Problem link : - https://www.codechef.com/problems/TWOGRS

Lets make it easy and clear !

Observation : - Answer is “NO” if (a+2*b+3*c) is odd. Agree?

If (a+2*b+3*c) is even:-

Answer is always “YES” , if a>=1 , b>=1 and c>=1

Proof:-

1)If a,b,c are even, answer is “YES”

2)If a,b,c are odd, answer is “YES”

3)If a=even and b,c=odd , this case is not allowed as the sum is odd

4) If a=odd and b,c=even, this case is not allowed as the sum is odd

5)If b=even and a,c=odd , answer is “YES”

6) If b=odd and a,c=even,answer is “YES”

5)If c=even and a,b=odd , this case is not allowed as the sum is odd

6) If c=odd and a,b=even,this case is not allowed as the sum is odd

Now, the only cases left are :- When one of the values (a,b,c) are zero or two of the values of (a,b,c) are zero.

I have discussed them here :- TWOGRS - Editorial

That exact post : -

This is the easiest I can explain guys -

1] If the sum (1*a+2*b+3*c==even) of all numbers is even, we check for something , else (Answer–>No).

(If sum is even, then only a set can be divided into 2-equal sets, agreed?)

2]If sum is even, and all a,b,c are positive. Answer is always Yes(you can try it yourself).

3)If sum is even and a=0 and c=0, just check the value of 'b'.

4)If sum is even, a=1 and c=odd number and b=0, answer is No.

5)If sum is even, b=1 and c=even number and a=0, answer is No.

6)For all others, answer is yes.

Link to my solution : -Very Short Code(https://www.codechef.com/viewsolution/26750930)