一个10位数....

新用户

有一个10位数www.ddhw.com

 

它的第一个数字 = 0在这个数中出现的次数

它的第二个数字 = 1在这个数中出现的次数

.......

它的第十个数字 = 9在这个数中出现的次数

 

请问，这个数是多少？www.ddhw.com

 

最好能给出分析步骤以及解法。

www.ddhw.com

 

新用户

I have read 每周一题(3) in WXC, and I haven't noticed it. Thank  you for telling me that.www.ddhw.com   I am going to ZT some good stuff from wxc and some other websites to here. At the same time, if you can find good one, you are very welcome to post it here. www.ddhw.com

新用户

  Perfect!!

fzy

This is a variation of 每周一题(3) in WXC. There are two solutions for 4 位数, one solution each for 5, 7, 8, 9, and 10, and no solution for 1, 2, 3 and 6.  www.ddhw.com

sean9991

The number is 6210001000.  www.ddhw.com Denotes the digits as x0, x1, …, x9, left to right.  Obviously, x0 + x1 + … + x9 = 10.www.ddhw.com (1)   x9 = 0 or 1 (o/w sum > 10).  If x9 = 1, then x1 >= 2 (obviously, x1 != 1), and some other x = 9, thus sum > 10.  Hence x9 = 0.www.ddhw.com (2)   Similarly x8 = 0.www.ddhw.com (3)   x7 = 0 or 1.  If x7 = 1, then x1 >= 2.  Let x1 = 2 and x2 =1, we can only have x0 = 7.  But the sum is 11 > 10. (4)   x6 =1, similarly as in (3), we have x1 = 2, x2 =1, x0 = 6, and all others are 0. www.ddhw.com