I have tough solved the question here but my concern is why it can’t be solved here taking 2 parameter( position of bit,total number of ones in a,b,c) here as unique state.
Why It Can't be solved taking 2d array
Total number of ones doesn’t uniquely define a state.For eg. if we have 5 number of ones in total then it could be due to 1+2+2 or 1+1+3 or 4+1+0.
Hence,it will not be unique and it is quite obvious that answer for each of the cases will be different.