一道中学竞赛题
2012 Australian Mathematics Competition Junior Q27
How many four-digit numbers containing no zeros have the property that whenever any one of its four digits is removed, the resulting three-digit number is divisible by 3?
我是这么想的，如果是任意删除一位数字，余下的部分还能被3整除，那么只能是3，6，9这几个数
ABCD 四位数，每次都有3种选择，所以 3 x 3 x 3 x 3 = 81
可答案是243，想不明白，望高人指点