Question

In the cryptarithm shown with sum 700, different letters stand for different digits, and no letter represents the digit 7 or 0. How many different numeric values for "SAT" are possible?

SAT+SUN=700

Answer 1

The number of possible numeric value for SAT are 8 possible numeric values

Explanation:

A cryptarithm is a form of mathematical game where unknown numbers represented by letters of the alphabet are used to form mathematical equations

The given cryptarithm is SAT + SUN = 700

The parameters are;

The digits represented by the letters are different

Non of the digits represented by the letters equals 7 or 0

We have;

T + N = 10

1 + A + U = 10

1 + S + S = 7

Therefore, S = (7 - 1)/2 = 3

S = 3

A + U = 10 - 1 = 9

A + U = 9

Therefore, A = 4 or 5 (2 choices)

From T + N = 10

T = 1, 2, 8, or 9 (4 choices) similarly, N = 1, 2, 8, or 9 (4 choices)

Therefore, the number of numeric values that SAT represent is given as follows;

(S = 1 choice) × (A = 2 choices) × (T = 4 choices) = 1 × 2 × 4 = 8 numeric values

SAT has 8 possible numeric value