Decoding the Code Language: AUCTION Puzzle

This problem requires us to figure out the pattern used to change words into codes. We are given two examples: 'LIBERTY' becomes 'NKDETVA', and 'TONIGHT' becomes 'VQPIIJV'. Our task is to apply this same pattern to find the code for 'AUCTION'.

Analyzing the LIBERTY Code Example

First, let's look at 'LIBERTY' and its code 'NKDETVA'. We'll find the position of each letter in the alphabet (A=1, B=2, ..., Z=26) and see how they change.

Original Word: L I B E R T Y

Alphabet Positions: 12 9 2 5 18 20 25

Coded Word: N K D E T V A

Coded Positions: 14 11 4 5 20 22 1

Now, let's calculate the difference in position (the shift) for each corresponding letter:

• L (12) to N (14): The shift is $14 - 12 = +2$.
• I (9) to K (11): The shift is $11 - 9 = +2$.
• B (2) to D (4): The shift is $4 - 2 = +2$.
• E (5) to E (5): The shift is $5 - 5 = +0$.
• R (18) to T (20): The shift is $20 - 18 = +2$.
• T (20) to V (22): The shift is $22 - 20 = +2$.
• Y (25) to A (1): The shift is calculated considering wrap-around. $25 + 2 = 27$. Since there are 26 letters, 27 corresponds to the 1st letter, A. So, the shift is $+2$.

From this example, we notice that most letters shift forward by 2 places. However, the 4th letter ('E') has a shift of 0.

Analyzing the TONIGHT Code Example

Let's check if this observation holds true for the second example: 'TONIGHT' coded as 'VQPIIJV'.

Original Word: T O N I G H T

Alphabet Positions: 20 15 14 9 7 8 20

Coded Word: V Q P I I J V

Coded Positions: 22 17 16 9 9 10 22

Calculating the shifts:

• T (20) to V (22): The shift is $22 - 20 = +2$.
• O (15) to Q (17): The shift is $17 - 15 = +2$.
• N (14) to P (16): The shift is $16 - 14 = +2$.
• I (9) to I (9): The shift is $9 - 9 = +0$. This is the 4th letter, matching the pattern observed in 'LIBERTY'.
• G (7) to I (9): The shift is $9 - 7 = +2$.
• H (8) to J (10): The shift is $10 - 8 = +2$.
• T (20) to V (22): The shift is $22 - 20 = +2$.

The analysis confirms our hypothesis: The coding pattern involves shifting letters forward by 2 positions in the alphabet, with a special rule for the 4th letter, which remains unchanged (shift of 0).

Identifying the Exact Coding Pattern

The rule for this code language is:

• Determine the alphabet position number for each letter (A=1, B=2, ... Z=26).
• For each letter, add a specific shift value to its position number. The result is the position of the coded letter. If the sum goes beyond 26, wrap around the alphabet (e.g., 27 becomes 1, 28 becomes 2).
• The standard shift value is $+2$.
• Important Exception: The shift value for the 4th letter in any given word is $0$.

Applying the Pattern to Encode 'AUCTION'

Let's apply this rule to the word 'AUCTION'.

The word is 'AUCTION'.

First, list the letters and their alphabet positions:

• A: 1
• U: 21
• C: 3
• T: 20 (This is the 4th letter)
• I: 9
• O: 15
• N: 14

Now, we apply the coding rule letter by letter:

• 1st letter (A): Position 1. Shift is $+2$. New position = $1 + 2 = 3$. The 3rd letter is C.
• 2nd letter (U): Position 21. Shift is $+2$. New position = $21 + 2 = 23$. The 23rd letter is W.
• 3rd letter (C): Position 3. Shift is $+2$. New position = $3 + 2 = 5$. The 5th letter is E.
• 4th letter (T): Position 20. The shift is $0$ (the exception rule). New position = $20 + 0 = 20$. The 20th letter is T.
• 5th letter (I): Position 9. Shift is $+2$. New position = $9 + 2 = 11$. The 11th letter is K.
• 6th letter (O): Position 15. Shift is $+2$. New position = $15 + 2 = 17$. The 17th letter is Q.
• 7th letter (N): Position 14. Shift is $+2$. New position = $14 + 2 = 16$. The 16th letter is P.

The Final Code for AUCTION

Putting the coded letters together, we get the code for 'AUCTION' as CWETKQP.

This sequence matches one of the options provided.