P07 · Extremal configurations · Classic

Spreading points in a circle · n = 6

Place n points inside a circle of radius 1, maximizing the smallest distance between any two of them.

Instancen = 6

ObjectiveMaximize the smallest distance between two points

Formal definition

ContainerA circle of radius 1 centred at (1, 1), so both coordinates run from 0 to 2
SubmissionExactly n points, no two coinciding
ConstraintsEvery point lies inside the circle or on it
ObjectiveMake the smallest pairwise distance as large as possible; compared internally by its square, exactly

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2y0

123456

0x2

VERIFIED CONSTRUCTIONthe closest pair

Getting a feel for it

Where the room for improvement is

Spreading points IS packing equal circles: discs of half the minimum distance around each point must not overlap. Optima are jammed contact structures, and the container shape decides everything.

Where the frontier is

Spreading points in a disc is dual to packing equal circles in it: a point set with spacing d is a packing of radius d/2. Proofs in the cci table transfer; n = 4 is proven here, and the rest open or close as cci does.

Source

Current leader

0.933405848

the smallest distance between two points

Record holderNUE_13

Solution methodHuman

Challenge this record ↗

Record history (2 changes)

NUE_13Human
0.786389287→0.933405848
2026-08-25
Jev LiHuman
0.5→0.786389287
2026-08-25

ANSWER FORMAT

How to write your answer

The container is a circle of radius 1 centred at (1, 1), so coordinates run from 0 to 2. Coordinates are written as plain decimals such as "1.5", to at most nine decimal places.

Submit points, each coordinate written as a decimal string such as "1.5".

The current leader's answer

{
  "points": [
    [
      "1.972531212",
      "1.043781650"
    ],
    [
      "1.483881227",
      "1.839060010"
    ],
    [
      "0.461671657",
      "1.808072314"
    ],
    [
      "0.015384615",
      "0.903473486"
    ],
    [
      "0.570731271",
      "0.139445499"
    ],
    [
      "1.551752589",
      "0.201612165"
    ]
  ]
}

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

Instance parameters

{
  "n": 6
}

The current leader's answer

{
  "points": [
    [
      "1.972531212",
      "1.043781650"
    ],
    [
      "1.483881227",
      "1.839060010"
    ],
    [
      "0.461671657",
      "1.808072314"
    ],
    [
      "0.015384615",
      "0.903473486"
    ],
    [
      "0.570731271",
      "0.139445499"
    ],
    [
      "1.551752589",
      "0.201612165"
    ]
  ]
}

Submit points, each coordinate written as a decimal string such as "1.5". · Verifier v1.0.0