P01 · Packing and covering · Classic · Hard

Equal-circle packing in a unit square · n = 270

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 = 270

ObjectiveMaximize common radius

Record comparison

common radius · Higher is better

Record	Value / interval	Author / holder	Source
External best known	[0.0319170304485, 0.0319170304495]	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

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270

0x1

VERIFIED CONSTRUCTIONr = 0.031917030

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": [
    [
      "0.03191703",
      "0.03191703"
    ],
    [
      "0.142480867",
      "0.03191703"
    ],
    [
      "0.252008512",
      "0.03191703"
    ],
    [
      "0.362572348",
      "0.03191703"
    ],
    [
      "0.472099993",
      "0.03191703"
    ],
    [
      "0.582663829",
      "0.03191703"
    ],
    [
      "0.693227666",
      "0.03191703"
    ],
    [
      "0.802755311",
      "0.03191703"
    ],
    [
      "0.913319147",
      "0.03191703"
    ],
    [
      "0.087198949",
      "0.063834061"
    ],
    [
      "0.30729043",
      "0.063834061"
    ],
    [
      "0.527381911",
      "0.063834061"
    ],
    [
      "0.637945748",
      "0.063834061"
    ],
    [
      "0.858037229",
      "0.063834061"
    ],
    [
      "0.197244689",
      "0.064715066"
    ],
    [
      "0.417336171",
      "0.064715066"
    ],
    [
      "0.747991488",
      "0.064715066"
    ],
    [
      "0.96808297",
      "0.064715066"
    ],
    [
      "0.03191703",
      "0.095751091"
    ],
    [
      "0.582663829",
      "0.095751091"
    ],
    [
      "0.141962771",
      "0.096632096"
    ],
    [
      "0.252526608",
      "0.096632096"
    ],
    [
      "0.362054252",
      "0.096632096"
    ],
    [
      "0.472618089",
      "0.096632096"
    ],
    [
      "0.69270957",
      "0.096632096"
    ],
    [
      "0.803273407",
      "0.096632096"
    ],
    [
      "0.912801051",
      "0.096632096"
    ],
    [
      "0.086680853",
      "0.128549126"
    ],
    [
      "0.197244689",
      "0.128549126"
    ],
    [
      "0.637427652",
      "0.128549126"
    ],
    [
      "0.747991488",
      "0.128549126"
    ],
    [
      "0.417336171",
      "0.128549126"
    ],
    [
      "0.527900007",
      "0.128549126"
    ],
    [
      "0.96808297",
      "0.128549126"
    ],
    [
      "0.30729043",
      "0.129430131"
    ],
    [
      "0.858037229",
      "0.129430131"
    ],
    [
      "0.141962771",
      "0.160466157"
    ],
    [
      "0.472618089",
      "0.160466157"
    ],
    [
      "0.69270957",
      "0.160466157"
    ],
    [
      "0.03191703",
      "0.161347162"
    ],
    [
      "0.252008512",
      "0.161347162"
    ],
    [
      "0.362572348",
      "0.161347162"
    ],
    [
      "0.582663829",
      "0.161347162"
    ],
    [
      "0.802755311",
      "0.161347162"
    ],
    [
      "0.913319147",
      "0.161347162"
    ],
    [
      "0.087198949",
      "0.193264192"
    ],
    [
      "0.196726593",
      "0.193264192"
    ],
    [
      "0.30729043",
      "0.193264192"
    ],
    [
      "0.417854267",
      "0.193264192"
    ],
    [
      "0.527381911",
      "0.193264192"
    ],
    [
      "0.637945748",
      "0.193264192"
    ],
    [
      "0.747473392",
      "0.193264192"
    ],
    [
      "0.858037229",
      "0.193264192"
    ],
    [
      "0.96808297",
      "0.194145197"
    ],
    [
      "0.03191703",
      "0.225181222"
    ],
    [
      "0.252008512",
      "0.225181222"
    ],
    [
      "0.362572348",
      "0.225181222"
    ],
    [
      "0.582663829",
      "0.225181222"
    ],
    [
      "0.802755311",
      "0.225181222"
    ],
    [
      "0.141962771",
      "0.226062227"
