Lights in a square

Place n unit lights in the unit square to maximize the minimum light intensity (sum of inverse squared distances) over the closed square. Values are certified by whole-square interval branch-and-bound to width 1e-6.

Beaten (24)

Lights in a square, n = 5

22.252232129 vs listed 22.213+
margin +3.92e-02 (0.177%)

Found by Erich Friedman in August 2026.

figure · coordinates

Lights in a square, n = 10

64.751953830 vs listed 62.408+
margin +2.3440 (3.756%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 15

115.159578 vs listed 113.191+
margin +1.9686 (1.739%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 16

125.458096 vs listed 124.553+
margin +9.05e-01 (0.727%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 17

135.166511 vs listed 133.907+
margin +1.2595 (0.941%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 18

147.341209 vs listed 141.556+
margin +5.7852 (4.087%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 19

159.385528 vs listed 152.854+
margin +6.5315 (4.273%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 20

174.655642 vs listed 165.272+
margin +9.3836 (5.678%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 21

184.439288 vs listed 172.658+
margin +11.7813 (6.823%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 22

195.360667 vs listed 195.050+
margin +3.11e-01 (0.159%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 23

206.538419 vs listed 205.756+
margin +7.82e-01 (0.380%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 24

219.197869 vs listed 215.573+
margin +3.6249 (1.682%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 25

229.700849 vs listed 225.100+
margin +4.6008 (2.044%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 26

242.004151 vs listed 234.759+
margin +7.2452 (3.086%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 27

254.776773 vs listed 242.055+
margin +12.7218 (5.256%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 28

269.239696 vs listed 252.447+
margin +16.7927 (6.652%)

Found by Satoshi Kishimoto and GPT-5.6 Sol Pro in July 2026.

figure · coordinates

Lights in a square, n = 29

285.128768 vs listed 282.856+
margin +2.2728 (0.804%)

Found by Shaoheng Lai and Codex in August 2026.

figure · coordinates

Lights in a square, n = 30

296.005084 vs listed 285.345+
margin +10.6601 (3.736%)

Found by Shaoheng Lai and Codex in August 2026.

figure · coordinates

Lights in a square, n = 31

307.962407 vs listed 305.298+
margin +2.6644 (0.873%)

Found by Shaoheng Lai and Codex in August 2026.

figure · coordinates

Lights in a square, n = 32

320.371046 vs listed 317.203+
margin +3.1680 (0.999%)

Found by Shaoheng Lai and Codex in August 2026.

figure · coordinates

Lights in a square, n = 33

334.037193 vs listed 330.595+
margin +3.4422 (1.041%)

Found by Shaoheng Lai and Codex in August 2026.

figure · coordinates

Lights in a square, n = 34

346.509177 vs listed 337.906+
margin +8.6032 (2.546%)

Found by Shaoheng Lai and Codex in August 2026.

figure · coordinates

Lights in a square, n = 35

359.463095 vs listed 347.195+
margin +12.2681 (3.533%)

Found by Shaoheng Lai and Codex in August 2026.

figure · coordinates

Lights in a square, n = 36

372.686420 vs listed 354.550+
margin +18.1364 (5.115%)

Found by Cody Moose in August 2026.

figure · coordinates

All cases

Data as of 2026-09-12 05:21 UTC. Every value is certified by an independent validator; none is a claim of optimality. Nothing has been submitted to the page.