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题&解
  • Orange Boy Can You Solve It Out? Ep. 59
    OBCYSIO

    Orange Boy Can You Solve It Out? Ep. 59

    思考题 in mid autumn This is hard version of Ep.58. If you prefer easier problems, please visit this link. LianLi Branches II Wulpit has drawn n nodes(indexed from 1 to n) and n-m edges on paper for homework assignments. They form m rooted trees (a……
    XGN 1天前
  • Orange Boy Can You Solve It Out? Ep. 58
    OBCYSIO

    Orange Boy Can You Solve It Out? Ep. 58

    Solved! Difficulty: Div2 C 思考题 in mid autumn This is easy version of Ep.59. If you prefer harder problems, please visit this link. LianLi Branches Wulpit has drawn n nodes(indexed from 1 to n) and n-m edges on paper for homework assignment……
    XGN 1天前
  • crimboiii[17] 拉格朗日茶香
    题&解

    crimboiii[17] 拉格朗日茶香

    题目背景 完整题解来自ox帅气lecturer, 我只能证明F<\mathbb C的情况 ;( ;( ;() 题面 V是域F上的一个线性空间, \dim V=n, 且有T\in L(V). 现取\lambda_1,...,\lambda_n\in F两两不等, 且任意\lambda_i都不是T的特征值. 试证明存在\alpha_1,...,\alpha_n\in F使得 \……
    HDD 6天前
  • crimboi[16] 搞笑群论
    题&解

    crimboi[16] 搞笑群论

    题目背景 人见人爱的代数小题 :] 惊人的是竟然在Hungerford II.2.8.9才出现, 还标了名字 😮 题面 A^ * is a normal subgroup of A, B^ * is a normal subgroup of B. Prove that: (i) A^ *(A\cap B^ *) is a normal subgroup of A^ *(A\cap B) (ii) B^ *(A^ *\cap B) i……
    HDD 2023年11月18日
  • crimboi[15] 序数拓扑(?)
    题&解

    crimboi[15] 序数拓扑(?)

    题目背景 本题竟然与xgn目前正在学习的序数有关, 真是可喜可贺!(crim boi在thu里有包含序数的课程吗?) 题面 If you don't remember what a topology is, please refer to this passage. Preliminary: Open sets in \mathbb R are just union (can be infinite) of som……
    HDD 2023年11月1日
  • Green Boy Can't You Solve It Out? Ep. 2
    OBCYSIO

    Green Boy Can't You Solve It Out? Ep. 2

    Solved! Difficulty: Div2B 1 problem for div3 participants. Beautiful Dice Painting When Epis is bored, she will draw dices. The canvas contains n*n dots. Initially they are all white. You need to paint exactly v dots black so that the final c……
    XGN 2023年10月22日
  • Crimboi [14] 开门红(?)
    题&解

    Crimboi [14] 开门红(?)

    题目背景 Rudin Real and Complex Analysis第一题, 真是开门红. 题面 We call a pairing (X,\mathfrak{M}) \sigma-algebra if \mathfrak{M} is a subset of P(X) satisfying the three properties below: (1) X\in\mathfrak{M} (2) If A\in\mathfrak{M}, A^c\in\mathf……
    HDD 2023年10月11日
  • Orange Boy Can You Solve It Out? Ep. 57
    OBCYSIO

    Orange Boy Can You Solve It Out? Ep. 57

    trivial 思考题 I am Banach This is a classic problem by Banach nearly without any change. There are N boys and M girls. Each boy loves a single girl and each girl loves a single boy. Your task is to divide the boys into two groups A_0 and A_1 and t……
    XGN 2023年10月7日
  • Announcement on Solutions for Orange Boy Can You Solve It Out
    OBCYSIO

    Announcement on Solutions for Orange Boy Can You Solve It Out

    Starting from today, we will try to write tutorials and rate difficulties for already solved Orange Boy Can You Solve It Out?(OBCYSIO) problems and separate them from unsolved/unsolvable ones. There's a new category called Solved OBCYSIO and you ca……
    XGN 2023年10月6日
  • Orange Boy Can You Solve It Out? Ep. 56
    OBCYSIO

    Orange Boy Can You Solve It Out? Ep. 56

    思考题 during OI recovery Rubbish Problem Maybe you have heard of the evil problem Hilbert's Hedge Maze and here's another very fun problem! You have n items arranged in rows. Each row contains r items and the items are arranged from left to right,……
    XGN 2023年10月6日