    ],
    [
      "0.731093302",
      "0.521288508"
    ],
    [
      "0.848587783",
      "0.521288508"
    ],
    [
      "0.966082265",
      "0.521288508"
    ],
    [
      "0.322269356",
      "0.551343045"
    ],
    [
      "0.090065359",
      "0.554559411"
    ],
    [
      "0.207181613",
      "0.555206243"
    ],
    [
      "0.437357098",
      "0.555206243"
    ],
    [
      "0.55485158",
      "0.555206243"
    ],
    [
      "0.672346061",
      "0.555206243"
    ],
    [
      "0.789840543",
      "0.555206243"
    ],
    [
      "0.907335024",
      "0.555206243"
    ],
    [
      "0.148434373",
      "0.589123979"
    ],
    [
      "0.265928854",
      "0.589123979"
    ],
    [
      "0.378609857",
      "0.589123979"
    ],
    [
      "0.496104339",
      "0.589123979"
    ],
    [
      "0.61359882",
      "0.589123979"
    ],
    [
      "0.731093302",
      "0.589123979"
    ],
    [
      "0.848587783",
      "0.589123979"
    ],
    [
      "0.966082265",
      "0.589123979"
    ],
    [
      "0.033917735",
      "0.592626396"
    ],
    [
      "0.207181613",
      "0.623041714"
    ],
    [
      "0.437357098",
      "0.623041714"
    ],
    [
      "0.55485158",
      "0.623041714"
    ],
    [
      "0.672346061",
      "0.623041714"
    ],
    [
      "0.789840543",
      "0.623041714"
    ],
    [
      "0.907335024",
      "0.623041714"
    ],
    [
      "0.322269356",
      "0.626904912"
    ],
    [
      "0.092286748",
      "0.627190964"
    ],
    [
      "0.496104339",
      "0.656959449"
    ],
    [
      "0.61359882",
      "0.656959449"
    ],
    [
      "0.731093302",
      "0.656959449"
    ],
    [
      "0.848587783",
      "0.656959449"
    ],
    [
      "0.966082265",
      "0.656959449"
    ],
    [
      "0.263522115",
      "0.660822647"
    ],
    [
      "0.381016596",
      "0.660822647"
    ],
    [
      "0.151033989",
      "0.661108699"
    ],
    [
      "0.033917735",
      "0.661755532"
    ],
    [
      "0.55485158",
      "0.690877184"
    ],
    [
      "0.672346061",
      "0.690877184"
    ],
    [
      "0.789840543",
      "0.690877184"
    ],
    [
      "0.907335024",
      "0.690877184"
    ],
    [
      "0.322269356",
      "0.694740383"
    ],
    [
      "0.439763837",
      "0.694740383"
    ],
    [
      "0.092664976",
      "0.695673267"
    ],
    [
      "0.198398088",
      "0.709670961"
    ],
    [
      "0.61359882",
      "0.72479492"
    ],
    [
      "0.731093302",
      "0.72479492"
    ],
    [
      "0.848587783",
      "0.72479492"
    ],
    [
      "0.966082265",
      "0.72479492"
    ],
    [
      "0.263522115",
      "0.728658118"
    ],
    [
      "0.381016596",
      "0.728658118"
    ],
    [
      "0.498511078",
      "0.728658118"
    ],
    [
      "0.033917735",
      "0.729591003"
    ],
    [
      "0.138483253",
      "0.745696628"
    ],
    [
      "0.672346061",
      "0.758712655"
    ],
    [
      "0.789840543",
      "0.758712655"
    ],
    [
      "0.907335024",
      "0.758712655"
    ],
    [
      "0.322269356",
      "0.762575853"
    ],
    [
      "0.439763837",
      "0.762575853"
    ],
    [
      "0.557258319",
      "0.762575853"
    ],
    [
      "0.198398088",
      "0.777506431"
    ],
    [
      "0.079736012",
      "0.779614363"
    ],
    [
      "0.731093302",
      "0.79263039"
    ],
    [
      "0.848587783",
      "0.79263039"
    ],
    [
      "0.966082265",
      "0.79263039"
    ],
    [
      "0.263522115",
      "0.796493588"
    ],
    [
      "0.381016596",
      "0.796493588"
    ],
    [
      "0.498511078",
      "0.796493588"
    ],
    [
      "0.616005559",
      "0.796493588"
    ],
    [
      "0.138483253",
      "0.813532098"
    ],
    [