    ],
    [
      "0.472618089",
      "0.226062227"
    ],
    [
      "0.69270957",
      "0.226062227"
    ],
    [
      "0.912801051",
      "0.226062227"
    ],
    [
      "0.30729043",
      "0.257098253"
    ],
    [
      "0.086680853",
      "0.257979258"
    ],
    [
      "0.197244689",
      "0.257979258"
    ],
    [
      "0.417336171",
      "0.257979258"
    ],
    [
      "0.527900007",
      "0.257979258"
    ],
    [
      "0.637427652",
      "0.257979258"
    ],
    [
      "0.747991488",
      "0.257979258"
    ],
    [
      "0.857519133",
      "0.257979258"
    ],
    [
      "0.96808297",
      "0.257979258"
    ],
    [
      "0.141962771",
      "0.289896288"
    ],
    [
      "0.252526608",
      "0.289896288"
    ],
    [
      "0.362054252",
      "0.289896288"
    ],
    [
      "0.472618089",
      "0.289896288"
    ],
    [
      "0.69270957",
      "0.289896288"
    ],
    [
      "0.912801051",
      "0.289896288"
    ],
    [
      "0.03191703",
      "0.290777293"
    ],
    [
      "0.582663829",
      "0.290777293"
    ],
    [
      "0.802755311",
      "0.290777293"
    ],
    [
      "0.197244689",
      "0.321813319"
    ],
    [
      "0.417336171",
      "0.321813319"
    ],
    [
      "0.96808297",
      "0.321813319"
    ],
    [
      "0.30729043",
      "0.322694323"
    ],
    [
      "0.527381911",
      "0.322694323"
    ],
    [
      "0.747473392",
      "0.322694323"
    ],
    [
      "0.858037229",
      "0.322694323"
    ],
    [
      "0.087198949",
      "0.322694323"
    ],
    [
      "0.637945748",
      "0.322694323"
    ],
    [
      "0.03191703",
      "0.354611354"
    ],
    [
      "0.142480867",
      "0.354611354"
    ],
    [
      "0.252008512",
      "0.354611354"
    ],
    [
      "0.362572348",
      "0.354611354"
    ],
    [
      "0.472099993",
      "0.354611354"
    ],
    [
      "0.582663829",
      "0.354611354"
    ],
    [
      "0.802755311",
      "0.354611354"
    ],
    [
      "0.913319147",
      "0.354611354"
    ],
    [
      "0.69270957",
      "0.355492358"
    ],
    [
      "0.087198949",
      "0.386528384"
    ],
    [
      "0.30729043",
      "0.386528384"
    ],
    [
      "0.527381911",
      "0.386528384"
    ],
    [
      "0.858037229",
      "0.386528384"
    ],
    [
      "0.197244689",
      "0.387409389"
    ],
    [
      "0.417336171",
      "0.387409389"
    ],
    [
      "0.637427652",
      "0.387409389"
    ],
    [
      "0.747991488",
      "0.387409389"
    ],
    [
      "0.96808297",
      "0.387409389"
    ],
    [
      "0.03191703",
      "0.418445415"
    ],
    [
      "0.141962771",
      "0.419326419"
    ],
    [
      "0.252526608",
      "0.419326419"
    ],
    [
      "0.362054252",
      "0.419326419"
    ],
    [
      "0.472618089",
      "0.419326419"
    ],
    [
      "0.582145733",
      "0.419326419"
    ],
    [
      "0.69270957",
      "0.419326419"
    ],
    [
      "0.803273407",
      "0.419326419"
    ],
    [
      "0.912801051",
      "0.419326419"
    ],
    [
      "0.086680853",
      "0.45124345"
    ],
    [
      "0.197244689",
      "0.45124345"
    ],
    [
      "0.417336171",
      "0.45124345"
    ],
    [
      "0.637427652",
      "0.45124345"
    ],
    [
      "0.747991488",
      "0.45124345"
    ],
    [
      "0.96808297",
      "0.45124345"
    ],
    [
      "0.30729043",
      "0.452124454"
    ],
    [
      "0.527381911",
      "0.452124454"
    ],
    [
      "0.858037229",
      "0.452124454"
    ],
    [
      "0.141962771",
      "0.48316048"
    ],
    [
      "0.69270957",
      "0.48316048"
    ],
    [
      "0.03191703",
      "0.484041485"
    ],
    [
      "0.252008512",
      "0.484041485"
    ],
    [
