# Cryptarithmetic problems with explanations

Cryptarithmetic problems are where numbers are replaced with alphabets. By using standard arithmetic rules we need to decipher the alphabet.

General Rules:
1. Each alphabet takes only one number from 0 to 9 uniquely.
2. Two single digit numbers sum can be maximum 19 with carryover. So carry over in problems of two number addition is always 1.
3. Try to solve left most digit in the given problem.
4. If a × b = kb, then the following are the possibilities
(3 × 5 = 15; 7 × 5 = 35; 9 × 5 = 45) or (2 × 6 = 12; 4 × 6 = 24; 8 × 6 = 48)

## Exercise

1. Find the sum of the values of A, B and C if $ABC = A! + B! + C!$ where ABC is a three digit number
a. 7
b. 8
c. 9
d. 10

2. Find the value of $T + E + N$ if

$$\begin{array}{*{20}{c}} {ONE} \\ {ONE} \\ {ONE} \\ {ONE} \\\hline TEN \\ \hline \end{array}$$

a. 11
b. 12
c. 15
d. 17

3. The following questions are based on the following multiplication, where each digit has been replaced by an alphabet.
$\begin{array}{r} &J\ \ \ \ E\\ &\times \ \ \ \ \ \ \ \ \ \ B\ \ \ \ B\\ \hline &J\ \ \ \ E\\ &J\ \ \ \ E\ \ \ \ A\\ \hline &B\ \ \ \ A\ \ \ \ D\ \ \ \ E \end{array}$
Find the value of J.
a. 9
b. 8
c. 7
d. 6

4. From the multiplication below, What is the value of N + A + M + E?
a. 15
b. 17
c. 18
d. 19

5. Find the value of MAY in the following multiplication Table
a. 328
b. 239
c. 146
d. 319

6. If SEND + MORE = MONEY then find M + O + N + E + Y
$\begin{array}{r} &S\ E\ N\ D \\ +&M\ O\ R\ E \\ \hline &M\ O\ N\ E\ Y \end{array}$
a. 11
b. 13
c. 14
d. 18

7. Find the value of B + A + D if each alphabet represent an unique single digit from 0 - 9
a. 14
b. 15
c. 16
d. 17

8. Find the value of A + S + K in the following multiplication
a. 7
b. 10
c. 13
d. 14

9. How many numbers satisfy the condition $A^3 + B^3 + C^3 = ABC$, where $ABC$ is a three digit number.
a. 1
b. 2
c. 3
d. 4