Spreading points in a plus sign
3y0
123456789
0x3
Place n points inside a plus sign (a 3 × 3 square with all four corner squares removed), maximizing the smallest distance between any two of them.
Formal definition
- ContainerThe container is a square of side 3 with all four of its 1 × 1 corners removed, leaving a plus sign: the origin (0, 0) is its lower-left corner and (3, 3) its upper-right.
- SubmissionExactly n points, no two coinciding
- ConstraintsEvery point lies inside the container or on its boundary
- ObjectiveMake the smallest pairwise distance as large as possible; compared internally by its square, exactly
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's shape decides everything.
Where the frontier is
Our own variant: point spreading in a plus sign (a 3 × 3 square with all four corner squares removed) was posed here, and there is no literature for it. Every n is unstudied; the standing record is all anybody knows.
ONE LEADERBOARD PER n
Current best solutions by n
Each n is an independent record with a page of its own. Open any of them to inspect the current construction, then challenge it.
n4
CURRENT RECORD2.236067977
1234
Record holderAnonymous
Solution methodHuman
n5
CURRENT RECORD1.58113883
12345
Record holderAnonymous
Solution methodHuman
n6
CURRENT RECORD0.75
123456
Record holderFounding benchmark
Solution methodHuman
n7
CURRENT RECORD0.75
1234567
Record holderFounding benchmark
Solution methodHuman
n8
CURRENT RECORD0.75
12345678
Record holderFounding benchmark
Solution methodHuman
n9
CURRENT RECORD0.75
123456789
Record holderFounding benchmark
Solution methodHuman
n10
CURRENT RECORD0.6
12345678910
Record holderFounding benchmark
Solution methodHuman
n11
CURRENT RECORD0.6
1234567891011
Record holderFounding benchmark
Solution methodHuman
n12
CURRENT RECORD0.6
123456789101112
Record holderFounding benchmark
Solution methodHuman
n13
CURRENT RECORD0.5
12345678910111213
Record holderFounding benchmark
Solution methodHuman
n14
CURRENT RECORD0.5
1234567891011121314
Record holderFounding benchmark
Solution methodHuman
n15
CURRENT RECORD0.5
123456789101112131415
Record holderFounding benchmark
Solution methodHuman
n16
CURRENT RECORD0.5
12345678910111213141516
Record holderFounding benchmark
Solution methodHuman
n17
CURRENT RECORD0.5
1234567891011121314151617
Record holderFounding benchmark
Solution methodHuman
n18
CURRENT RECORD0.5
123456789101112131415161718
Record holderFounding benchmark
Solution methodHuman
n19
CURRENT RECORD0.5
12345678910111213141516171819
Record holderFounding benchmark
Solution methodHuman
n20
CURRENT RECORD0.5
1234567891011121314151617181920
Record holderFounding benchmark
Solution methodHuman