101 位数的前、后 50 位分别是 8、9，中间那个数等于几才能使该数为 7 的倍数？...

王守恩

题目：101 位数的前、后 50 位分别是 8、9，中间那个数等于几才能使该数为 7 的倍数？

从简单算起(最笨也是最有效的,尤其在考场)。
\(819\equiv0\)
\(88599\equiv0\)
\(8881999\equiv0\)
\(888809999\equiv0\)
\(88888399999\equiv0\)
\(8888880999999\equiv0\)
\(888888819999999\equiv0\)
\(88888888599999999\equiv0\)
\(8888888881999999999\equiv0\)
\(888888888809999999999\equiv0\)

\(马后炮(题目可以改)。\)
\(888888888\cdots\)
\(146520146\)
\(742368742\)

\(\cdots999999999\)
\(\ \ \ \ \ 659014659\)
\(\ \ \ \ \ 340985340\)

\(819\)
\(119\equiv0\)
\(88599\)
\(\ \ 455\equiv0\)
\(8881999\)
\(\ \ \ \ 616\equiv0\)
\(888809999\)
\(\ \ \ \ \ \ 504\equiv0\)
\(88888399999\)
\(\ \ \ \ \ \ \ \ 231\equiv0\)
\(8888880999999\)
\(\ \ \ \ \ \ \ \ \ \ 000\equiv0\)
\(888888819999999\)
\(\ \ \ \ \ \ \ \ \ \ \ \ 119\equiv0\)
\(88888888599999999\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ 455\equiv0\)
.........