diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index f2eb4f72..f38735e5 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -7738,7 +7738,9 @@
             "20220624\t王伟叶, 余利成"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023290"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -26474,7 +26476,9 @@
             "20220624\t朱敏慧, 王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023281"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -137595,7 +137599,9 @@
             "20220709\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023277"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -346204,7 +346210,9 @@
             "20221213\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023282"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -402024,7 +402032,9 @@
             "20230221\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023289"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -404646,7 +404656,9 @@
             "20230312\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023279"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -404962,7 +404974,9 @@
             "20230312\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023282"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -410860,7 +410874,9 @@
             "20230411\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023291"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -464452,7 +464468,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023277"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -464540,7 +464558,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023279"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -501277,7 +501297,9 @@
             "20230706\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023278"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -525273,7 +525295,9 @@
             "20230930\t余利成\t刘灿文\t周双"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023279"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -550515,7 +550539,9 @@
             "20221231\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023286"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -565112,7 +565138,9 @@
             "20230101\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023278"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -604199,7 +604227,9 @@
             "20230905\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023286"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -609084,7 +609114,9 @@
             "20231109\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023287"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -616460,7 +616492,9 @@
             "20231225\t徐慧"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023286"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -623003,6 +623037,414 @@
         "space": "4em",
         "unrelated": []
     },
+    "023277": {
+        "id": "023277",
+        "content": "某单位共有老、中、青职工 $430$ 人, 其中青年职工 $160$ 人, 中年职工人数是老年职工人数的 $2$ 倍. 为了解职工身体状况, 现采用分层抽样方法进行调查, 在抽取的样本中有青年职工 $32$ 人, 则该样本中的老年职工人数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "017150",
+            "031753",
+            "004480"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023278": {
+        "id": "023278",
+        "content": "在下列抽样试验中, 适合用抽签法的是\\bracket{20}.\n\\onech{从某厂生产的 $3000$ 件产品中抽取 $600$ 件进行质量检验}{从某厂生产的两箱(每箱 $10$ 件)产品中抽取 $6$ 件进行质量检验}{从甲、乙两厂各取五箱产品, 在十箱产品(每箱 $10$ 件, 共 $100$ 件)中抽取 $10$ 件进行质量检验}{从某厂生产的 $3000$ 件产品中抽取 $10$ 件进行质量检验}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "018793",
+            "021155"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023279": {
+        "id": "023279",
