问题: How many different values of N are there?
Let N be a possitive integer less than 10^2002.When the digit 1 is placed after the last digit of N,the number formed is three times the number formed when the digit 1 is placed in front of the first digit of N.How many different values of N are there?
解答:
10N＋1＝3×（10^n＋N），n表示N的位数，n＝1，2...2002
7N＝3×10^n－1
n值 7N的值 余数 N
7 / 1 29 1
2 299 5
3 2999 3
4 29999 4
5 299999 0 42857
6 2999999 2
7 29999999 1
8 299999999 5
...................
6个一循环
2002/6＝333余4
所以答案为333
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