think logically not mathematically [part-7]

Let A = n , then B = n+1 , and C =n+2 ( as given that A , B , C are consecutive positive integer in order )

So, ( n )+ ( n + 1 ) = n + 2 => n = 1 only solution so the three consecutive positive integers are 1 ,2 , 3 .

WLOG assume $b>a$ ,

Since a and bare positive, $c>a,b$

Now we can assume $b=a+1, c=a+2$

$a+a+1=a+2\Rightarrow a=1$

So only possible solution is $(1,2,3),(2,1,3)$

Shouldn't you mention unordered pairs there?