      "0.789840543",
      "0.826548125"
    ],
    [
      "0.907335024",
      "0.826548125"
    ],
    [
      "0.033917735",
      "0.829637723"
    ],
    [
      "0.322269356",
      "0.830411324"
    ],
    [
      "0.439763837",
      "0.830411324"
    ],
    [
      "0.557258319",
      "0.830411324"
    ],
    [
      "0.6747528",
      "0.830411324"
    ],
    [
      "0.198398088",
      "0.845341902"
    ],
    [
      "0.848587783",
      "0.860465861"
    ],
    [
      "0.966082265",
      "0.860465861"
    ],
    [
      "0.092664976",
      "0.863555459"
    ],
    [
      "0.263522115",
      "0.864329059"
    ],
    [
      "0.381016596",
      "0.864329059"
    ],
    [
      "0.498511078",
      "0.864329059"
    ],
    [
      "0.616005559",
      "0.864329059"
    ],
    [
      "0.733500041",
      "0.864329059"
    ],
    [
      "0.907335024",
      "0.894383596"
    ],
    [
      "0.033927626",
      "0.897499174"
    ],
    [
      "0.322269356",
      "0.898246794"
    ],
    [
      "0.439763837",
      "0.898246794"
    ],
    [
      "0.557258319",
      "0.898246794"
    ],
    [
      "0.6747528",
      "0.898246794"
    ],
    [
      "0.792247282",
      "0.898246794"
    ],
    [
      "0.147058648",
      "0.904089143"
    ],
    [
      "0.214516741",
      "0.911234542"
    ],
    [
      "0.966082265",
      "0.928301331"
    ],
    [
      "0.381016596",
      "0.932164529"
    ],
    [
      "0.498511078",
      "0.932164529"
    ],
    [
      "0.616005559",
      "0.932164529"
    ],
    [
      "0.733500041",
      "0.932164529"
    ],
    [
      "0.850994522",
      "0.932164529"
    ],
    [
      "0.033977295",
      "0.965354408"
    ],
    [
      "0.101928719",
      "0.965948303"
    ],
    [
      "0.174599597",
      "0.966082265"
    ],
    [
      "0.254433885",
      "0.966082265"
    ],
    [
      "0.322269356",
      "0.966082265"
    ],
    [
      "0.439763837",
      "0.966082265"
    ],
    [
      "0.557258319",
      "0.966082265"
    ],
    [
      "0.6747528",
      "0.966082265"
    ],
    [
      "0.792247282",
      "0.966082265"
    ],
    [
      "0.909741763",
      "0.966082265"
    ]
  ],
  "radius": "0.033917734"
}

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

Instance parameters

{
  "n": 236
}

Starter answer

{
  "centers": [
    [
      "0.033917735",
      "0.033917735"
    ],
    [
      "0.151412217",
      "0.033917735"
    ],
    [
      "0.268906698",
      "0.033917735"
    ],
    [
      "0.38640118",
      "0.033917735"
    ],
    [
      "0.503895661",
      "0.033917735"
    ],
    [
      "0.621390143",
      "0.033917735"
    ],
    [
      "0.734071146",
      "0.033917735"
    ],
    [
      "0.851565627",
      "0.033917735"
    ],
    [
      "0.96605558",
      "0.033946563"
    ],
    [
      "0.092664976",
      "0.067835471"
    ],
    [
      "0.210159457",
      "0.067835471"
    ],
    [
      "0.327653939",
      "0.067835471"
    ],
    [
      "0.44514842",
      "0.067835471"
    ],
    [
      "0.562642902",
      "0.067835471"
    ],
    [
      "0.792818387",
      "0.067835471"
    ],
    [
      "0.677730644",
      "0.071698669"
    ],
    [
      "0.907713252",
      "0.071984721"
    ],
    [
      "0.033917735",
      "0.101753206"
    ],
    [
      "0.151412217",
      "0.101753206"
    ],
    [
      "0.268906698",
      "0.101753206"
    ],
    [
      "0.38640118",
      "0.101753206"
    ],
    [
      "0.503895661",
      "0.101753206"
    ],
    [
      "0.618983404",
      "0.105616404"
    ],
    [
      "0.736477885",
      "0.105616404"
    ],
    [
      "0.848966011",
      "0.105902456"
    ],
    [
      "0.966082265",
      "0.106549289"
    ],
    [
      "0.092664976",
