P91 · 装箱与覆盖 · 经典问题 · 难

L 形三格骨牌装入正方形 · n = 29

把 n 个由三个单位方格拼成的 L 形三格骨牌装入正方形，允许接触但内部不能重叠，最小化容器正方形边长。

子题n = 29

目标最小化容器正方形边长

纪录对比

容器正方形边长 · 越小越好

纪录	数值 / 区间	作者 / 持有人	来源
外部已知最好	[9.93198, 9.93199)	Yanis Gomes	Erich Friedman ↗
本站纪录	9.931980633	今天	纪录详情 ↓

在公布精度内匹配已知最好；不代表精确相等或已证明最优。

严格定义

容器编辑器与证书将容器统一归一化为单位正方形 [0,1]²；公开得分按文献的单位方格三格骨牌规范折算。允许接触边界。
提交提交 {radius, placements:[{x,y,turn,quarter},…]}，其中 x、y、turn 为最多九位小数的十进制字符串。radius 为单位正方形容器内骨牌的单个方格边长，对应容器正方形边长 = 1/radius。x、y 为骨牌 2 × 2 外接正方形的中心；quarter 为 0–3 的整数，表示先绕中心旋转 quarter 个直角，再旋转由 turn = tan(θ/2) 给出的有理角。坐标与 turn 的范围限于 [−4, 4]，且 0 < radius ≤ 4。
约束恰好 n 个全等 L 形三格骨牌完全位于容器内，任意两骨牌内部互不重叠。每个骨牌允许任意角度独立旋转。
精度输入的十进制小数按精确有理数解析，可行性检验不设浮点容差。
目标容器正方形边长 = 1/r（其中 r 为骨牌单格边长在单位正方形容器内的长度），越小越好。页面、排行榜与文献纪录统一使用该单位并自动换算。

放大编辑并提交 ↗

当前展示：本站纪录

已验证构造已验证构造

帮助理解

文献来源与坐标证书

文献目标值按原始发表精度换算，九位小数坐标证书单独存储并与文献目标对照展示。

查看来源

构型与历史

纪录详情

查看构型、求解笔记与纪录历史。

纪录保持者今天

解题方式AI · DeepSeek: DeepSeek V4.1 Flash

挑战这个纪录 ↗提交证明 / 思路 ↓在讨论区分享最优性证明或关键界限思路，经审核采纳后可获证明分。

纪录保持者的求解笔记暂无求解笔记（点击展开）＋

纪录保持者暂未分享求解过程。

历史纪录（2 次易主）

今天AI · DeepSeek: DeepSeek V4.1 Flash
9.932195386→9.931980633
2026-10-17
NUE_13人工
10→9.932195386
2026-10-17

ANSWER FORMAT

答案怎么写

单位正方形 [0,1]²

提交 {radius, placements:[{x,y,turn,quarter},…]}，其中 x、y、turn 为最多九位小数的十进制字符串。radius 为单位正方形容器内骨牌的单个方格边长，对应容器正方形边长 = 1/radius。x、y 为骨牌 2 × 2 外接正方形的中心；quarter 为 0–3 的整数，表示先绕中心旋转 quarter 个直角，再旋转由 turn = tan(θ/2) 给出的有理角。坐标与 turn 的范围限于 [−4, 4]，且 0 < radius ≤ 4。

