Formulas For Cryptarithmetic

Question: 3

NO + GUN + NO = HUNT, Find the value of HUNT.

Options:

a. 1079

b. 1080

c. 1088

d. 1082

Answer: d. 1082

Explanation:

        N O
+  G U N
        N O
—————
   H U N T

Step 1: Here H = 1, from the NUNN column we must have “carry 1”, so G = 9, U = zero.

Since we have “carry” zero or 1 or 2 from the ONOT column,

Correspondingly we have N + U = 10 or 9 or 8. But duplication is not allowed, so N = 8 with “carry 2” from ONOT.

Hence, O + O = T + 20 – 8 = T + 12.

Testing for T = 2, 4 or 6, we find only T = 2 acceptable, O = 7.

So we have 87 + 908 + 87 = 1082

Question: 4

P A R I S  +  F R A N C E  =  L O N D O N. Find the value of LONDON.

Options:

a. 23

b. 25

c. 27

d. 29

Answers: a.23

Explanation:

Step 1:

Starting from the rightmost column, we have S + E = N.

Since no two letters can have the same value, S and E must be different digits.

The pairs of digits that sum to a number ending in N (N can be 0 or 1, considering the carry from the next column) are (S=7, E=9) or (S=8, E=1). Let’s consider the first pair: S=7 and E=9.

This means N = 6 (from the carry).

Step 2:

In the next column, we have I + C + N (carry from the previous step) = O. Since I + C must be at least 10 (assuming I=1 and C=9), O = 0.

Step 3:

Now, we have R + E + N (carry from the previous step) = N. Since N is 6 (from Step 1), the only valid pair is (R=2).

Step 4:

In the following column, A + F + N (carry from the previous step) = D. Since D can’t be 0 (from Step 2), the only valid option is (A=5 and F=8).

Step 5:

In the leftmost column, P + R + L (carry from the previous step) = L. Since no two letters can have the same value, P and R must be different.

The pairs of digits that sum to a number ending in L (L can be 0 or 1, considering the carry from the next column) are (P=4, R=6) or (P=3, R=7).

Let’s consider the first pair: P=4 and R=6.

This means L = 1 (from the carry).

Now we can calculate the sum:

P + A + R + I + S = 4 + 5 + 6 + 1 + 7 = 23

So, P + A + R + I + S = 23.

Therefore, the correct answer is 23.

Question: 5

S T A R S  +  P L U T O =  P L A N E T.  Find the value of PLANET.

Options:

a. 23

b. 21

c. 27

d. 29

Answer: b. 21

Explanation:

Step 1:

Starting from the rightmost column, we have S + O = T.

Since no two letters can have the same value, S and O must be different digits.

Pairs of digits that sum to a number ending in T (T can be 0 or 1, considering the carry from the next column) are (S=7, O=9) or (S=8, O=1).

Let’s consider the first pair: S=7 and O=9. This means T = 6 (from the carry).

Step 2:

In the next column, we have R + U + N (carry from the previous step) = E.

Since E can’t be 0 (from the leftmost column), the only valid option is (R=3, U=2, and N=1).

Step 3:

Now, we have A + T + N (carry from the previous step) = T.

Since T is 6 (from Step 1) and A + N must be at least 10, the only valid pair is (A=4 and N=7).

Step 4:

In the leftmost column, S + P (carry from the previous step) = P.

Since no two letters can have the same value, S and P must be different.

Pairs of digits that sum to a number ending in P (P can be 0 or 1, considering the carry from the next column) are (S=5, P=6) or (S=4, P=5).

Let’s consider the first pair: S=5 and P=6. This means the carry to the next column is 1.

Now we can calculate the sum:

S + A + T + U + R + N = 5 + 4 + 6 + 2 + 3 + 1 = 21

So, S + A + T + U + R + N = 21