      "0.362572348",
      "0.484041485"
    ],
    [
      "0.472099993",
      "0.484041485"
    ],
    [
      "0.582663829",
      "0.484041485"
    ],
    [
      "0.802755311",
      "0.484041485"
    ],
    [
      "0.913319147",
      "0.484041485"
    ],
    [
      "0.087198949",
      "0.515958515"
    ],
    [
      "0.196726593",
      "0.515958515"
    ],
    [
      "0.30729043",
      "0.515958515"
    ],
    [
      "0.527381911",
      "0.515958515"
    ],
    [
      "0.637945748",
      "0.515958515"
    ],
    [
      "0.747473392",
      "0.515958515"
    ],
    [
      "0.858037229",
      "0.515958515"
    ],
    [
      "0.417336171",
      "0.51683952"
    ],
    [
      "0.96808297",
      "0.51683952"
    ],
    [
      "0.03191703",
      "0.547875546"
    ],
    [
      "0.252008512",
      "0.547875546"
    ],
    [
      "0.582663829",
      "0.547875546"
    ],
    [
      "0.802755311",
      "0.547875546"
    ],
    [
      "0.141962771",
      "0.54875655"
    ],
    [
      "0.362054252",
      "0.54875655"
    ],
    [
      "0.472618089",
      "0.54875655"
    ],
    [
      "0.69270957",
      "0.54875655"
    ],
    [
      "0.912801051",
      "0.54875655"
    ],
    [
      "0.086680853",
      "0.580673581"
    ],
    [
      "0.197244689",
      "0.580673581"
    ],
    [
      "0.417336171",
      "0.580673581"
    ],
    [
      "0.527900007",
      "0.580673581"
    ],
    [
      "0.637427652",
      "0.580673581"
    ],
    [
      "0.747991488",
      "0.580673581"
    ],
    [
      "0.857519133",
      "0.580673581"
    ],
    [
      "0.96808297",
      "0.580673581"
    ],
    [
      "0.306772334",
      "0.580673581"
    ],
    [
      "0.141962771",
      "0.612590611"
    ],
    [
      "0.472618089",
      "0.612590611"
    ],
    [
      "0.69270957",
      "0.612590611"
    ],
    [
      "0.912801051",
      "0.612590611"
    ],
    [
      "0.362054252",
      "0.612590611"
    ],
    [
      "0.03191703",
      "0.613471616"
    ],
    [
      "0.252008512",
      "0.613471616"
    ],
    [
      "0.582663829",
      "0.613471616"
    ],
    [
      "0.802755311",
      "0.613471616"
    ],
    [
      "0.417336171",
      "0.644507642"
    ],
    [
      "0.96808297",
      "0.644507642"
    ],
    [
      "0.087198949",
      "0.645388646"
    ],
    [
      "0.196726593",
      "0.645388646"
    ],
    [
      "0.30729043",
      "0.645388646"
    ],
    [
      "0.527381911",
      "0.645388646"
    ],
    [
      "0.637945748",
      "0.645388646"
    ],
    [
      "0.747473392",
      "0.645388646"
    ],
    [
      "0.858037229",
      "0.645388646"
    ],
    [
      "0.252008512",
      "0.677305677"
    ],
    [
      "0.362572348",
      "0.677305677"
    ],
    [
      "0.03191703",
      "0.677305677"
    ],
    [
      "0.472099993",
      "0.677305677"
    ],
    [
      "0.582663829",
      "0.677305677"
    ],
    [
      "0.802755311",
      "0.677305677"
    ],
    [
      "0.913319147",
      "0.677305677"
    ],
    [
      "0.141962771",
      "0.678186681"
    ],
    [
      "0.69270957",
      "0.678186681"
    ],
    [
      "0.30729043",
      "0.709222707"
    ],
    [
      "0.527381911",
      "0.709222707"
    ],
    [
      "0.858037229",
      "0.709222707"
    ],
    [
      "0.086680853",
      "0.710103712"
    ],
    [
      "0.197244689",
      "0.710103712"
    ],
    [
      "0.417336171",
      "0.710103712"
    ],
    [
      "0.637427652",
      "0.710103712"
    ],
    [
      "0.747991488",
      "0.710103712"
    ],
    [
      "0.96808297",
      "0.710103712"
    ],
    [
      "0.141962771",
      "0.742020742"
    ],
    [
      "0.252526608",
      "0.742020742"
    ],
    [
      "0.362054252",
