Decoding the Code: ATHLETE to GYLOIYK

This problem involves figuring out a secret code or pattern used to change the word ATHLETE into GYLOIYK. Once we find the pattern, we need to apply it to the word VILLAIN to find its coded form.

Analyzing the ATHLETE Encoding Pattern

Let's look at how each letter in ATHLETE corresponds to the letters in GYLOIYK and see if there's a pattern in the shift (how many positions each letter moved in the alphabet).

We can represent the letters by their position in the alphabet (A=1, B=2, ..., Z=26).

From the table, we can see the pattern of shifts applied to ATHLETE is: +6, +5, +4, +3, +4, +5, +6. The shifts decrease from +6 down to +3 and then increase back up to +6.

Applying the Pattern to VILLAIN

Now, we'll use the same sequence of shifts (+6, +5, +4, +3, +4, +5, +6) to encode the word VILLAIN.

First, let's list the letters of VILLAIN and their positions in the alphabet:

• V is the 22nd letter.
• I is the 9th letter.
• L is the 12th letter.
• L is the 12th letter.
• A is the 1st letter.
• I is the 9th letter.
• N is the 14th letter.

Now, let's apply the shifts step-by-step:

Explanation of Calculations:

• For the first letter V (position 22), we add 6: $22 + 6 = 28$. Since there are only 26 letters, we find the remainder when divided by 26 ($28 \pmod{26}$), which is 2. The 2nd letter is B.
• For I (position 9), add 5: $9 + 5 = 14$. The 14th letter is N.
• For L (position 12), add 4: $12 + 4 = 16$. The 16th letter is P.
• For the second L (position 12), add 3: $12 + 3 = 15$. The 15th letter is O.
• For A (position 1), add 4: $1 + 4 = 5$. The 5th letter is E.
• For the second I (position 9), add 5: $9 + 5 = 14$. The 14th letter is N.
• For N (position 14), add 6: $14 + 6 = 20$. The 20th letter is T.

Final Coded Word for VILLAIN

Combining the encoded letters, we get BNPOENT.