Topic 14. CRYPTARITHM

In the following cryptarithm, all different letters stand for different dig-its. Find the sum (A + B + C).

(a)  

Answer explanation

1. From the cryptarithm, we can easily see that A = 1. Then, A + C = 9 →
   C = 8, B = 4. So, the sum of A, B and C is 13.

In the following subtraction, M and N represent different digits. What is the value of M + N?

(a)  

Answer explanation

1. • 4 - N= 6, so N = 8.

• M - 3 - 1 = 1, so M = 5.

Therefore, M + N = 11

In the following cryptarithm, all different letters stand for different digits. Find the product of A and B.

(a)  

Answer explanation

B x B = 9, so B can be either 3(3 × 3 = 9) or 7(7x7 = 49).

• if B = 3, then 3 x A = AA, contradiction.

• If B = 7, then 7 x A + 4 = AA, which leads to A = 1.

So, the product of A and B is 7 × 1 = 7.

In following multiplication, different letters stand for different digits, and ABC and DBC each represents a three-digit number. Given that C + 6, what number does DBC represent?

(a)  

Answer explanation

In the given problem C x C = _C, the units digit does not change. It can be

possible only in 3 cases, C = 1, C = 5 or C = 6.

• If C = 1, ABC x 1 = ABC. As it is not ABC but DBC, C cannot be 1.

• If C = 5, then C × C = 25 and B x 5 = B → B can only be 2 or 7. Also, A x C should be a single digit number D → A can be only be 1.

Therefore, as C # 6, ABC can be 125 or 175 → DBC can be 625 or 875.

In the following alphabetic, all the different letters stand for different digits. Find the sum of A + L + L.

(a)  

In the following alphametic, all the different letters stand for different digits. Find the two-digit sum SO.

(a)  

In the following cryptarithm, all the different letters stand for different digits. Find the product of A, B and C.

(a)  

In the following, all different letters stand for different digits. Find the sum of I, A and T.

(a)  

In the algorithm below, the letters a, b and c represent different digits from 0 to 9. What is the three-digit number abc?

(a)  

In the following cryptarithm, all different letters stand for different digits. Find the product of A and B.

(a)