      "0.742020742"
    ],
    [
      "0.472618089",
      "0.742020742"
    ],
    [
      "0.582145733",
      "0.742020742"
    ],
    [
      "0.69270957",
      "0.742020742"
    ],
    [
      "0.803273407",
      "0.742020742"
    ],
    [
      "0.912801051",
      "0.742020742"
    ],
    [
      "0.03191703",
      "0.742901747"
    ],
    [
      "0.197244689",
      "0.773937773"
    ],
    [
      "0.417336171",
      "0.773937773"
    ],
    [
      "0.637427652",
      "0.773937773"
    ],
    [
      "0.747991488",
      "0.773937773"
    ],
    [
      "0.96808297",
      "0.773937773"
    ],
    [
      "0.087198949",
      "0.774818778"
    ],
    [
      "0.30729043",
      "0.774818778"
    ],
    [
      "0.527381911",
      "0.774818778"
    ],
    [
      "0.858037229",
      "0.774818778"
    ],
    [
      "0.69270957",
      "0.805854803"
    ],
    [
      "0.03191703",
      "0.806735808"
    ],
    [
      "0.142480867",
      "0.806735808"
    ],
    [
      "0.252008512",
      "0.806735808"
    ],
    [
      "0.362572348",
      "0.806735808"
    ],
    [
      "0.472099993",
      "0.806735808"
    ],
    [
      "0.582663829",
      "0.806735808"
    ],
    [
      "0.802755311",
      "0.806735808"
    ],
    [
      "0.913319147",
      "0.806735808"
    ],
    [
      "0.087198949",
      "0.838652838"
    ],
    [
      "0.30729043",
      "0.838652838"
    ],
    [
      "0.527381911",
      "0.838652838"
    ],
    [
      "0.637945748",
      "0.838652838"
    ],
    [
      "0.747473392",
      "0.838652838"
    ],
    [
      "0.858037229",
      "0.838652838"
    ],
    [
      "0.197244689",
      "0.839533843"
    ],
    [
      "0.417336171",
      "0.839533843"
    ],
    [
      "0.96808297",
      "0.839533843"
    ],
    [
      "0.03191703",
      "0.870569869"
    ],
    [
      "0.582663829",
      "0.870569869"
    ],
    [
      "0.802755311",
      "0.870569869"
    ],
    [
      "0.69270957",
      "0.871450874"
    ],
    [
      "0.141962771",
      "0.871450874"
    ],
    [
      "0.252526608",
      "0.871450874"
    ],
    [
      "0.362054252",
      "0.871450874"
    ],
    [
      "0.472618089",
      "0.871450874"
    ],
    [
      "0.912801051",
      "0.871450874"
    ],
    [
      "0.086680853",
      "0.903367904"
    ],
    [
      "0.197244689",
      "0.903367904"
    ],
    [
      "0.417336171",
      "0.903367904"
    ],
    [
      "0.527900007",
      "0.903367904"
    ],
    [
      "0.637427652",
      "0.903367904"
    ],
    [
      "0.747991488",
      "0.903367904"
    ],
    [
      "0.857519133",
      "0.903367904"
    ],
    [
      "0.96808297",
      "0.903367904"
    ],
    [
      "0.30729043",
      "0.904248909"
    ],
    [
      "0.141962771",
      "0.935284934"
    ],
    [
      "0.472618089",
      "0.935284934"
    ],
    [
      "0.69270957",
      "0.935284934"
    ],
    [
      "0.912801051",
      "0.935284934"
    ],
    [
      "0.03191703",
      "0.936165939"
    ],
    [
      "0.252008512",
      "0.936165939"
    ],
    [
      "0.362572348",
      "0.936165939"
    ],
    [
      "0.582663829",
      "0.936165939"
    ],
    [
      "0.802755311",
      "0.936165939"
    ],
    [
      "0.968082023",
      "0.968082023"
    ],
    [
      "0.087198949",
      "0.96808297"
    ],
    [
      "0.196726593",
      "0.96808297"
    ],
    [
      "0.30729043",
      "0.96808297"
    ],
    [
      "0.417854267",
      "0.96808297"
    ],
    [
      "0.527381911",
      "0.96808297"
    ],
    [
      "0.637945748",
      "0.96808297"
    ],
    [
      "0.747473392",
      "0.96808297"
    ],
    [
      "0.858037229",
      "0.96808297"
    ]
  ],
  "radius": "0.03191703"
}

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

Instance parameters

{
  "n": 270
}

Starter answer

{
  "centers": [
    [
      "0.03191703",
      "0.03191703"
    ],
    [
      "0.142480867",
      "0.03191703"
    ],
    [
      "0.252008512",
      "0.03191703"
    ],
    [
      "0.362572348",
      "0.03191703"
    ],
    [
      "0.472099993",
      "0.03191703"
    ],
    [
      "0.582663829",
      "0.03191703"
    ],
    [
      "0.693227666",
      "0.03191703"
    ],
    [
      "0.802755311",
      "0.03191703"
    ],
    [
      "0.913319147",
      "0.03191703"
    ],
    [
      "0.087198949",
      "0.063834061"
    ],
    [
      "0.30729043",
      "0.063834061"
    ],
    [
      "0.527381911",
      "0.063834061"
    ],
    [
      "0.637945748",
      "0.063834061"
    ],
    [
      "0.858037229",
      "0.063834061"
    ],
    [
      "0.197244689",
      "0.064715066"
    ],
    [
      "0.417336171",
      "0.064715066"
    ],
    [
      "0.747991488",
      "0.064715066"
    ],
    [
      "0.96808297",
      "0.064715066"
    ],
    [
      "0.03191703",
      "0.095751091"
    ],
    [
      "0.582663829",
      "0.095751091"
    ],
    [
      "0.141962771",
      "0.096632096"
    ],
    [
      "0.252526608",
      "0.096632096"
    ],
    [
      "0.362054252",
      "0.096632096"
    ],
    [
      "0.472618089",
      "0.096632096"
    ],
    [
      "0.69270957",
      "0.096632096"
    ],
    [
      "0.803273407",
      "0.096632096"
    ],
    [
      "0.912801051",
      "0.096632096"
    ],
    [
      "0.086680853",
      "0.128549126"
    ],
    [
      "0.197244689",
      "0.128549126"
    ],
    [
      "0.637427652",
      "0.128549126"
    ],
    [
      "0.747991488",
      "0.128549126"
    ],
    [
      "0.417336171",
      "0.128549126"
    ],
    [
      "0.527900007",
      "0.128549126"
    ],
    [
      "0.96808297",
      "0.128549126"
    ],
    [
      "0.30729043",
      "0.129430131"
    ],
    [
      "0.858037229",
      "0.129430131"
    ],
    [
      "0.141962771",
      "0.160466157"
    ],
    [
      "0.472618089",
      "0.160466157"
    ],
    [
      "0.69270957",
      "0.160466157"
    ],
    [
      "0.03191703",
      "0.161347162"
    ],
    [
      "0.252008512",
      "0.161347162"
    ],
    [
      "0.362572348",
      "0.161347162"
    ],
    [
      "0.582663829",
      "0.161347162"
    ],
    [
      "0.802755311",
      "0.161347162"
    ],
    [
      "0.913319147",
      "0.161347162"
    ],
    [
      "0.087198949",
      "0.193264192"
    ],
    [
      "0.196726593",
      "0.193264192"
    ],
    [
      "0.30729043",
      "0.193264192"
    ],
    [
      "0.417854267",
      "0.193264192"
    ],
    [
      "0.527381911",
      "0.193264192"
    ],
    [
      "0.637945748",
      "0.193264192"
    ],
    [
      "0.747473392",
      "0.193264192"
    ],
    [
      "0.858037229",
      "0.193264192"
    ],
    [
      "0.96808297",
      "0.194145197"
    ],
    [
      "0.03191703",
      "0.225181222"
    ],
    [
      "0.252008512",
      "0.225181222"
    ],
    [
      "0.362572348",
      "0.225181222"
    ],
    [
      "0.582663829",
      "0.225181222"
    ],
    [
      "0.802755311",
      "0.225181222"
    ],
    [
      "0.141962771",
      "0.226062227"
    ],
    [
      "0.472618089",
      "0.226062227"
    ],
    [
      "0.69270957",
      "0.226062227"
    ],
    [
      "0.912801051",
      "0.226062227"
    ],
    [
      "0.30729043",
      "0.257098253"
    ],
    [
      "0.086680853",
      "0.257979258"
    ],
    [
      "0.197244689",
      "0.257979258"
    ],
    [
