Question

5. What is the integer c, if (a + b) + c = a + (b + c)?​

Answer 1

Answer —— for a+b+c=n, number of triplets a,b,c is given by, (n+1)(n+2)/2
This can be derived as follows,
consider (x+y+z)
n

for all the terms in the equation, sum of powers=n
therefore the number triplets such that a+b+c=n is equal to the number of terms in (x+y+z)
n

number of terms in (x+y+z)
n
is
2
(n+1)(n+2)
​

a+b+c<=8, a,b,c >0 minimum value of a,b,c=1. so replace a by a+1,b by b+!, c by c+1
Then, a+b+c<=5
a+b+c≤5=∑
r=0
5
​
n(a+b+c=r)
Solving the above equation, we get number of triplets=56