Challenging Mathematical Problems with Elementary Solutions, 第 1 卷Holden-Day, 1964 - 440 頁 |
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第 89 頁
... kings on the board in such a way that no one controls another ; one way to do this is shown in fig . 37a . Consequently , the maximum number of kings in such an arrangement is 16 . 39b . If n is even : n = 2k , then the problem can be ...
... kings on the board in such a way that no one controls another ; one way to do this is shown in fig . 37a . Consequently , the maximum number of kings in such an arrangement is 16 . 39b . If n is even : n = 2k , then the problem can be ...
第 90 頁
... kings on an n × n board for which none of the kings lies on a square controlled by another one . For even n ( in particular , for n = 8 ) there are many different arrangements of [ ( n + 1 ) / 2 ] 2 kings such that none of the kings ...
... kings on an n × n board for which none of the kings lies on a square controlled by another one . For even n ( in particular , for n = 8 ) there are many different arrangements of [ ( n + 1 ) / 2 ] 2 kings such that none of the kings ...
第 91 頁
... kings is ( k + 1 ) 2 = ( n + 2 ) 2 9 Using the symbol for integral part , the results obtained can be combined as follows : the minimum number of kings which can be arranged on an n n chessboard in such way as. ( n + 1 ) 2 9. III ...
... kings is ( k + 1 ) 2 = ( n + 2 ) 2 9 Using the symbol for integral part , the results obtained can be combined as follows : the minimum number of kings which can be arranged on an n n chessboard in such way as. ( n + 1 ) 2 9. III ...
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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