      "0.417336171",
      "0.257979258"
    ],
    [
      "0.527900007",
      "0.257979258"
    ],
    [
      "0.637427652",
      "0.257979258"
    ],
    [
      "0.747991488",
      "0.257979258"
    ],
    [
      "0.857519133",
      "0.257979258"
    ],
    [
      "0.96808297",
      "0.257979258"
    ],
    [
      "0.141962771",
      "0.289896288"
    ],
    [
      "0.252526608",
      "0.289896288"
    ],
    [
      "0.362054252",
      "0.289896288"
    ],
    [
      "0.472618089",
      "0.289896288"
    ],
    [
      "0.69270957",
      "0.289896288"
    ],
    [
      "0.912801051",
      "0.289896288"
    ],
    [
      "0.03191703",
      "0.290777293"
    ],
    [
      "0.582663829",
      "0.290777293"
    ],
    [
      "0.802755311",
      "0.290777293"
    ],
    [
      "0.197244689",
      "0.321813319"
    ],
    [
      "0.417336171",
      "0.321813319"
    ],
    [
      "0.96808297",
      "0.321813319"
    ],
    [
      "0.30729043",
      "0.322694323"
    ],
    [
      "0.527381911",
      "0.322694323"
    ],
    [
      "0.747473392",
      "0.322694323"
    ],
    [
      "0.858037229",
      "0.322694323"
    ],
    [
      "0.087198949",
      "0.322694323"
    ],
    [
      "0.637945748",
      "0.322694323"
    ],
    [
      "0.03191703",
      "0.354611354"
    ],
    [
      "0.142480867",
      "0.354611354"
    ],
    [
      "0.252008512",
      "0.354611354"
    ],
    [
      "0.362572348",
      "0.354611354"
    ],
    [
      "0.472099993",
      "0.354611354"
    ],
    [
      "0.582663829",
      "0.354611354"
    ],
    [
      "0.802755311",
      "0.354611354"
    ],
    [
      "0.913319147",
      "0.354611354"
    ],
    [
      "0.69270957",
      "0.355492358"
    ],
    [
      "0.087198949",
      "0.386528384"
    ],
    [
      "0.30729043",
      "0.386528384"
    ],
    [
      "0.527381911",
      "0.386528384"
    ],
    [
      "0.858037229",
      "0.386528384"
    ],
    [
      "0.197244689",
      "0.387409389"
    ],
    [
      "0.417336171",
      "0.387409389"
    ],
    [
      "0.637427652",
      "0.387409389"
    ],
    [
      "0.747991488",
      "0.387409389"
    ],
    [
      "0.96808297",
      "0.387409389"
    ],
    [
      "0.03191703",
      "0.418445415"
    ],
    [
      "0.141962771",
      "0.419326419"
    ],
    [
      "0.252526608",
      "0.419326419"
    ],
    [
      "0.362054252",
      "0.419326419"
    ],
    [
      "0.472618089",
      "0.419326419"
    ],
    [
      "0.582145733",
      "0.419326419"
    ],
    [
      "0.69270957",
      "0.419326419"
    ],
    [
      "0.803273407",
      "0.419326419"
    ],
    [
      "0.912801051",
      "0.419326419"
    ],
    [
      "0.086680853",
      "0.45124345"
    ],
    [
      "0.197244689",
      "0.45124345"
    ],
    [
      "0.417336171",
      "0.45124345"
    ],
    [
      "0.637427652",
      "0.45124345"
    ],
    [
      "0.747991488",
      "0.45124345"
    ],
    [
      "0.96808297",
      "0.45124345"
    ],
    [
      "0.30729043",
      "0.452124454"
    ],
    [
      "0.527381911",
      "0.452124454"
    ],
    [
      "0.858037229",
      "0.452124454"
    ],
    [
      "0.141962771",
      "0.48316048"
    ],
    [
      "0.69270957",
      "0.48316048"
    ],
    [
      "0.03191703",
      "0.484041485"
    ],
    [
      "0.252008512",
      "0.484041485"
    ],
    [
      "0.362572348",
      "0.484041485"
    ],
    [
      "0.472099993",
      "0.484041485"
    ],
    [
      "0.582663829",
      "0.484041485"
    ],
    [
      "0.802755311",
      "0.484041485"
    ],
    [
      "0.913319147",
