英文的，数学题
howmanywholenumberfrom0to1000havedigitswithasunof10?请用最简便的方法做出来...
how many whole number from 0 to 1000 have digits with a sun of 10?
请用最简便的方法做出来 展开
请用最简便的方法做出来 展开
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for one digit number, there is 0;
for two digits numbers, there are 9 which sum of digits is 10;
because for every tens from 1 to 9, there is only one two digits number meets that condition.
for three digits numbers, if hundreds are:
1, there are 10 numbers
2, there are 9 numbers
3, there are 8 numbers
4, there are 7 numbers
5, there are 6 numbers
6, there are 5 numbers
7, there are 4 numbers
8 , there are 3 numbers
9, there are 2 numbers
Why are there 10 numbers when hundreds is 1?
because 0-9 can be tens, and when tens fixed, this three digit number is fixed.
when hundreds is 2, only 0 - 8 can be tens;
same as 3 - 9.
Total is: 9 + 10+9+8+7+6+5+4+3+2
63
for two digits numbers, there are 9 which sum of digits is 10;
because for every tens from 1 to 9, there is only one two digits number meets that condition.
for three digits numbers, if hundreds are:
1, there are 10 numbers
2, there are 9 numbers
3, there are 8 numbers
4, there are 7 numbers
5, there are 6 numbers
6, there are 5 numbers
7, there are 4 numbers
8 , there are 3 numbers
9, there are 2 numbers
Why are there 10 numbers when hundreds is 1?
because 0-9 can be tens, and when tens fixed, this three digit number is fixed.
when hundreds is 2, only 0 - 8 can be tens;
same as 3 - 9.
Total is: 9 + 10+9+8+7+6+5+4+3+2
63
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