Question

5. Solve the following Cryptarithm:
AB + BA = DAD
​

Answer 1

Step-by-step explanation:

Clearly, AB and BA are two digit numbers. So, maximum value of their sum is 99+99 = 198. This means that the number DAD is at most equal to 198. So, D must be equal to 1. Note that D can not be zero as DAD is a three digit number.

Now,

AB + BA = DAD

(10A+B)+(10B+A) = 1A1

11A+11B = 1A1

11(A+B) = 1A1 --------- (i)

Clearly, LHS of this equation is a multiple of 11. So, RHS must be a multiple of 11 having digits at units and hundreds place as unity. RHS can take ten values viz. 101,111,121,131,........,191. Out of these values only 121 is a multiple of 11. Therefore, A= 2.

Substituting A = 2 in (i), we get

11(2+B) = 121 => 2+B = 11 => B = 9

Hence, A = 2, B = 9, D = 1.