      "0.484041485"
    ],
    [
      "0.087198949",
      "0.515958515"
    ],
    [
      "0.196726593",
      "0.515958515"
    ],
    [
      "0.30729043",
      "0.515958515"
    ],
    [
      "0.527381911",
      "0.515958515"
    ],
    [
      "0.637945748",
      "0.515958515"
    ],
    [
      "0.747473392",
      "0.515958515"
    ],
    [
      "0.858037229",
      "0.515958515"
    ],
    [
      "0.417336171",
      "0.51683952"
    ],
    [
      "0.96808297",
      "0.51683952"
    ],
    [
      "0.03191703",
      "0.547875546"
    ],
    [
      "0.252008512",
      "0.547875546"
    ],
    [
      "0.582663829",
      "0.547875546"
    ],
    [
      "0.802755311",
      "0.547875546"
    ],
    [
      "0.141962771",
      "0.54875655"
    ],
    [
      "0.362054252",
      "0.54875655"
    ],
    [
      "0.472618089",
      "0.54875655"
    ],
    [
      "0.69270957",
      "0.54875655"
    ],
    [
      "0.912801051",
      "0.54875655"
    ],
    [
      "0.086680853",
      "0.580673581"
    ],
    [
      "0.197244689",
      "0.580673581"
    ],
    [
      "0.417336171",
      "0.580673581"
    ],
    [
      "0.527900007",
      "0.580673581"
    ],
    [
      "0.637427652",
      "0.580673581"
    ],
    [
      "0.747991488",
      "0.580673581"
    ],
    [
      "0.857519133",
      "0.580673581"
    ],
    [
      "0.96808297",
      "0.580673581"
    ],
    [
      "0.306772334",
      "0.580673581"
    ],
    [
      "0.141962771",
      "0.612590611"
    ],
    [
      "0.472618089",
      "0.612590611"
    ],
    [
      "0.69270957",
      "0.612590611"
    ],
    [
      "0.912801051",
      "0.612590611"
    ],
    [
      "0.362054252",
      "0.612590611"
    ],
    [
      "0.03191703",
      "0.613471616"
    ],
    [
      "0.252008512",
      "0.613471616"
    ],
    [
      "0.582663829",
      "0.613471616"
    ],
    [
      "0.802755311",
      "0.613471616"
    ],
    [
      "0.417336171",
      "0.644507642"
    ],
    [
      "0.96808297",
      "0.644507642"
    ],
    [
      "0.087198949",
      "0.645388646"
    ],
    [
      "0.196726593",
      "0.645388646"
    ],
    [
      "0.30729043",
      "0.645388646"
    ],
    [
      "0.527381911",
      "0.645388646"
    ],
    [
      "0.637945748",
      "0.645388646"
    ],
    [
      "0.747473392",
      "0.645388646"
    ],
    [
      "0.858037229",
      "0.645388646"
    ],
    [
      "0.252008512",
      "0.677305677"
    ],
    [
      "0.362572348",
      "0.677305677"
    ],
    [
      "0.03191703",
      "0.677305677"
    ],
    [
      "0.472099993",
      "0.677305677"
    ],
    [
      "0.582663829",
      "0.677305677"
    ],
    [
      "0.802755311",
      "0.677305677"
    ],
    [
      "0.913319147",
      "0.677305677"
    ],
    [
      "0.141962771",
      "0.678186681"
    ],
    [
      "0.69270957",
      "0.678186681"
    ],
    [
      "0.30729043",
      "0.709222707"
    ],
    [
      "0.527381911",
      "0.709222707"
    ],
    [
      "0.858037229",
      "0.709222707"
    ],
    [
      "0.086680853",
      "0.710103712"
    ],
    [
      "0.197244689",
      "0.710103712"
    ],
    [
      "0.417336171",
      "0.710103712"
    ],
    [
      "0.637427652",
      "0.710103712"
    ],
    [
      "0.747991488",
      "0.710103712"
    ],
    [
      "0.96808297",
      "0.710103712"
    ],
    [
      "0.141962771",
      "0.742020742"
    ],
    [
      "0.252526608",
      "0.742020742"
    ],
    [
      "0.362054252",
      "0.742020742"
    ],
    [
      "0.472618089",
      "0.742020742"
    ],
    [
      "0.582145733",
      "0.742020742"
    ],
    [
      "0.69270957",
      "0.742020742"
    ],
    [
      "0.803273407",
      "0.742020742"
    ],
    [
      "0.912801051",
      "0.742020742"
    ],
    [
      "0.03191703",
      "0.742901747"
    ],
    [
      "0.197244689",
      "0.773937773"
    ],
    [
      "0.417336171",
      "0.773937773"
    ],
    [
      "0.637427652",
      "0.773937773"
    ],
    [
      "0.747991488",
      "0.773937773"
    ],
    [
      "0.96808297",
      "0.773937773"
    ],
    [
      "0.087198949",
      "0.774818778"
    ],
    [
      "0.30729043",
      "0.774818778"
    ],
    [
      "0.527381911",
      "0.774818778"
    ],
    [
      "0.858037229",
      "0.774818778"
    ],
    [
      "0.69270957",
      "0.805854803"
    ],
    [
      "0.03191703",
      "0.806735808"
    ],
    [
      "0.142480867",
      "0.806735808"
    ],
    [
      "0.252008512",
      "0.806735808"
    ],
    [
      "0.362572348",
      "0.806735808"
    ],
    [
      "0.472099993",
      "0.806735808"
    ],
    [
      "0.582663829",
      "0.806735808"
    ],
    [
      "0.802755311",
      "0.806735808"
    ],
    [
      "0.913319147",
      "0.806735808"
    ],
    [
      "0.087198949",
      "0.838652838"
    ],
    [
      "0.30729043",
      "0.838652838"
    ],
    [
      "0.527381911",
      "0.838652838"
    ],
    [
      "0.637945748",
      "0.838652838"
    ],
    [
      "0.747473392",
      "0.838652838"
    ],
    [
      "0.858037229",
      "0.838652838"
    ],
    [
      "0.197244689",
      "0.839533843"
    ],
    [
      "0.417336171",
      "0.839533843"
    ],
    [
      "0.96808297",
      "0.839533843"
    ],
    [
      "0.03191703",
      "0.870569869"
    ],
    [
      "0.582663829",
      "0.870569869"
    ],
    [
      "0.802755311",
      "0.870569869"
    ],
    [
      "0.69270957",
      "0.871450874"
    ],
    [
      "0.141962771",
      "0.871450874"
    ],
    [
      "0.252526608",
      "0.871450874"
    ],
    [
      "0.362054252",
      "0.871450874"
    ],
    [
      "0.472618089",
      "0.871450874"
    ],
    [
      "0.912801051",
      "0.871450874"
    ],
    [
      "0.086680853",
      "0.903367904"
    ],
    [
      "0.197244689",
      "0.903367904"
    ],
    [
      "0.417336171",
      "0.903367904"
    ],
    [
      "0.527900007",
      "0.903367904"
    ],
    [
      "0.637427652",
      "0.903367904"
    ],
    [
      "0.747991488",
      "0.903367904"
    ],
    [
      "0.857519133",
      "0.903367904"
    ],
    [
      "0.96808297",
      "0.903367904"
    ],
    [
      "0.30729043",
      "0.904248909"
    ],
    [
      "0.141962771",
      "0.935284934"
    ],
    [
      "0.472618089",
      "0.935284934"
    ],
    [
      "0.69270957",
      "0.935284934"
    ],
    [
      "0.912801051",
      "0.935284934"
    ],
    [
      "0.03191703",
      "0.936165939"
    ],
    [
      "0.252008512",
      "0.936165939"
    ],
    [
      "0.362572348",
      "0.936165939"
    ],
    [
      "0.582663829",
      "0.936165939"
    ],
    [
      "0.802755311",
      "0.936165939"
    ],
    [
      "0.968082023",
      "0.968082023"
    ],
    [
      "0.087198949",
      "0.96808297"
    ],
    [
      "0.196726593",
      "0.96808297"
    ],
    [
      "0.30729043",
      "0.96808297"
    ],
    [
      "0.417854267",
      "0.96808297"
    ],
    [
      "0.527381911",
      "0.96808297"
    ],
    [
      "0.637945748",
      "0.96808297"
    ],
    [
      "0.747473392",
      "0.96808297"
    ],
    [
      "0.858037229",
      "0.96808297"
    ]
  ],
  "radius": "0.03191703"
}

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