题目背景 南大几把选拔中最水的题(T3), 适合出在初中竞赛里. 另外这期写解答方便以后想考南大几把的学生😇, 篇幅太长除了题面不写中文了. 不过题面也是pmt提供的, 不一定完全准确. 题面 记排列P的置换环数量为c(P),排列P,Q的复合记为P\oplus Q，已知长度为n的排列f_1,f……

思考题 with hard-to-write checker and interactor Peripheral Lightup! Note: this is not a traditional problem. Follow the instruction in the statement to help construct your solution Lead-in: The Palace is celebrating a festival with LED lights! Ins……

思考题 in dreamland Construct it XGN dreamt about the following problem when sleeping: You are given a positive integer n (2\leq n\leq 10^8). Output an arithmetic expression that yields the value n with the following requirements: The expression s……

题目背景 贴吧范畴论帅哥问的一道题, 题目还算基础, 不过确实很容易伪证, 是名副其实的脑筋急转弯. 题面 对一个拓扑空间X, 定义集合S为稠密集当且仅当\text{Cl}(S)=X, R为无处稠密集当且仅当X-\text{Cl}(R)为稠密集. 定义集合A的边界\text{Bd}(A)=\text{Cl}(A)\cap\te……

题目背景 总有人喜欢在高考数学中嚷嚷"仿射变换", 于是一道纯正射影几何高考"创新题"应运而生(其实还顺便测试一下QuickLaTex). 题面 如上图, , , 共线, , , 共线, , , 共线, 且, , 不共线, , , 不共线. (1) 若与不是同一平面, 求证与的交点, 与的交点, 与的交点共线.……

思考题 which is an adaptation from a popular problem. The source problem is very popular. IDK if this adaptation has been made or not. Adaptation There are N people indexed from 1 to N in a room. Each of them is given a hat of a random color. The t……

Finally some geometry! Maybe very easy though. Currently I am undergoing the College Entrance Exam(GK) so I don't have many ideas for Competitive Programming problems. This problem is inspired by some math problem in GK Simulation. Of course, this ……

思考题 of Div2B-C Elevator Welcome back to OBCYSIO! Orange Boy has been promoted to LGM boy so this series is in an awkward situation. This problem is very easy. Consider an elevator with a max speed of v_m m/s and an acceleration of a m/s^2. When ……

题目背景 庆祝Crimson Boy提前一步进入大学殿堂, 特此准备一道来自他所在的大学的隔壁敌对大学的微积分题目! 题面 \forall x\in[1,+\infty), f(x)>0, f''(x)\leq0且\lim\limits_{x\rightarrow+\infty}f(x)=+\infty. 计算\lim\limits_{s\rightarrow0^+}\sum\limits_{n=……