Challenging Mathematical Problems with Elementary Solutions: Combinatorial analysis and probability theoryHolden-Day, 1964 |
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第 1 到 3 筆結果,共 86 筆
第 頁
... solution by himself . After solving the problem , he should check his answer against the one given in the book . If the answers do not coincide , he should try to find his error ; if they do , he should compare his solution with the one ...
... solution by himself . After solving the problem , he should check his answer against the one given in the book . If the answers do not coincide , he should try to find his error ; if they do , he should compare his solution with the one ...
第 185 頁
... solution given on page 120 ) to be known , we obtain from it a new ( fourth ) solution to problem 83a for the special case of m = n . 84b . The solution of this problem is closely related to the solution of part a above ; it differs ...
... solution given on page 120 ) to be known , we obtain from it a new ( fourth ) solution to problem 83a for the special case of m = n . 84b . The solution of this problem is closely related to the solution of part a above ; it differs ...
第 229 頁
... solution . Given the answer to the problem , it is not hard to verify its validity by mathematical induction . Third solution . Consider the n + m arrangements which are obtained from a given arrangement by successively moving the first ...
... solution . Given the answer to the problem , it is not hard to verify its validity by mathematical induction . Third solution . Consider the n + m arrangements which are obtained from a given arrangement by successively moving the first ...
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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 polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks S₁ segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices