英语翻译

题目

英语翻译
Ponder This Challenge:
N lamps are set in a circle,and for each integer M you have a tool that can toggle the state (on/off) of any set of M consecutive lamps.
Find a possible N which satisfies the following statements:
The sum of its digits is less than 10.
By applying the tool for M=105 several times,we can toggle a single lamp.
If we remove one lamp and start from a random initial setting for the remaining N-1 lamps,the probability that there exists a way to apply the tool for M=32 several times and switch all the lamps off is less than 0.001%.

答案

思考这个挑战：n灯设置在一个圆圈,并为每个整数m,你有一个工具,可以切换状态（开/关）的任何一组的M个连续灯.找到一个可能的n满足下列语句：的数字之和小于10.通过应用工具,M = 105几次,我们可以切换单灯.如果我们从...