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1985年武汉市高二数学竞赛第五题是一道关于二色排列的问题。原题是这样的:如图1所示的一列方格摆着n颗黑子(记作x),n颗白子(记作0),n≥2。并给出如下的变换条件:从这一系列棋子中每次取出相邻的两颗放到这一列的中间或者紧挨着这2n颗棋子的两端的任意两个相邻的空格中,放下时这两颗棋子的顺序可以颠倒(如“○x”可以放成“X○”),但在这两颗没有放下之前,不得挪动其它棋子。试设计一种变换程序,使得至多不超过多少次变换,可将这一列棋子改变为一白一黑相间且任二子之间没有空格的一列。文[1]已对本题的解法作了一般性的讨论,其中命题二指出,按照上述题设条什,对于n≥2的一列,可设计一类变换方案,使得不超过n次变换,将该列变为合于题断要求的一列。
The fifth question of the Wuhan High School Mathematics Competition in 1985 was on the issue of two-color arrangement. The original question is this: As shown in Figure 1, a column of squares contains n sunspots (marked as x), n whites (marked as 0), n≥2. And give the following transformation conditions: From each series of pieces, each time two adjacent pieces are placed in the middle of this column, or in any two adjacent spaces immediately adjacent to both ends of the 2n piece, when they are put down The order of these two pieces can be reversed (eg “○x” can be placed as “X○”), but other pieces must not be moved before these two pieces are not put down. Try to design a transformation program so that at most no more than a few transformations can be made to change this chess piece to a white, black, and white column with no spaces between the two. The paper [1] has made a general discussion of the solution of this problem, in which Proposition 2 points out that according to the above problem, even for a column with n≥2, a type of transformation scheme can be designed so that no more than n transformations will be performed. The column becomes a column that meets the requirements for the statement.