In a certain coding language: A. RED is coded as 360. B. BLACK is coded as…

Concept

In alphabet-position product coding, each letter is replaced by its position: A = 1, B = 2, …, Z = 26, and the positions are multiplied.

A candidate rule is accepted only when it reproduces every given code.

Application

1. For RED, R = 18, E = 5, and D = 4. Therefore, 18 × 5 × 4 = 360, which reproduces the given code.

2. For BLACK, B = 2, L = 12, A = 1, C = 3, and K = 11. Therefore, 2 × 12 × 1 × 3 × 11 = 792, which also reproduces the given code.

3. For BLUE, B = 2, L = 12, U = 21, and E = 5. Therefore, 2 × 12 × 21 × 5 = 2520.

Cross-check

Dividing 2520 successively by 5, 21, and 12 leaves 2, recovering the alphabet positions of E, U, L, and B in reverse order. This independently confirms the product.

Result

Hence, BLUE is coded as 2520.