      "0.135670941"
    ],
    [
      "0.210159457",
      "0.135670941"
    ],
    [
      "0.327653939",
      "0.135670941"
    ],
    [
      "0.44514842",
      "0.135670941"
    ],
    [
      "0.560236163",
      "0.139534139"
    ],
    [
      "0.677730644",
      "0.139534139"
    ],
    [
      "0.907335024",
      "0.140467024"
    ],
    [
      "0.792625509",
      "0.143683389"
    ],
    [
      "0.033917735",
      "0.169588676"
    ],
    [
      "0.151412217",
      "0.169588676"
    ],
    [
      "0.268906698",
      "0.169588676"
    ],
    [
      "0.38640118",
      "0.169588676"
    ],
    [
      "0.501488922",
      "0.173451875"
    ],
    [
      "0.618983404",
      "0.173451875"
    ],
    [
      "0.966082265",
      "0.174384759"
    ],
    [
      "0.733878268",
      "0.177601125"
    ],
    [
      "0.850994522",
      "0.178247957"
    ],
    [
      "0.092664976",
      "0.203506412"
    ],
    [
      "0.210159457",
      "0.203506412"
    ],
    [
      "0.327653939",
      "0.203506412"
    ],
    [
      "0.442741681",
      "0.20736961"
    ],
    [
      "0.560236163",
      "0.20736961"
    ],
    [
      "0.675131028",
      "0.21151886"
    ],
    [
      "0.792247282",
      "0.212165693"
    ],
    [
      "0.909741763",
      "0.212165693"
    ],
    [
      "0.033917735",
      "0.237424147"
    ],
    [
      "0.151412217",
      "0.237424147"
    ],
    [
      "0.268906698",
      "0.237424147"
    ],
    [
      "0.383994441",
      "0.241287345"
    ],
    [
      "0.501488922",
      "0.241287345"
    ],
    [
      "0.616383787",
      "0.245436595"
    ],
    [
      "0.733500041",
      "0.246083428"
    ],
    [
      "0.850994522",
      "0.246083428"
    ],
    [
      "0.966082265",
      "0.249946626"
    ],
    [
      "0.092664976",
      "0.271341882"
    ],
    [
      "0.210159457",
      "0.271341882"
    ],
    [
      "0.3252472",
      "0.27520508"
    ],
    [
      "0.442741681",
      "0.27520508"
    ],
    [
      "0.557636546",
      "0.27935433"
    ],
    [
      "0.6747528",
      "0.280001163"
    ],
    [
      "0.792247282",
      "0.280001163"
    ],
    [
      "0.907335024",
      "0.283864361"
    ],
    [
      "0.033917735",
      "0.305259617"
    ],
    [
      "0.151412217",
      "0.305259617"
    ],
    [
      "0.266499959",
      "0.309122816"
    ],
    [
      "0.383994441",
      "0.309122816"
    ],
    [
      "0.498889305",
      "0.313272066"
    ],
    [
      "0.616005559",
      "0.313918898"
    ],
    [
      "0.733500041",
      "0.313918898"
    ],
    [
      "0.848587783",
      "0.317782097"
    ],
    [
      "0.966082265",
      "0.317782097"
    ],
    [
      "0.092664976",
      "0.339177353"
    ],
    [
      "0.207752718",
      "0.343040551"
    ],
    [
      "0.3252472",
      "0.343040551"
    ],
    [
      "0.440142065",
      "0.347189801"
    ],
    [
      "0.557258319",
      "0.347836634"
    ],
    [
      "0.6747528",
      "0.347836634"
    ],
    [
      "0.789840543",
      "0.351699832"
    ],
    [
      "0.907335024",
      "0.351699832"
    ],
    [
      "0.033917735",
      "0.373095088"
    ],
    [
      "0.149005478",
      "0.376958286"
    ],
    [
      "0.266499959",
      "0.376958286"
    ],
    [
      "0.381394824",
      "0.381107536"
    ],
    [
      "0.498511078",
      "0.381754369"
    ],
    [
      "0.616005559",
      "0.381754369"
    ],
    [
      "0.731093302",
      "0.385617567"
    ],
    [
      "0.848587783",
      "0.385617567"
    ],
    [
      "0.966082265",
      "0.385617567"
    ],
    [
      "0.090258237",
      "0.410876021"
    ],
    [
      "0.207752718",
      "0.410876021"
    ],
    [
      "0.322647583",
      "0.415025271"
