python编程比赛–将1-8几个数字填写下边表格，要求每一列数字比右边大，每一行数字比下边大，有几种填法？

题目描述：

题目：将1-8几个数字填写下边表格，要求每一列数字比右边大，每一行数字比下边大，有几种填法？

代码

count=0
for a in range(1,9):
    for b in range(1, 9):
        for c in range(1, 9):
            for d in range(1, 9):
                for e in range(1, 9):
                    for f in range(1, 9):
                        for g in range(1, 9):
                            for h in range(1, 9):
                                if (a!=b and a!=c and a!=d and a!=e and a!=f and a!=g and a!=h
                                and b!=c and b!=d and b!=e and b!=f and b!=g and b!=h
                                and c != d and c != e and c != f and c != g and c != h
                                and d != e and d != f and d != g and d != h
                                and e != f and e != g and e != h
                                and f != g and f != h
                                and g!=f
                                ):
                                    if ((a>b) and (b>c) and (c>d)and(e>f)and(f>g)and(g>h)
                                      and (a>e)and(b>f) and (c>g)and(d>h)):
                                        print(a,b,c,d)
                                        print(e,f,g,h)
                                        count=count+1
                                        print(count)

运行结果

编程思想：

每一个字母表示都有8种可能所以所以8层循环，遍历出所有结果：

for a in range(1,9):
    for b in range(1, 9):
        for c in range(1, 9):
            for d in range(1, 9):
                for e in range(1, 9):
                    for f in range(1, 9):
                        for g in range(1, 9):
                            for h in range(1, 9):

但是每一个字母表示的值并不相同，换句话说，如果a取1的话，那么b,c,d,e,f,g,h都不能取1。后面的取值一样。

  if (a!=b and a!=c and a!=d and a!=e and a!=f and a!=g and a!=h
                                and b!=c and b!=d and b!=e and b!=f and b!=g and b!=h
                                and c != d and c != e and c != f and c != g and c != h
                                and d != e and d != f and d != g and d != h
                                and e != f and e != g and e != h
                                and f != g and f != h
                                and g!=f
                                ):

筛选出左边数值大于右边，上边大于下边

(a>b) and (b>c) and (c>d)and(e>f)and(f>g)and(g>h) #左边大于右边
and (a>e)and(b>f) and (c>g)and(d>h)#上边大于下边