diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 8f370586..e8e7d2f5 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -14249,7 +14249,9 @@
             "20221105\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023496"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -100045,7 +100047,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023490"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -100283,7 +100287,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023496"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -100712,7 +100718,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023492"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -101850,7 +101858,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023494"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -114839,7 +114849,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023491"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -193371,7 +193383,9 @@
             "20220720\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023493"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -237849,7 +237863,9 @@
             "20220726\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023485"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -299502,7 +299518,9 @@
             "20220806\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023496"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -622515,7 +622533,9 @@
             "20240106\t杨懿荔"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023495"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -627423,6 +627443,406 @@
         "space": "4em",
         "unrelated": []
     },
+    "023482": {
+        "id": "023482",
+        "content": "已知数列 $\\{a_n\\}$ 中, $a_1=1$, $a_na_{n-1}=a_{n-1}+(-1)^n(n \\geq 2, n$ 为正整数), 则 $\\dfrac{a_3}{a_5}$ 的值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023483": {
+        "id": "023483",
+        "content": "已知数列 $\\{\\dfrac{n+2}{n}\\}$, 欲使它的前 $n$ 项的乘积大于 36 , 则 $n$ 的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023484": {
+        "id": "023484",
+        "content": "等差数列 $7,4,1,-2,-5, \\cdots$ 的第 20 项是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023485": {
+        "id": "023485",
+        "content": "对于无穷数列$\\{a_n\\}$, ``数列 $\\{a_n\\}$ 是等差数列''是``数列 $\\{a_n+a_{n+1}\\}$ 是等差数列''成立的条件.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "008417"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023486": {
+        "id": "023486",
+        "content": "有穷数列 $5,8,11, \\cdots, 3 n+11$ ($n$ 为正整数) 的项数是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023487": {
+        "id": "023487",
+        "content": "已知等差数列中, $a_3=13$, $a_{15}=41$, 则 $a_9=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "030839"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023488": {
+        "id": "023488",
+        "content": "在等比数列 $\\{a_n\\}$ 中, 已知 $a_1+a_2+a_3=6$, $a_4+a_5+a_6=48$, 则 $a_5+a_6+a_7=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023489": {
+        "id": "023489",
+        "content": "已知数列 $\\{a_n\\}$ 满足 $a_1a_2\\cdots a_n=2^{n^2}$, 则数列 $\\{a_n\\}$ \\blank{50}为等比数列; (填``是''``不是'')",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023490": {
+        "id": "023490",
+        "content": "已知数列 $\\{a_n\\}$ 的通项公式为 $a_n=4 n+\\dfrac{9}{n}$, 则 $n=$\\blank{50}时, 数列 $\\{a_n\\}$ 有最小项.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003203"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023491": {
+        "id": "023491",
+        "content": "设 $S_n$ 是等差数列 $\\{a_n\\}$ 的前 $n$ 项和, 若 $\\dfrac{S_3}{S_6}=\\dfrac{1}{3}$, 则 $\\dfrac{S_6}{S_{12}}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003713"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023492": {
+        "id": "023492",
+        "content": "在两个不等正数 $a, b$ 之间插入 $n$ 个数, 使它们与 $a, b$ 组成等差数列 $\\{a_n\\}$, 公差为 $d_1$, 再插入 $m$ 个数, 使它们与 $a, b$ 组成等差数列 $\\{b_n\\}$, 公差为 $d_2$, 则 $\\dfrac{d_1}{d_2}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003225"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023493": {
+        "id": "023493",
+        "content": "有穷等差数列 $\\{a_n\\}$ 的公差 $d=-3$, 共有偶数项, 其中奇数项之和与偶数项之和的比是 $11: 8$, 所有项之和为 95 , 求其项数 $n$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "006657"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023494": {
+        "id": "023494",
+        "content": "已知数列 $\\{a_n\\}$ 的前 $n$ 项和 $S_n=12 n-n^2$, 求数列 $\\{|a_n|\\}$ 的前 $n$ 项和 $T_n$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003264"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023495": {
+        "id": "023495",
+        "content": "数列 $\\{b_n\\}$ 中, $b_1=1$, $b_2=2$, $b_{n+2}=b_{n+1}-b_n$ ($n$ 为正整数), 则 $b_6=$\\blank{50}, $b_{2014}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "023245"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023496": {
+        "id": "023496",
+        "content": "已知数列 $a_n=3 n^2-\\lambda n$ ($n$ 为正整数) 是一个递增数列, 则实数 $\\lambda$ 的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003211",
+            "000403",
+            "010778"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023497": {
+        "id": "023497",
+        "content": "等差数列 $\\{a_n\\}$ 中, $a_3=10$, 且 $a_3, a_7, a_{16}$ 组成等比数列中相邻的项, 则公比 $q=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023498": {
+        "id": "023498",
+        "content": "已知数列 $\\{a_n\\}$ 中, $a_n=n^5-2 n+1$ ($n$ 为正整数), 试判断 2015 是不是这个数列中的项? 若是, 是第几项? 若不是, 为什么?",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023499": {
+        "id": "023499",
+        "content": "在等差数列 $\\{a_n\\}$ 中, 公差 $d \\neq 0$, $a_kx^2+2 a_{k+1}x+a_{k+2}=0$ ($k$ 为正整数).\\\\\n(1) 求证: 对不同的 $\\mathrm{k}$ 值, 方程都有公共根.\\\\\n(2) 若方程除公共根外的根依次为 $b_1, b_2, b_3, \\cdots, b_k, \\cdots$, 求证: 数列 $\\{\\dfrac{1}{b_k+1}\\}$ 是等差数列.\\\\\n(3) 设$\\{b_n\\}$是(2)中定义的数列. 若 $b_1=2$, 求 $b_{10}$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023500": {
+        "id": "023500",
+        "content": "如图, $64$ 个正数排成 $8$ 行 $8$ 列方阵. 符号 $a_{i j}$($1 \\leq i \\leq 8$, $1 \\leq j \\leq 8$, $i$、$j$ 均为正整数) 表示位于第 $i$ 行第 $j$ 列的正数. 已知每一行的数成等差数列, 每一列的数成等比数列, 且各列数的公比都等于 $q$. 若 $a_{11}=\\dfrac{1}{2}$, $a_{24}=1$, $a_{32}=\\dfrac{1}{4}$. \n\\begin{center}\n\\begin{tabular}{ccccc}\n$a_{11}$& $a_{12}$& $a_{13}$& $\\cdots$ & $a_{18}$\\\\\n$a_{21}$& $a_{22}$& $a_{23}$& $\\cdots$ & $a_{28}$\\\\\n$\\cdots$ & $\\cdots$ & $\\cdots$ & $\\cdots$ & $\\cdots$\\\\\n$a_{81}$& $a_{82}$& $a_{83}$& $\\cdots$ & $a_{88}$\n\\end{tabular}\n\\end{center}\n(1) 求 $\\{a_{i j}\\}$ 的通项公式;\\\\\n(2) 已知 $k$ 为正整数, 记第 $k$ 行各项和为 $A_k$ , 求 $A_1$ 的值及数列 $\\{A_k\\}$ 的通项公式;\\\\\n(3) 接着上面的第(2)题, 若 $A_k<1$, 求 $k$ 的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "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.",
@@ -652162,7 +652582,9 @@
             "20230108\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023487"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []