Understanding Letter Coding and Decoding

This question involves a coding-decoding pattern based on the letters of a word and their positions in the alphabet. We are given an example: the word 'ROUBST' is coded as 61. We need to find the code for the word 'FORTUNATE' using the same logic.

Analyzing the Coding of ROUBST

Let's analyze the word 'ROUBST'. It has 6 letters. First, let's consider the alphabetical position of each letter:

• R is the 18th letter
• O is the 15th letter
• U is the 21st letter
• B is the 2nd letter
• S is the 19th letter
• T is the 20th letter

The sum of these positions is $ 18 + 15 + 21 + 2 + 19 + 20 = 95 $. This sum, 95, is not 61.

Let's consider the reverse alphabetical position of each letter (where A=26, B=25, ..., Z=1). The reverse position can be calculated as $ 27 - \text{Alphabetical Position} $.

• R: $ 27 - 18 = 9 $
• O: $ 27 - 15 = 12 $
• U: $ 27 - 21 = 6 $
• B: $ 27 - 2 = 25 $
• S: $ 27 - 19 = 8 $
• T: $ 27 - 20 = 7 $

Now, let's sum these reverse alphabetical positions:

$ 9 + 12 + 6 + 25 + 8 + 7 = 67 $

The sum of reverse positions is 67. The given code for 'ROUBST' is 61. The difference is $ 67 - 61 = 6 $. The word 'ROUBST' has 6 letters. This suggests the logic is: Sum of Reverse Alphabetical Positions - Number of Letters.

Let's verify this logic for 'ROUBST': $ 67 - 6 = 61 $. This matches the given code.

Applying the Logic to FORTUNATE

Now, we apply the same logic to the word 'FORTUNATE'. This word has 9 letters.

First, find the reverse alphabetical position for each letter:

• F: $ 27 - 6 = 21 $
• O: $ 27 - 15 = 12 $
• R: $ 27 - 18 = 9 $
• T: $ 27 - 20 = 7 $
• U: $ 27 - 21 = 6 $
• N: $ 27 - 14 = 13 $
• A: $ 27 - 1 = 26 $
• T: $ 27 - 20 = 7 $
• E: $ 27 - 5 = 22 $

Next, sum these reverse alphabetical positions:

$ 21 + 12 + 9 + 7 + 6 + 13 + 26 + 7 + 22 = 123 $

Calculating the Final Code for FORTUNATE

Using the logic derived from 'ROUBST', the code for 'FORTUNATE' is the sum of its reverse alphabetical positions minus the number of letters in the word.

Sum of Reverse Positions = 123

Number of letters in 'FORTUNATE' = 9

Code for 'FORTUNATE' = $ \text{Sum of Reverse Positions} - \text{Number of Letters} $

Code for 'FORTUNATE' = $ 123 - 9 = 114 $

Therefore, the code for 'FORTUNATE' is 114.

Revision Table: Letter Positions and Values

Here's a table summarizing the letter positions used:

Additional Information on Coding-Decoding Puzzles

Coding-decoding questions test your ability to decipher a hidden pattern or rule used to encode words or messages. Common patterns include:

• Using alphabetical positions (A=1, B=2, etc.) or reverse positions (A=26, B=25, etc.).
• Adding or subtracting a fixed number to letter positions.
• Reversing the order of letters.
• Using the sum or product of letter positions.
• Applying different rules to vowels and consonants.
• Using a substitution code.

Solving these problems requires careful observation, trial and error with different potential patterns, and applying the discovered rule consistently. Look for relationships between the letters or words and the numbers or codes provided.