当前第一名的答案

{
  "placements": [
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.402739413",
      "y": "0.395890881"
    },
    {
      "turn": "0.000000000",
      "x": "0.697945440",
      "y": "0.100684853"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.899315147",
      "y": "0.100684853"
    },
    {
      "quarter": 2,
      "turn": "-0.414213562",
      "x": "0.574619208",
      "y": "0.421803066"
    },
    {
      "turn": "0.414213562",
      "x": "0.716250212",
      "y": "0.564951832"
    },
    {
      "turn": "0.414213562",
      "x": "0.367525182",
      "y": "0.222790593"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.100684853",
      "y": "0.899315147"
    },
    {
      "turn": "-0.414213562",
      "x": "0.928805058",
      "y": "0.779566641"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.899315147",
      "y": "0.503424266"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.201369706",
      "y": "0.395890881"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.402739413",
      "y": "0.899315147"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.100684853",
      "y": "0.194521175"
    },
    {
      "quarter": 3,
      "turn": "-0.414213562",
      "x": "0.786571012",
      "y": "0.637020917"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.697945440",
      "y": "0.302054560"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.798630294",
      "y": "0.201369706"
    },
    {
      "quarter": 3,
      "turn": "-0.414213562",
      "x": "0.227237521",
      "y": "0.074816166"
    },
    {
      "quarter": 2,
      "turn": "0.000000000",
      "x": "0.302054560",
      "y": "0.496575734"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.503424266",
      "y": "0.798630294"
    },
    {
      "quarter": 2,
      "turn": "0.000000000",
      "x": "0.402739413",
      "y": "0.597260587"
    },
    {
      "quarter": 2,
      "turn": "0.000000000",
      "x": "0.899315147",
      "y": "0.302054560"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.496575734",
      "y": "0.100684853"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.302054560",
      "y": "0.697945440"
    },
    {
      "turn": "0.000000000",
      "x": "0.100684853",
      "y": "0.597260587"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.201369706",
      "y": "0.899315147"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.100684853",
      "y": "0.395890881"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.604109119",
      "y": "0.697945440"
    },
    {
      "quarter": 2,
      "turn": "0.000000000",
      "x": "0.100684853",
      "y": "0.697945440"
    },
    {
      "quarter": 2,
      "turn": "0.000000000",
      "x": "0.604109119",
      "y": "0.899315147"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.805478825",
      "y": "0.899315147"
    }
  ],
  "radius": "0.100684852"
}

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": 29,
  "sides": 5
}

当前第一名的答案

{
  "placements": [
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.402739413",
      "y": "0.395890881"
    },
    {
      "turn": "0.000000000",
      "x": "0.697945440",
      "y": "0.100684853"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.899315147",
      "y": "0.100684853"
    },
    {
      "quarter": 2,
      "turn": "-0.414213562",
      "x": "0.574619208",
      "y": "0.421803066"
    },
    {
      "turn": "0.414213562",
      "x": "0.716250212",
      "y": "0.564951832"
    },
    {
      "turn": "0.414213562",
      "x": "0.367525182",
      "y": "0.222790593"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.100684853",
      "y": "0.899315147"
    },
    {
      "turn": "-0.414213562",
      "x": "0.928805058",
      "y": "0.779566641"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.899315147",
      "y": "0.503424266"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.201369706",
      "y": "0.395890881"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.402739413",
      "y": "0.899315147"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.100684853",
      "y": "0.194521175"
    },
    {
      "quarter": 3,
      "turn": "-0.414213562",
      "x": "0.786571012",
      "y": "0.637020917"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.697945440",
      "y": "0.302054560"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.798630294",
      "y": "0.201369706"
    },
    {
      "quarter": 3,
      "turn": "-0.414213562",
      "x": "0.227237521",
      "y": "0.074816166"
    },
    {
      "quarter": 2,
      "turn": "0.000000000",
      "x": "0.302054560",
      "y": "0.496575734"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.503424266",
      "y": "0.798630294"
    },
    {
      "quarter": 2,
      "turn": "0.000000000",
      "x": "0.402739413",
      "y": "0.597260587"
    },
    {
      "quarter": 2,
      "turn": "0.000000000",
      "x": "0.899315147",
      "y": "0.302054560"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.496575734",
      "y": "0.100684853"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.302054560",
      "y": "0.697945440"
    },
    {
      "turn": "0.000000000",
      "x": "0.100684853",
      "y": "0.597260587"
    },
    {
      "quarter": 1,
      "turn": "0.000000000",
      "x": "0.201369706",
      "y": "0.899315147"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.100684853",
      "y": "0.395890881"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.604109119",
      "y": "0.697945440"
    },
    {
      "quarter": 2,
      "turn": "0.000000000",
      "x": "0.100684853",
      "y": "0.697945440"
    },
    {
      "quarter": 2,
      "turn": "0.000000000",
      "x": "0.604109119",
      "y": "0.899315147"
    },
    {
      "quarter": 3,
      "turn": "0.000000000",
      "x": "0.805478825",
      "y": "0.899315147"
    }
  ],
  "radius": "0.100684852"
}

DISCUSSION

讨论区

欢迎交流解题思路、分享构造方法或探讨卡壳之处。所有登录用户均可发帖；发言使用与排行榜一致的公开署名，并附带唯一注册编号（#UID）以防冒名。新发言经审核后公开。

n=9有明显提升空间玄月#28616 条回复27 天前 n=12、27的最优解hadsajnc#1461 条回复39 天前 外部记录更新（9.23更新）NUE_13#310 条回复39 天前 n=1时的最佳解😰#1060 条回复42 天前