The code works by assigning numerical values to each letter based on its alphabetical position and then summing those values. Let's break it down:

• CAT: C (3) + A (1) + T (20) = 24. However, the code gives 9. This suggests a secondary operation is involved, possibly involving squaring the root of the sum or a similar operation that maps 24 to 9.
• MOUSE: M (13) + O (15) + U (21) + S (19) + E (5) = 73. The code gives 25. Again, a secondary operation is needed to map 73 to 25.

Let's examine the pattern more closely. Notice that \( \sqrt{24} \approx 4.89 \) and \( \sqrt{73} \approx 8.54 \). If we round these down to the nearest whole number (4 and 8 respectively) and square them we get 16 and 64. This doesn't work. Let's try a different approach.

Let's consider the sum of the squares of the letter's position in the alphabet. For CAT: \(3^2 + 1^2 + 20^2 = 9 + 1 + 400 = 410\). For MOUSE: \(13^2 + 15^2 + 21^2 + 19^2 + 5^2 = 169 + 225 + 441 + 361 + 25 = 1221\).

If we look at the total sum of alphabetical positions, we have: CAT (24) and MOUSE (73). Perhaps, the code involves finding a factor, or other operation. Let's try something else. Instead, let's look at the number of letters in each word. CAT has 3 letters, and 3 squared is 9. MOUSE has 5 letters and 5 squared is 25. This matches the given codes. This means the code is simply the square of the number of letters in the word.

TROUBLE: TROUBLE has 7 letters. Therefore, the code for TROUBLE is \(7^2 = 49\).

Therefore, the correct answer is 49.