+        "content": "某公司决定利用随机数表对今年新招聘的 $800$ 名员工进行抽样调查他们对目前工作的满意程度, 先将这 $800$ 名员工进行编号, 编号分别为 $001,002, \\cdots, 799,800$, 从中抽取 $80$ 名进行调查, 下面提供随机数表的第 $4$ 行到第 $6$ 行:\n\\begin{center}\\begin{tabular}{lllllllll}3221183429 & 7864540732 & 5242064438 & 1223435677 & 3578905642 \\\\\n8442125331 & 3457860736 & 2530073286 & 2345788907 & 2368960804 \\\\\n3256780843 & 6789535577 & 3489948375 & 2253557832 & 4377892345\n\\end{tabular}\\end{center}若从表中第 $5$ 行第 $6$ 列开始向右依次连续读取 $3$ 个数字作为一个编号, 则抽到的第 $5$ 名员工的编号是\\bracket{20}.\n\\fourch{007}{253}{328}{736}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "019851",
+            "017154",
+            "014629"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023280": {
+        "id": "023280",
+        "content": "为了解某地区中小学生的视力情况, 拟从该地区的中小学生中抽取部分学生进行调查,事先已经了解到该地区小学、初中、高中三个学段学生的视力情况有较大差异, 而男女生的视力情况差异不大. 在下面的抽样方法中, 合理的抽样方法是\\bracket{20}.\n\\fourch{抽签法}{按性别分层抽样}{按学段分层抽样}{随机数法}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023281": {
+        "id": "023281",
+        "content": "我国古代数学名著《九章算术》有``米谷粒分''题: 发仓募粮, 所募粒中秕不足百三则收之 (不超过 3\\%), 现抽样取米一把, 取得 $235$ 粒米中夹秕 $n$ 粒, 若这批米合格, 则 $n$ 不超过\\bracket{20}.\n\\fourch{$6$}{$7$}{$8$}{$9$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "000720"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023282": {
+        "id": "023282",
+        "content": "某班有男生 $36$ 人, 女生 $18$ 人, 用分层抽样的方法从该班全体学生中抽取一个容量为 $9$ 的样本, 则抽取的女生人数为\\bracket{20}.\n\\fourch{$6$}{$4$}{$3$}{$2$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "012493",
+            "014639"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023283": {
+        "id": "023283",
+        "content": "某校高一、高二、高三年级的学生人数之比为 $4: 4: 3$, 现按年级用分层抽样的方法抽取若干人, 若抽取的高三年级的学生人数为 $15$ , 则抽取的样本容量为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023284": {
+        "id": "023284",
+        "content": "某企业三个分厂生产同一种电子产品, 三个分厂产量分布如图所示, 现在用分层抽样方法从三个分厂生产的该产品中共抽取 $100$ 件做使用寿命的测试, 则第一分厂应抽取的件数为\\blank{50}; 由所得样品的测试结果计算出从第一、二、三分厂取出的产品的使用寿命平均值分别为 $1020$ 小时、 $980$ 小时、 $1030$ 小时, 估计这个企业所生产的该产品的平均使用寿命为\\blank{50}小时.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\fill [pattern = north west lines] (0,1) arc (90:-90:1) --cycle;\n\\fill [pattern = horizontal lines] (0,1) arc (90:198:1) -- (0,0) -- cycle;\n\\draw (0,0) circle (1);\n\\draw (0,1) -- (0,-1) (0,0) -- (198:1);\n\\draw (0:0.5) --++ (0.7,0.7) --++ (0.2,0) node [right] {第一分厂($50\\%$)};\n\\draw (234:0.5) --++ (-0.7,-0.7) --++ (-0.2,0) node [left] {第二分厂($20\\%$)};\n\\draw (144:0.5) --++ (-0.7,0.7) --++ (-0.2,0) node [left] {第三分厂($30\\%$)};\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023285": {
+        "id": "023285",
+        "content": "已知数列 $\\{a_n\\}$ 是等比数列, 公比为 $q$, 且 $a_2 \\cdot a_4 \\cdot a_6=8$, $a_7=54$, 则 $q=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023286": {
+        "id": "023286",
+        "content": "已知 $S_n$ 为 $\\{a_n\\}$ 的前 $n$ 项之和, $S_n=n^2-n+5$, 则通项公式 $a_n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "022966",
+            "022541",
+            "020711"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023287": {
+        "id": "023287",
+        "content": "已知数列 $\\{a_n\\}$ 满足 $a_1=5$, $a_{n+1}=2 a_n-3$, $n \\in \\mathbf{N}$, $n \\geq 1$, 则数列 $\\{a_n\\}$ 的通项公式为 $a_n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "022723"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023288": {
+        "id": "023288",
+        "content": "已知数列 $\\{a_n\\}$ 的通项公式为 $a_n=\\begin{cases}2 n+4,&  n=2 k,\\\\(\\sqrt{2})^{n+1},&  n=2 k-1,\\end{cases}(k \\in \\mathbf{N}, k \\geq 1)$. $S_n$ 是其前 $n$ 项和, 则 $S_{38}=$\\blank{50}. (结果用数字作答)",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023289": {
+        "id": "023289",
+        "content": "在等差数列 $\\{a_n\\}$ 中, $\\dfrac{a_{11}}{a_{10}}<-1$, 且它的前 $n$ 项和 $S_n$ 有最大值. 那么, 当 $S_n$ 取得最小正值时, $n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "014535"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023290": {
+        "id": "023290",
