Question

帮忙回答下面一道数学题

How many whole number from 0 to 1,000 have digits with a sum of 10？ 希望帮忙回答这个问题并且解释每一个步骤最好用英文 28=2+8=10这样的话82=8+2=10 ，127=1+2+7=10 217=2+1+7=10 当然280=2+8+0=10 。像这样子，一个整数把每一位数都拆成个位的，相加能等于10的，在0至1000里，有多少个。并且最好能够用英文解释每一个步骤为什么这样做

Answer 1

共63个

若是三位数时：因为当最高位为1时，那么接下来的那一位是0-9、当最高位为2时，那么接下来的那一位是0-8、……当最高位为9时，那么接下来的那一位是0-1（对应的就是901,910），这样共有10+9+……+2=54,
若是两位数，则只能是91,28……19共9个

sixty-three.
as a number with 3 digits,when the highest digit is 9,the second digit and the lowest digit only have ,10 minus 9 and then plus 1,
two changes 1-0;0-1
when the highest digit is 8,the second digit and the lowest digit have ,10 minus 8 and then plus 1,three changes 2-0;1-1;0-2
the rest may be deduced by analogy
when the highest digit is 1,the second digit and the lowest digit have ,10 minus 1 and then plus 1,10 changes 9-0;8-1;7-2;6-3;5-4;4-5;3-6;2-7;1-8;0-9
when the highest digit is 0,the second digit and the lowest digit have 9 changes,9-2;8-2;7-3;6-4;5-5;4-6;3-7;2-8;1-9

so,made the problems as below:
10+9+8+7+6+5+4+3+2+9=63

10 and 9 and 8 and 7 and 6 and 5 and 4 and 3 and 2 and 9 is 63

Answer 2

共63个

若是三位数时：因为当最高位为1时，那么接下来的那一位是0-9、当最高位为2时，那么接下来的那一位是0-8、……当最高位为9时，那么接下来的那一位是0-1（对应的就是901,910），这样共有10+9+……+2=54,
若是两位数，则只能是91,28……19共9个

Answer 3

sixty-three.
as a number with 3 digits,when the highest digit is 9,the second digit and the lowest digit only have ,10 minus 9 and then plus 1,
two changes 1-0;0-1
when the highest digit is 8,the second digit and the lowest digit have ,10 minus 8 and then plus 1,three changes 2-0;1-1;0-2
the rest may be deduced by analogy
when the highest digit is 1,the second digit and the lowest digit have ,10 minus 1 and then plus 1,10 changes 9-0;8-1;7-2;6-3;5-4;4-5;3-6;2-7;1-8;0-9
when the highest digit is 0,the second digit and the lowest digit have 9 changes,9-2;8-2;7-3;6-4;5-5;4-6;3-7;2-8;1-9

so,made the problems as below:
10+9+8+7+6+5+4+3+2+9=63

10 and 9 and 8 and 7 and 6 and 5 and 4 and 3 and 2 and 9 is 63