The number is 6210001000.
Denotes the digits as x0, x1, …, x9, left to right. Obviously, x0 + x1 + … + x9 = 10. (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. (2) Similarly x8 = 0. (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. |
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. |
I have read 每周一题(3) in WXC, and I haven't noticed it. Thank you for telling me that. 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. |
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