Challenging Mathematical Problems with Elementary Solutions, 第 1 卷Holden-Day, 1964 - 440 頁 |
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第 1 到 3 筆結果,共 9 筆
第 73 頁
... partition of n into m distinct parts , arranged so that x1 > x2 >> xm . Since xm≥ 1 , we must have ≥ 2 , xm - 2 ... partition of n − m ( m + 1 ) / 2 into at most m parts . Conversely , given a partition of n — m ( m + 1 ) / 2 into at ...
... partition of n into m distinct parts , arranged so that x1 > x2 >> xm . Since xm≥ 1 , we must have ≥ 2 , xm - 2 ... partition of n − m ( m + 1 ) / 2 into at most m parts . Conversely , given a partition of n — m ( m + 1 ) / 2 into at ...
第 74 頁
... partition n = 21 + + 2ar +2013+ ... +20 .3 + 2.5 + + 2 ° · 5 + .. is the only partition of n into distinct parts to which the given partition is associated under the correspondence described above . .... Sk - 1 33b . This is a ...
... partition n = 21 + + 2ar +2013+ ... +20 .3 + 2.5 + + 2 ° · 5 + .. is the only partition of n into distinct parts to which the given partition is associated under the correspondence described above . .... Sk - 1 33b . This is a ...
第 75 頁
... partition of ʼn into parts not divisible by k . It follows from this that for any ʼn there are as many partitions of ... partition n = kr + x1 + x2 + ··· + xm of the set A , we can associate to it the partition k times n = = r + r + + r ...
... partition of ʼn into parts not divisible by k . It follows from this that for any ʼn there are as many partitions of ... partition n = kr + x1 + x2 + ··· + xm of the set A , we can associate to it the partition k times n = = r + r + + r ...
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A₁ A₂ An+m arrangements b₁ B₂ binomial coefficients binomial theorem bishops black squares C₁ chessboard chord circle coefficient color column compute the number Consequently consider corresponding customers denote determine the number diagonals digits dihedral angle divided divisible draw equally likely possible equation equidistant equivalence classes exactly example experiment favorable outcomes follows formula given Hence inclusion and exclusion intersection k-gons knights L₁ length mathematical induction maximum number n-gon number of different number of favorable number of paths number of shortest obtain pairs partition passengers plane points A1 polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices