Class 08 CRYPTOGRAM OR CRYPTARITHMETIC

A mathematical puzzle written by using alphabets in place of digits is called a Cryptogram. Every letter of the English alphabet stands for a different digit throughout the problem. 

Solve this interesting Cryptogram.

Solution: 

If left hand digit in the sum is a single digit, it must be 1. ∴ M = 1  

2. S + M should be at least 10.

M = 1, therefore, S can either be 9 or 8. 

S = 9 if there is no carry over from E + 0. 

S = 8, if there is a carry over from E + 0.

If S = 8 or 9, S + M can be 10 or 11.

11 can be rejected because then O will be 1

O cannot take the same value as M.

O = 0 .. we have S = 9

M = 1,0 = 0

3. E + 0 = N and O = 0

But, E cannot be equal to N.

 There must be a carry over from previous column. 

N must be = E + 1. Let E = 5 :: N = 6

4. N + R = E

6 + R = ends at 5 = 15 

R = 9 (or 8, if carry over from previous column is there) 

R cannot be 9 (QS = 9). Therefore, R = 8

5. The digit left with us are 2, 3, 4, 7D cannot be taken as 2 or 3 or 4 because, D + 5 has to be greater than 10 (1 is to be carried over to next column)

 D = 7

And the final solution is:

So, we have S = 9, E = 5, N = 6, D = 7, M = 1, 0 = 0, R = 8, Y = 2

Do Yourself:

Replace each of the letters with one of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, so that the additions are correct

Is there more than one possible answer?

 2. Replace each of the letters by one of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 so that the subtractions are correct.

Is there more than one possible answer?