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 59 筆
第 10 頁
... lies . ( See fig . 2a ; the square on which the king lies is marked with a circle and the squares controlled by the king are marked with crosses . ) A knight controls those squares which can be reached by moving one square horizontally ...
... lies . ( See fig . 2a ; the square on which the king lies is marked with a circle and the squares controlled by the king are marked with crosses . ) A knight controls those squares which can be reached by moving one square horizontally ...
第 76 頁
... lies , it is necessary and sufficient that no two rooks lie in the same row or in the same column . Hence the total number of rooks cannot exceed n ; on the other hand , it is possible for n rooks to be arranged on the board in such a ...
... lies , it is necessary and sufficient that no two rooks lie in the same row or in the same column . Hence the total number of rooks cannot exceed n ; on the other hand , it is possible for n rooks to be arranged on the board in such a ...
第 94 頁
... lie is twice the column number . The remaining k queens lie in the ( k + 1 ) st through 2k - th columns ; the column number of the square in which one of these queens lies is thus of the form k + s , where s is a positive integer at ...
... lie is twice the column number . The remaining k queens lie in the ( k + 1 ) st through 2k - th columns ; the column number of the square in which one of these queens lies is thus of the form k + s , where s is a positive integer at ...
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常見字詞
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