    ],
    [
      "0.439763837",
      "0.415672104"
    ],
    [
      "0.557258319",
      "0.415672104"
    ],
    [
      "0.672346061",
      "0.419535302"
    ],
    [
      "0.789840543",
      "0.419535302"
    ],
    [
      "0.907335024",
      "0.419535302"
    ],
    [
      "0.149005478",
      "0.444793757"
    ],
    [
      "0.033917735",
      "0.448656955"
    ],
    [
      "0.263900342",
      "0.448943007"
    ],
    [
      "0.381016596",
      "0.449589839"
    ],
    [
      "0.498511078",
      "0.449589839"
    ],
    [
      "0.61359882",
      "0.453453038"
    ],
    [
      "0.731093302",
      "0.453453038"
    ],
    [
      "0.848587783",
      "0.453453038"
    ],
    [
      "0.966082265",
      "0.453453038"
    ],
    [
      "0.092664976",
      "0.48257469"
    ],
    [
      "0.205153102",
      "0.482860742"
    ],
    [
      "0.322269356",
      "0.483507575"
    ],
    [
      "0.439763837",
      "0.483507575"
    ],
    [
      "0.55485158",
      "0.487370773"
    ],
    [
      "0.672346061",
      "0.487370773"
    ],
    [
      "0.789840543",
      "0.487370773"
    ],
    [
      "0.907335024",
      "0.487370773"
    ],
    [
      "0.033917735",
      "0.516492425"
    ],
    [
      "0.263522115",
      "0.51742531"
    ],
    [
      "0.381016596",
      "0.51742531"
    ],
    [
      "0.1488126",
      "0.520641675"
    ],
    [
      "0.496104339",
      "0.521288508"
    ],
    [
      "0.61359882",
      "0.521288508"
    ],
    [
      "0.731093302",
      "0.521288508"
    ],
    [
      "0.848587783",
      "0.521288508"
    ],
    [
      "0.966082265",
      "0.521288508"
    ],
    [
      "0.322269356",
      "0.551343045"
    ],
    [
      "0.090065359",
      "0.554559411"
    ],
    [
      "0.207181613",
      "0.555206243"
    ],
    [
      "0.437357098",
      "0.555206243"
    ],
    [
      "0.55485158",
      "0.555206243"
    ],
    [
      "0.672346061",
      "0.555206243"
    ],
    [
      "0.789840543",
      "0.555206243"
    ],
    [
      "0.907335024",
      "0.555206243"
    ],
    [
      "0.148434373",
      "0.589123979"
    ],
    [
      "0.265928854",
      "0.589123979"
    ],
    [
      "0.378609857",
      "0.589123979"
    ],
    [
      "0.496104339",
      "0.589123979"
    ],
    [
      "0.61359882",
      "0.589123979"
    ],
    [
      "0.731093302",
      "0.589123979"
    ],
    [
      "0.848587783",
      "0.589123979"
    ],
    [
      "0.966082265",
      "0.589123979"
    ],
    [
      "0.033917735",
      "0.592626396"
    ],
    [
      "0.207181613",
      "0.623041714"
    ],
    [
      "0.437357098",
      "0.623041714"
    ],
    [
      "0.55485158",
      "0.623041714"
    ],
    [
      "0.672346061",
      "0.623041714"
    ],
    [
      "0.789840543",
      "0.623041714"
    ],
    [
      "0.907335024",
      "0.623041714"
    ],
    [
      "0.322269356",
      "0.626904912"
    ],
    [
      "0.092286748",
      "0.627190964"
    ],
    [
      "0.496104339",
      "0.656959449"
    ],
    [
      "0.61359882",
      "0.656959449"
    ],
    [
      "0.731093302",
      "0.656959449"
    ],
    [
      "0.848587783",
      "0.656959449"
    ],
    [
      "0.966082265",
      "0.656959449"
    ],
    [
      "0.263522115",
      "0.660822647"
    ],
    [
      "0.381016596",
      "0.660822647"
    ],
    [
      "0.151033989",
      "0.661108699"
    ],
    [
      "0.033917735",
      "0.661755532"
    ],
    [
      "0.55485158",
      "0.690877184"
    ],
    [
      "0.672346061",
      "0.690877184"
    ],
    [
      "0.789840543",
      "0.690877184"
    ],
    [
      "0.907335024",
      "0.690877184"
    ],
    [
      "0.322269356",
      "0.694740383"
    ],
    [
      "0.439763837",
      "0.694740383"
    ],
    [
      "0.092664976",
      "0.695673267"
    ],
    [
      "0.198398088",
      "0.709670961"
    ],
    [
      "0.61359882",
      "0.72479492"
    ],
    [
      "0.731093302",
      "0.72479492"
    ],
    [
      "0.848587783",
      "0.72479492"
    ],
    [
      "0.966082265",
      "0.72479492"
    ],
    [
      "0.263522115",
      "0.728658118"
    ],
    [
      "0.381016596",
      "0.728658118"
    ],
    [
      "0.498511078",
      "0.728658118"
    ],
    [
      "0.033917735",
      "0.729591003"
    ],
    [
      "0.138483253",
      "0.745696628"
    ],
    [
      "0.672346061",
      "0.758712655"
    ],
    [
      "0.789840543",
      "0.758712655"
    ],
    [
      "0.907335024",
      "0.758712655"
    ],
    [
      "0.322269356",
      "0.762575853"
    ],
    [
      "0.439763837",
      "0.762575853"
    ],
    [
      "0.557258319",
      "0.762575853"
    ],
    [
      "0.198398088",
      "0.777506431"
    ],
    [
      "0.079736012",
      "0.779614363"
    ],
    [
      "0.731093302",
      "0.79263039"
    ],
    [
      "0.848587783",
      "0.79263039"
    ],
    [
      "0.966082265",
      "0.79263039"
    ],
    [
      "0.263522115",
      "0.796493588"
    ],
    [
      "0.381016596",
      "0.796493588"
    ],
    [
      "0.498511078",
      "0.796493588"
    ],
    [
      "0.616005559",
      "0.796493588"
    ],
    [
      "0.138483253",
      "0.813532098"
    ],
    [
      "0.789840543",
      "0.826548125"
    ],
    [
      "0.907335024",
      "0.826548125"
    ],
    [
      "0.033917735",
      "0.829637723"
    ],
    [
      "0.322269356",
      "0.830411324"
    ],
    [
      "0.439763837",
      "0.830411324"
    ],
    [
      "0.557258319",
      "0.830411324"
    ],
    [
      "0.6747528",
      "0.830411324"
    ],
    [
      "0.198398088",
      "0.845341902"
    ],
    [
      "0.848587783",
      "0.860465861"
    ],
    [
      "0.966082265",
      "0.860465861"
    ],
    [
      "0.092664976",
      "0.863555459"
    ],
    [
      "0.263522115",
      "0.864329059"
    ],
    [
      "0.381016596",
      "0.864329059"
    ],
    [
      "0.498511078",
      "0.864329059"
    ],
    [
      "0.616005559",
      "0.864329059"
    ],
    [
      "0.733500041",
      "0.864329059"
    ],
    [
      "0.907335024",
      "0.894383596"
    ],
    [
      "0.033927626",
      "0.897499174"
    ],
    [
      "0.322269356",
      "0.898246794"
    ],
    [
      "0.439763837",
      "0.898246794"
    ],
    [
      "0.557258319",
      "0.898246794"
    ],
    [
      "0.6747528",
      "0.898246794"
    ],
    [
      "0.792247282",
      "0.898246794"
    ],
    [
      "0.147058648",
      "0.904089143"
    ],
    [
      "0.214516741",
      "0.911234542"
    ],
    [
      "0.966082265",
      "0.928301331"
    ],
    [
      "0.381016596",
      "0.932164529"
    ],
    [
      "0.498511078",
      "0.932164529"
    ],
    [
      "0.616005559",
      "0.932164529"
    ],
    [
      "0.733500041",
      "0.932164529"
    ],
    [
      "0.850994522",
      "0.932164529"
    ],
    [
      "0.033977295",
      "0.965354408"
    ],
    [
      "0.101928719",
      "0.965948303"
    ],
    [
      "0.174599597",
      "0.966082265"
    ],
    [
      "0.254433885",
      "0.966082265"
    ],
    [
      "0.322269356",
      "0.966082265"
    ],
    [
      "0.439763837",
      "0.966082265"
    ],
    [
      "0.557258319",
      "0.966082265"
    ],
    [
      "0.6747528",
      "0.966082265"
    ],
    [
      "0.792247282",
      "0.966082265"
    ],
    [
      "0.909741763",
      "0.966082265"
    ]
  ],
  "radius": "0.033917734"
}

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