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 44 筆
第 56 頁
... Remark . As in the remark to problem 13 , the principle of inclusion and exclusion for m sets can be applied to prove the following generalization of the result just obtained : If N is a positive integer , and N = P1a1p2 Pmam is its ...
... Remark . As in the remark to problem 13 , the principle of inclusion and exclusion for m sets can be applied to prove the following generalization of the result just obtained : If N is a positive integer , and N = P1a1p2 Pmam is its ...
第 60 頁
... Remark . The same reasoning leads immediately to the fact that if N has a factorization into prime factors of the form N = P1 P2 P * , P1a1p22 • T ( N ) = ( a1 + 1 ) ( a2 + 1 ) · · · ( ax + 1 ) , then and σ ( N ) pai + 1 - +1 − 1 på 2 ...
... Remark . The same reasoning leads immediately to the fact that if N has a factorization into prime factors of the form N = P1 P2 P * , P1a1p22 • T ( N ) = ( a1 + 1 ) ( a2 + 1 ) · · · ( ax + 1 ) , then and σ ( N ) pai + 1 - +1 − 1 på 2 ...
第 153 頁
... remark . Let us suppose , however , that instead of being given a blank sheet of paper , A is given a slip already marked with a plus . He can then either leave it alone or change it to a minus , and the probability that he leaves it ...
... remark . Let us suppose , however , that instead of being given a blank sheet of paper , A is given a slip already marked with a plus . He can then either leave it alone or change it to a minus , and the probability that he leaves it ...
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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 G₁ given Hence inclusion and exclusion intersection k-gons knights 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 total number triangle unfavorable values vertex vertices