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How many 3-digit numbers between 100 and 200 have a digit that is the average of
How many 3-digit numbers between 100 and 200 have a digit that is the average of
游客
2025-02-23
39
管理
问题
How many 3-digit numbers between 100 and 200 have a digit that is the average of the other 2 digits?
选项
A、10
B、7
C、9
D、11
E、19
答案
D
解析
应该说这是一道难题,假设x,y,z代表三位数的三位数字,至于分别代表哪一位,我们先不管。这样得到x+y=2z,x,y,z都属于0~9.由于这个三位数在100到200之间,因此必然有一个数字为1。
当z=1,x+y=2,那么x,y的组合有(0,2),(1,1),即代表数字102,120,111;
当y=1,那么x+1=2z,那么满足等式(x,z)的组合有(1,1),(3,2),(5,3),(7,4),(9,5),即代表数字111,123,132,153,135,147,174,195,159,其中111和z=1时重复。这样结合得到一共有11个这样的三位数。
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