# Digit sum

How many are three-digit numbers that have a digit sum of 6?

n =  21

### Step-by-step explanation:

$n=21=21$

The equations have the following integer solutions:
6 = a+b+c
a>0
b>=0
c>=0

Number of solutions found: 21
##### a1=1, b1=0, c1=5a2=1, b2=1, c2=4a3=1, b3=2, c3=3a4=1, b4=3, c4=2a5=1, b5=4, c5=1a6=1, b6=5, c6=0a7=2, b7=0, c7=4a8=2, b8=1, c8=3a9=2, b9=2, c9=2a10=2, b10=3, c10=1a11=2, b11=4, c11=0a12=3, b12=0, c12=3a13=3, b13=1, c13=2a14=3, b14=2, c14=1a15=3, b15=3, c15=0a16=4, b16=0, c16=2a17=4, b17=1, c17=1a18=4, b18=2, c18=0a19=5, b19=0, c19=1a20=5, b20=1, c20=0a21=6, b21=0, c21=0

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