+        "content": "一个盒子中装有 $4$ 张卡片, 卡片上分别写有数字 $1$、$2$、$3$、$4$. 现从盒子中随机抽取卡片.\\\\\n(1) 若一次抽取 $3$ 张卡片, 事件 $A$ 表示``3 张卡片上数字之和大于 $7$'', 求 $P(A)$;\\\\\n(2) 若第一次抽取 $1$ 张卡片, 放回后再抽取 $1$ 张卡片, 事件 $B$ 表示``两次抽取的卡片上数字之和大于 $6$ \", 求 $P(B)$;\\\\\n(3) 若一次抽取 $2$ 张卡片, 事件 $C$ 表示``2 张卡片上数字之和是 $3$ 的倍数'', 事件 $D$ 表示``2 张卡片上数字之积是 $4$ 的倍数''. 验证 $C$、$D$ 是独立的.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "000228"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023291": {
+        "id": "023291",
+        "content": "在数列 $\\{a_n\\}$ 中, $a_1=12$, $a_4=3$, 且满足 $a_{n+2}+a_n=2 a_{n+1}$, $n \\in \\mathbf{N}$, $n \\geq 1$.\\\\\n(1) 求数列 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 设 $b_n=\\dfrac{1}{n(21-a_n)}$, $n \\in \\mathbf{N}$, $n \\geq 1$, 求数列 $\\{b_n\\}$ 的前 $n$ 项和 $T_n$ *",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "014859"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023292": {
+        "id": "023292",
+        "content": "小威初三参加某高中学校的数学自主招生考试, 这次考试由十道选择题组成. 得分要求是: 做对一道题得 $1$ 分, 做错一道题扣去 $1$ 分, 不做得 $0$ 分, 总得分 $7$ 分就算及格. 小威的目标是至少得 $7$ 分获得及格. 在这次考试中, 小感确定他做的前六题全对, 记 $6$ 分; 而他做余下的四道题中每道题做对的概率均为 $p$($0<p<1$). 考试中, 小威思量: 从余下的四道题中再做一道并且及格的概率 $P_1=p$; 从余下的四道题中恰做两道并且及格的概率 $P_2=p^2$. 他发现 $P_1>P_2$, 只做一道更容易及格.\\\\\n(1) 求: 小威从余下的四道题中恰做三道并且及格的概率 $P_3$; 从余下的四道题中全做并且及格的概率 $P_4$.\\\\\n(2) 由于 $p$ 的大小影响, 请你帮小威讨论: 小威从余下的四道题中恰做几道并且及格的概率最大?",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023293": {
+        "id": "023293",
+        "content": "设 $k \\in \\mathbf{R}$, 数列 $\\{a_n\\}$ 满足 $a_n=2 n+k$, 数列 $\\{b_n\\}$ 的通项公式为 $b_n=3^{n-1}$.\\\\\n(1) 已知 $a_1+a_2+a_3+a_4+a_5=25$, 求 $k$ 的值;\\\\\n(2) 若 $k=-113$, 以 $c_n=\\dfrac{a_n}{b_n}$, 求数列 $\\{c_n\\}$ 最大项及相应 $n$ 的值;\\\\\n(3) 设 $S_n$ 为数列 $\\{b_n\\}$ 其前 $n$ 项和, 令 $d_n=\\dfrac{b_n}{S_n S_{n+1}}$, 数列 $\\{d_n\\}$ 的前 $n$ 项和为 $S_n$. 证明: $\\dfrac{1}{4}\\leq T_n<\\dfrac{1}{3}$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023294": {
+        "id": "023294",
+        "content": "如图, 长方体中 $ABCD-A_1B_1C_1D_1$ 中, $DA=2$, $DC=2 \\sqrt{2}$, $DD_1=\\sqrt{3}, M, N$ 分别为棱 $AB, BC$ 的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{{2*sqrt(2)}}\n\\def\\m{2}\n\\def\\n{3}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\n,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\n,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\n,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\draw ($(A)!0.5!(B)$) node [below] {$M$} coordinate (M);\n\\draw ($(B)!0.5!(C)$) node [below right] {$N$} coordinate (N);\n\\draw [dashed] (M)--(N)(M)--(D)(M)--(D_1)(D_1)--(N);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: 平面 $D_1MN \\perp$ 平面 $D_1DM$;\\\\\n(2) 求点 $D$ 到平面 $D_1MN$ 的距离.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023295": {
+        "id": "023295",
+        "content": "设四边形 $ABCD$ 为矩形, 点 $P$ 为平面 $ABCD$ 外一点, 且 $PA \\perp$ 平面 $ABCD$, 若 $|PA|=|AB| =1$, $|BC|=2$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale =2]\n\\draw (0,0,0) node [below] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$D$} coordinate (D);\n\\draw (2,0,1) node [below] {$C$} coordinate (C);\n\\draw (0,0,1) node [below] {$B$} coordinate (B);\n\\draw (0,1,0) node [above] {$P$} coordinate (P);\n\\draw (P)--(B)--(C)--(D)--cycle(P)--(C);\n\\draw [dashed] (B)--(A)--(D)(A)--(P);\n\\end{tikzpicture}\n\\end{center}\n(1) 求四棱锥 $P-ABCD$ 的体积;\\\\\n(2) 在 $BC$ 边上是否存在一点 $G$, 使得点 $D$ 到平面 $PAG$ 的距离为 $\\sqrt{2}$, 若存在, 求出 $|BG|$ 的值, 若不存在, 请说明理由;\\\\\n(3) 若点 $E$ 是 $PD$ 的中点, 在 $\\triangle PAB$ 内确定一点 $H$, 使 $|CH|+|EH|$ 的值最小, 并求此时 $|HB|$ 的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "25届周末卷补充题目",
+        "edit": [
+            "20240107\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
@@ -670512,7 +670954,9 @@
             "20230730\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023277"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []