Solving the Code Language Problem

This question is a classic example of a coding-decoding problem frequently encountered in logical reasoning sections of various exams. We are given two words, 'ESCAPE' and 'PRISON', and their corresponding numerical codes, '49' and '91', respectively. Our task is to decipher the underlying rule used for coding and then apply it to find the code for the word 'FREEDOM'.

Analyzing the Given Codes: ESCAPE and PRISON

Let's look at the letters in the words and their positions in the English alphabet. A=1, B=2, C=3, and so on, up to Z=26.

Code for ESCAPE

The word 'ESCAPE' has 6 letters:

Let's try summing up these alphabetical positions:

\( \text{Sum} = 5 + 19 + 3 + 1 + 16 + 5 \)

\( \text{Sum} = 24 + 3 + 1 + 16 + 5 \)

\( \text{Sum} = 27 + 1 + 16 + 5 \)

\( \text{Sum} = 28 + 16 + 5 \)

\( \text{Sum} = 44 + 5 \)

\( \text{Sum} = 49 \)

The sum of the alphabetical positions of the letters in 'ESCAPE' is 49, which matches the given code.

Code for PRISON

Now let's check if the same logic applies to 'PRISON'. The word 'PRISON' has 6 letters:

Let's sum up these alphabetical positions:

\( \text{Sum} = 16 + 18 + 9 + 19 + 15 + 14 \)

\( \text{Sum} = 34 + 9 + 19 + 15 + 14 \)

\( \text{Sum} = 43 + 19 + 15 + 14 \)

\( \text{Sum} = 62 + 15 + 14 \)

\( \text{Sum} = 77 + 14 \)

\( \text{Sum} = 91 \)

The sum of the alphabetical positions of the letters in 'PRISON' is 91, which also matches the given code.

It is clear that the rule for this code language is to sum the alphabetical positions of all the letters in the word.

Finding the Code for FREEDOM

Now we apply the same rule to the word 'FREEDOM'. The word 'FREEDOM' has 7 letters:

Let's sum up these alphabetical positions:

\( \text{Sum} = 6 + 18 + 5 + 5 + 4 + 15 + 13 \)

\( \text{Sum} = 24 + 5 + 5 + 4 + 15 + 13 \)

\( \text{Sum} = 29 + 5 + 4 + 15 + 13 \)

\( \text{Sum} = 34 + 4 + 15 + 13 \)

\( \text{Sum} = 38 + 15 + 13 \)

\( \text{Sum} = 53 + 13 \)

\( \text{Sum} = 66 \)

Therefore, the code for 'FREEDOM' in this language is 66.

Conclusion

Based on the analysis of 'ESCAPE' and 'PRISON', the coding logic is the sum of the alphabetical positions of the letters. Applying this logic to 'FREEDOM' gives us the value 66.

Revision Table: Key Takeaways

Additional Information on Coding Decoding

Coding-decoding questions test your ability to identify patterns and rules in coded messages. Common patterns include:

• Letter Shifting: Each letter is shifted a fixed number of positions forward or backward in the alphabet (e.g., A becomes C, B becomes D, etc.).
• Reverse Alphabetical Positions: Using the position from the end of the alphabet (Z=1, Y=2, ... A=26).
• Sum of Positions: Adding the numerical values of the letter positions, as seen in this problem.
• Difference/Product/Other Operations: Using other mathematical operations on letter positions.
• Jumbling of Letters: Rearranging the letters within the word or between words according to a specific pattern.
• Using Opposite Letters: Replacing each letter with its corresponding letter from the other half of the alphabet (A-Z, B-Y, etc.).

Practicing various types helps in quickly identifying the logic during exams.