从1到n这n个数中任取若干个数,不能取相邻的数,并且至少取1个,要求n=12时共有多少种不同的取法
有数学方法。最少可以取1个数，最多可取(n+1)/2个（断尾取整）。
以n=12为例，可以取1到6个数。先计算12选6的方案数，12!/6!/(12-6)! = 924种。再分别算每种取数时有相邻数的方案数，加以扣除。例如，取3个数时，有2数相邻和3数相邻。3数相邻有10种方案；2数相邻有11种方案。但是，到了取数更大时，相邻数的情形更多，分析过程繁复，容易出错。工作量近乎枚举。
因此，编程可能更加高效。计算结果，n=12时，有376种取法。
附：计算结果和fortran代码，每个括号内是一种取法
(1)；(1,3)；(1,3,5)；(1,3,5,7)；(1,3,5,7,9)；(1,3,5,7,9,11)；(1,3,5,7,9,12)；(1,3,5,7,10)；(1,3,5,7,10,12)；(1,3,5,7,11)；(1,3,5,7,12)；(1,3,5,8)；(1,3,5,8,10)；(1,3,5,8,10,12)；(1,3,5,8,11)；(1,3,5,8,12)；(1,3,5,9)；(1,3,5,9,11)；(1,3,5,9,12)；(1,3,5,10)；(1,3,5,10,12)；(1,3,5,11)；(1,3,5,12)；(1,3,6)；(1,3,6,8)；(1,3,6,8,10)；(1,3,6,8,10,12)；(1,3,6,8,11)；(1,3,6,8,12)；(1,3,6,9)；(1,3,6,9,11)；(1,3,6,9,12)；(1,3,6,10)；(1,3,6,10,12)；(1,3,6,11)；(1,3,6,12)；(1,3,7)；(1,3,7,9)；(1,3,7,9,11)；(1,3,7,9,12)；(1,3,7,10)；(1,3,7,10,12)；(1,3,7,11)；(1,3,7,12)；(1,3,8)；(1,3,8,10)；(1,3,8,10,12)；(1,3,8,11)；(1,3,8,12)；(1,3,9)；(1,3,9,11)；(1,3,9,12)；(1,3,10)；(1,3,10,12)；(1,3,11)；(1,3,12)；(1,4)；(1,4,6)；(1,4,6,8)；(1,4,6,8,10)；(1,4,6,8,10,12)；(1,4,6,8,11)；(1,4,6,8,12)；(1,4,6,9)；(1,4,6,9,11)；(1,4,6,9,12)；(1,4,6,10)；(1,4,6,10,12)；(1,4,6,11)；(1,4,6,12)；(1,4,7)；(1,4,7,9)；(1,4,7,9,11)；(1,4,7,9,12)；(1,4,7,10)；(1,4,7,10,12)；(1,4,7,11)；(1,4,7,12)；(1,4,8)；(1,4,8,10)；(1,4,8,10,12)；(1,4,8,11)；(1,4,8,12)；(1,4,9)；(1,4,9,11)；(1,4,9,12)；(1,4,10)；(1,4,10,12)；(1,4,11)；(1,4,12)；(1,5)；(1,5,7)；(1,5,7,9)；(1,5,7,9,11)；(1,5,7,9,12)；(1,5,7,10)；(1,5,7,10,12)；(1,5,7,11)；(1,5,7,12)；(1,5,8)；(1,5,8,10)；(1,5,8,10,12)；(1,5,8,11)；(1,5,8,12)；(1,5,9)；(1,5,9,11)；(1,5,9,12)；(1,5,10)；(1,5,10,12)；(1,5,11)；(1,5,12)；(1,6)；(1,6,8)；(1,6,8,10)；(1,6,8,10,12)；(1,6,8,11)；(1,6,8,12)；(1,6,9)；(1,6,9,11)；(1,6,9,12)；(1,6,10)；(1,6,10,12)；(1,6,11)；(1,6,12)；(1,7)；(1,7,9)；(1,7,9,11)；(1,7,9,12)；(1,7,10)；(1,7,10,12)；(1,7,11)；(1,7,12)；(1,8)；(1,8,10)；(1,8,10,12)；(1,8,11)；(1,8,12)；(1,9)；(1,9,11)；(1,9,12)；(1,10)；(1,10,12)；(1,11)；(1,12)；(2)；(2,4)；(2,4,6)；(2,4,6,8)；(2,4,6,8,10)；(2,4,6,8,10,12)；(2,4,6,8,11)；(2,4,6,8,12)；(2,4,6,9)；(2,4,6,9,11)；(2,4,6,9,12)；(2,4,6,10)；(2,4,6,10,12)；(2,4,6,11)；(2,4,6,12)；(2,4,7)；(2,4,7,9)；(2,4,7,9,11)；(2,4,7,9,12)；(2,4,7,10)；(2,4,7,10,12)；(2,4,7,11)；(2,4,7,12)；(2,4,8)；(2,4,8,10)；(2,4,8,10,12)；(2,4,8,11)；(2,4,8,12)；(2,4,9)；(2,4,9,11)；(2,4,9,12)；(2,4,10)；(2,4,10,12)；(2,4,11)；(2,4,12)；(2,5)；(2,5,7)；(2,5,7,9)；(2,5,7,9,11)；(2,5,7,9,12)；(2,5,7,10)；(2,5,7,10,12)；(2,5,7,11)；(2,5,7,12)；(2,5,8)；(2,5,8,10)；(2,5,8,10,12)；(2,5,8,11)；(2,5,8,12)；(2,5,9)；(2,5,9,11)；(2,5,9,12)；(2,5,10)；(2,5,10,12)；(2,5,11)；(2,5,12)；(2,6)；(2,6,8)；(2,6,8,10)；(2,6,8,10,12)；(2,6,8,11)；(2,6,8,12)；(2,6,9)；(2,6,9,11)；(2,6,9,12)；(2,6,10)；(2,6,10,12)；(2,6,11)；(2,6,12)；(2,7)；(2,7,9)；(2,7,9,11)；(2,7,9,12)；(2,7,10)；(2,7,10,12)；(2,7,11)；(2,7,12)；(2,8)；(2,8,10)；(2,8,10,12)；(2,8,11)；(2,8,12)；(2,9)；(2,9,11)；(2,9,12)；(2,10)；(2,10,12)；(2,11)；(2,12)；(3)；(3,5)；(3,5,7)；(3,5,7,9)；(3,5,7,9,11)；(3,5,7,9,12)；(3,5,7,10)；(3,5,7,10,12)；(3,5,7,11)；(3,5,7,12)；(3,5,8)；(3,5,8,10)；(3,5,8,10,12)；(3,5,8,11)；(3,5,8,12)；(3,5,9)；(3,5,9,11)；(3,5,9,12)；(3,5,10)；(3,5,10,12)；(3,5,11)；(3,5,12)；(3,6)；(3,6,8)；(3,6,8,10)；(3,6,8,10,12)；(3,6,8,11)；(3,6,8,12)；(3,6,9)；(3,6,9,11)；(3,6,9,12)；(3,6,10)；(3,6,10,12)；(3,6,11)；(3,6,12)；(3,7)；(3,7,9)；(3,7,9,11)；(3,7,9,12)；(3,7,10)；(3,7,10,12)；(3,7,11)；(3,7,12)；(3,8)；(3,8,10)；(3,8,10,12)；(3,8,11)；(3,8,12)；(3,9)；(3,9,11)；(3,9,12)；(3,10)；(3,10,12)；(3,11)；(3,12)；(4)；(4,6)；(4,6,8)；(4,6,8,10)；(4,6,8,10,12)；(4,6,8,11)；(4,6,8,12)；(4,6,9)；(4,6,9,11)；(4,6,9,12)；(4,6,10)；(4,6,10,12)；(4,6,11)；(4,6,12)；(4,7)；(4,7,9)；(4,7,9,11)；(4,7,9,12)；(4,7,10)；(4,7,10,12)；(4,7,11)；(4,7,12)；(4,8)；(4,8,10)；(4,8,10,12)；(4,8,11)；(4,8,12)；(4,9)；(4,9,11)；(4,9,12)；(4,10)；(4,10,12)；(4,11)；(4,12)；(5)；(5,7)；(5,7,9)；(5,7,9,11)；(5,7,9,12)；(5,7,10)；(5,7,10,12)；(5,7,11)；(5,7,12)；(5,8)；(5,8,10)；(5,8,10,12)；(5,8,11)；(5,8,12)；(5,9)；(5,9,11)；(5,9,12)；(5,10)；(5,10,12)；(5,11)；(5,12)；(6)；(6,8)；(6,8,10)；(6,8,10,12)；(6,8,11)；(6,8,12)；(6,9)；(6,9,11)；(6,9,12)；(6,10)；(6,10,12)；(6,11)；(6,12)；(7)；(7,9)；(7,9,11)；(7,9,12)；(7,10)；(7,10,12)；(7,11)；(7,12)；(8)；(8,10)；(8,10,12)；(8,11)；(8,12)；(9)；(9,11)；(9,12)；(10)；(10,12)；(11)；(12)
total = 376
