N1 = 10, As for 1 length string it can be only digit so 10 strings possible
N2 = 100, Again as the string has to start and end with digits so 10*10 strings possible
We would have to find N3 and N4 and then need to compute a and b by solving equation
N3 = 10*4*10 (because starts and ends with digit so 10 choices and in between 4 choice of operators) + 10*10*10 (all three digits) = 1400
Similarly
N4 = 10*4*10*10 + 10*10*4*10 + 10*10*10*10 = 18000
so we get two equation,
1400 = 100a + 10b [ N2 = 100, N1 = 10] – eq 1
18000 = 1400a + 100b [N3 = 1400, N2 = 100] -eq 2
Solving the above Linear Equation;
Multiplying eq 1 with 14 on both sides
19600 = 1400a + 140b
18000 = 1400a + 100b -eq2
=> 1600 = 40b
=> b = 40
And from eq1 e can get a = 10.
Hence, a + b = 50