Tips, Tricks and Shortcuts to Solve Cryptarithmetic Questions

Below mentioned is an example supporting the above tips and tricks, for better understanding of the students:

Question 1:

LEMON + ORANGE = FRUIT, Check whether the equation is correct or not.

Solution:

According to Rule 1, we must assign unique digits to each letter. Since “LEMON,” “ORANGE,” and “FRUIT” all contain unique letters, we can assign distinct digits to them.

Now, let’s find values for L, E, M, O, N, R, A, G, F, U, I, and T such that the equation LEMON + ORANGE = FRUIT holds.

Since the result is one more than the operand, F must be 1.

Now, we have:

LEMON + ORANGE = 1RUIT

The leftmost column indicates that L + O must be greater than or equal to 10, so L = 9 and O = 8 (the only digits that fit).

Now, we have:

9EMON + 8RANGE = 1RUIT

Since the digits must be unique, R cannot be 1. Let’s try R = 2:

9EMON + 82ANGE = 12UIT

Now, we can assign values to E, M, A, G, U, and I.

They must be 3, 4, 5, 6, 7, and 0 (or vice versa) to satisfy:

9434N + 82546 = 1247T

Now, it’s clear that N and T must be 1 and 7 (or vice versa).

So, the solution is:
L = 9
E = 3
M = 4
O = 8
N = 1
R = 2
A = 5
G = 6
F = 1
U = 7
I = 0
T = 7

LEMON + ORANGE = FRUIT is satisfied with the values above.

Question 2:

APPLE + BANANA = CHERRY, Check whether the equation is correct or not.

Solution:

According to Rule 1, we must assign unique digits to each letter.

Since “APPLE,” “BANANA,” “CHERRY” all contain unique letters, we can assign distinct digits to them.

Now, let’s find values for A, P, L, E, B, N, C, H, R, Y such that the equation APPLE + BANANA = CHERRY holds.

Since the result is one more than the operand, C must be 1.

Now, we have:

APPLE + BANANA = 1HERRY

The leftmost column indicates that A + B must be greater than or equal to 10, so A = 9 and B = 2 (the only digits that fit).

Now, we have:

9PPL9 + 29292 = 19HERRY

Since the digits must be unique, R cannot be 1. Let’s try R = 4:

9PPL9 + 29292 = 194HERY

Now, we can assign values to P, L, E, H, and Y. They must be 3, 5, 6, 7, and 0 (or vice versa) to satisfy:

93596 + 29292 = 19474

Now, it’s clear that Y must be 4.

So, the solution is:
A = 9
P = 3
L = 5
E = 6
B = 2
N = 9
C = 1
H = 7
R = 4
Y = 4

Hence, the equation is satisfied with the values.

Question 3:

WATER + WINE = JUICE

Solution:

According to Rule 1, we must assign unique digits to each letter.

Since “WATER,” “WINE,” “JUICE” all contain unique letters, we can assign distinct digits to them.

Now, let’s find values for W, A, T, E, R, I, N, J, U, C such that the equation WATER + WINE = JUICE holds.

Since the result is one more than the operand, J must be 1.

Now, we have:

WATER + WINE = 1UICE

The leftmost column indicates that W + W must be greater than or equal to 10, so W = 5 (the only digit that fits).

Now, we have:

5ATER + 5INE = 1UICE

Since the digits must be unique, U cannot be 1. Let’s try U = 2:

5ATER + 5INE = 12ICE

Now, we can assign values to A, T, E, I, N, and C. They must be 9, 4, 3, 8, 7, and 0 (or vice versa) to satisfy:

59493 + 59438 = 12131

Now, it’s clear that C must be 1.

So, the solution is:
W = 5
A = 9
T = 4
E = 3
R = 8
I = 7
N = 2
J = 1
U = 6
C = 1

So, the equation is satisfied with derived values.