How many three-digit numbers are there that have the sum of their digits equal to $5$? (For example, $122$ is such a number, because $1+2+2=5$.)． 
Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers
Method 1:  $104, 113, 122, 131, 140$;  $203, 212, 221, 230$;  $302, 311, 320$;  $401, 410$;  $500$  $5+4+3+2+1=15$  Method 2:$5=0+0+5=0+1+4=0+2+3=1+1+3=1+2+2$  When the three-digit number is formed by $0$, $0$, $5$, it can only be $500$, therefore $1$ number;  when the three-digit number is formed by $0$, $1$, $4$, it can be $104$, $140$, $401$ or $410$, therefore $4$ numbers;  when the three-digit number is formed by $0$, $2$, $3$, it can be $203$, $230$, $302$, or $320$, therefore $4$ numbers；  when the three-digit number is formed by $1$, $1$, $3$, it can be $113$, $131$, or $311$, therefore $3$ numbers;  when the three-digit number is formed by $1$, $2$, $2$, it can be $122$, $212$, or $221$, therefore $3$ numbers;  in total there are $1+4+4+3+3=15$ numbers that meet the requirement of the question. 