Find the missing entry in the following chart. 2A 4B 3C 20C ? 24B 10B 5C 8A

Concept

In a number–letter matrix, test one consistent rule down each column and a separate cyclic rule for the letters. A valid completion must satisfy both rules at the same position.

Here, the middle number in each column is obtained by multiplying the top and bottom numbers, while the letters A, B, and C each occur once in every row and column.

Application

1. First column: 2 × 10 = 20, confirming the column-product rule.

2. Third column: 3 × 8 = 24, confirming the same rule independently.

3. Second column: 4 × 5 = 20, so the missing number is 20.

4. In the middle row, the visible letters are C and B; the unused letter is A. The second column also contains B and C, so A completes its letter cycle.

Cross-check

The completed rows contain A, B, and C once each, and all three middle-row numbers equal the product of the numbers above and below them.

Result

The missing entry is 20A.