Understanding the Coding Language Logic

This question asks us to decipher a specific coding language where words are converted into numbers. We are given two examples to help us find the underlying rule or pattern:

• 'ROCKET' is coded as '36'
• 'MASON' is coded as '25'

Our goal is to apply this same pattern to the word 'SERVITUDE' to find its code.

Analyzing the Examples to Find the Pattern

Let's look at the examples closely and see if we can find a relationship between the words and their numerical codes.

Example 1: ROCKET

• The word is 'ROCKET'.
• Let's count the number of letters in 'ROCKET'. There are 6 letters (R, O, C, K, E, T).
• The code given for 'ROCKET' is 36.
• Is there a mathematical relationship between the number of letters (6) and the code (36)? Yes, we observe that ${6^2 = 36}$.

Example 2: MASON

• The word is 'MASON'.
• Let's count the number of letters in 'MASON'. There are 5 letters (M, A, S, O, N).
• The code given for 'MASON' is 25.
• Is there a mathematical relationship between the number of letters (5) and the code (25)? Yes, we observe that ${5^2 = 25}$.

From these two examples, it appears that the coding rule is to count the number of letters in the word and then square that number.

Applying the Coding Pattern to SERVITUDE

Now that we have identified the pattern, we can apply it to the word 'SERVITUDE' to find its code.

• The word is 'SERVITUDE'.
• Let's count the number of letters in 'SERVITUDE'. There are 9 letters (S, E, R, V, I, T, U, D, E).
• According to the pattern, the code should be the square of the number of letters.
• Number of letters in 'SERVITUDE' = 9.
• Code for 'SERVITUDE' = ${9^2}$.
• ${9^2 = 9 \times 9 = 81}$.

Therefore, the code for 'SERVITUDE' is 81.

Conclusion

Based on the pattern observed in the examples ('ROCKET' coded as 36 and 'MASON' coded as 25), where the code is the square of the number of letters in the word, the word 'SERVITUDE' which has 9 letters, will be coded as ${9^2 = 81}$.

The final answer is 81.

Revision Table - Coding Language Logic

Additional Information - Number-Based Coding

Coding language questions often involve finding a mathematical or logical pattern based on the letters or properties of a word. Common patterns include:

• Position of letters: Using the alphabetical position of letters (A=1, B=2, etc.) and applying operations like addition, subtraction, multiplication, or squaring.
• Number of vowels/consonants: The code might relate to the count of vowels or consonants in the word.
• Sum/Product of letter positions: Summing or multiplying the numerical positions of the letters.
• Length of the word: As seen in this problem, the code can be directly related to the number of letters in the word, often involving squaring, cubing, or simple multiplication/addition.
• Skipping letters/Reverse order: In letter-to-letter coding, patterns might involve skipping a fixed number of letters or reversing the order.

Identifying the correct pattern requires careful observation and testing different possibilities based on the given examples. For number-based codes, looking at the number of letters is often a good starting point, especially if the resulting numbers are perfect squares or cubes.