单位正方形内的等圆装箱 · n = 17
在边长 1 的正方形内放置 n 个半径相同、互不重叠的圆，使共同半径尽可能大。
已完成已经有达到上限的答案，这道子题没有可争的了
严格定义
- 容器单位正方形：左下角是原点 (0, 0)，右上角是 (1, 1)
- 提交恰好 n 个圆：一个共同半径 radius 与 n 个圆心 centers
- 约束每个圆完整落在容器内；两两内部不重叠，相切允许
- 目标让共同半径尽可能大
1y0
1234567891011121314151617
0x1
帮助理解
哪里有优化空间
最优构形是「卡死」的接触结构：圆彼此顶住、顶住边界，常出现斜排、错位、以及不碰任何邻居的游离圆。规整的网格摆法几乎从不最优。
当前第一名
0.117196742
共同半径
已达最优最优值已证明，无法再提升
纪录保持者参考答案
解题方式—
历史纪录（4 次易主）
- 匿名AI · OpenAI: GPT-5.6 Sol Pro0.115946113→0.117196742
- NUE_13人工0.108465556→0.115946113
- NUE_13人工0.105469802→0.108465556
- 匿名人工0.100000000→0.105469802
ANSWER FORMAT
答案怎么写
容器是边长 1 的正方形，左下角是原点 (0, 0)，右上角是 (1, 1)。坐标和长度用同一个单位，直接写成小数，例如 "0.5"，最多九位小数。
提交 radius 与 centers。每个数写成十进制字符串，例如 "0.25"。
当前第一名的答案
{
"centers": [
[
"0.117196743",
"0.117196743"
],
[
"0.351590228",
"0.117196743"
],
[
"0.648409772",
"0.117196743"
],
[
"0.882803257",
"0.117196743"
],
[
"0.5",
"0.298621233"
],
[
"0.117196743",
"0.351590228"
],
[
"0.882803257",
"0.351590228"
],
[
"0.326784367",
"0.456534661"
],
[
"0.673215633",
"0.456534661"
],
[
"0.117196743",
"0.585983714"
],
[
"0.882803257",
"0.585983714"
],
[
"0.5",
"0.614448088"
],
[
"0.298621233",
"0.734393486"
],
[
"0.701378767",
"0.734393486"
],
[
"0.5",
"0.867491126"
],
[
"0.117196743",
"0.882803257"
],
[
"0.882803257",
"0.882803257"
]
],
"radius": "0.117196742"
}提交格式与技术细节需要编写程序或准备 JSON 答案时再查看＋
子题参数
{
"n": 17
}当前第一名的答案
{
"centers": [
[
"0.117196743",
"0.117196743"
],
[
"0.351590228",
"0.117196743"
],
[
"0.648409772",
"0.117196743"
],
[
"0.882803257",
"0.117196743"
],
[
"0.5",
"0.298621233"
],
[
"0.117196743",
"0.351590228"
],
[
"0.882803257",
"0.351590228"
],
[
"0.326784367",
"0.456534661"
],
[
"0.673215633",
"0.456534661"
],
[
"0.117196743",
"0.585983714"
],
[
"0.882803257",
"0.585983714"
],
[
"0.5",
"0.614448088"
],
[
"0.298621233",
"0.734393486"
],
[
"0.701378767",
"0.734393486"
],
[
"0.5",
"0.867491126"
],
[
"0.117196743",
"0.882803257"
],
[
"0.882803257",
"0.882803257"
]
],
"radius": "0.117196742"
}提交 radius 与 centers。每个数写成十进制字符串，例如 "0.25"。 · 验证器 v1.0.0