Decoding the AGENT & CHAIR Coding Pattern

The question asks us to find the coded representation of the word 'FAITH' based on the provided examples: 'AGENT' is coded as 'ZHGOG' and 'CHAIR' is coded as 'XICJI'. To solve this, we need to identify the specific coding logic or pattern used.

Let's analyze the relationship between the letters in the original words and their corresponding coded letters. We'll use the position of each letter in the English alphabet (A=1, B=2, ..., Z=26).

Analyzing the AGENT to ZHGOG Code

• A (1st letter) maps to Z (26th letter). This is a reverse alphabet mapping (Position 1 maps to 26, since $1 + 26 = 27$).
• G (7th letter) maps to H (8th letter). This is a shift of +1 ($7 + 1 = 8$).
• E (5th letter) maps to G (7th letter). This is a shift of +2 ($5 + 2 = 7$).
• N (14th letter) maps to O (15th letter). This is a shift of +1 ($14 + 1 = 15$).
• T (20th letter) maps to G (7th letter). This is a reverse alphabet mapping (Position 20 maps to 7, since $20 + 7 = 27$).

The pattern observed for 'AGENT' is: Reverse, +1, +2, +1, Reverse.

Analyzing the CHAIR to XICJI Code

Let's verify this pattern with the second example:

• C (3rd letter) maps to X (24th letter). This is a reverse alphabet mapping ($3 + 24 = 27$).
• H (8th letter) maps to I (9th letter). This is a shift of +1 ($8 + 1 = 9$).
• A (1st letter) maps to C (3rd letter). This is a shift of +2 ($1 + 2 = 3$).
• I (9th letter) maps to J (10th letter). This is a shift of +1 ($9 + 1 = 10$).
• R (18th letter) maps to I (9th letter). This is a reverse alphabet mapping ($18 + 9 = 27$).

The pattern holds true for 'CHAIR' as well: Reverse, +1, +2, +1, Reverse.

Applying the Pattern to FAITH

Now, we apply the confirmed pattern (Reverse, +1, +2, +1, Reverse) to the word 'FAITH':

The word is FAITH. Let's find the positions of its letters:

• F is the 6th letter.
• A is the 1st letter.
• I is the 9th letter.
• T is the 20th letter.
• H is the 8th letter.

Applying the pattern step-by-step:

• 1st letter (F): Apply Reverse mapping. The position is 6. $27 - 6 = 21$. The 21st letter is U.
• 2nd letter (A): Apply +1 shift. The position is 1. $1 + 1 = 2$. The 2nd letter is B.
• 3rd letter (I): Apply +2 shift. The position is 9. $9 + 2 = 11$. The 11th letter is K.
• 4th letter (T): Apply +1 shift. The position is 20. $20 + 1 = 21$. The 21st letter is U.
• 5th letter (H): Apply Reverse mapping. The position is 8. $27 - 8 = 19$. The 19th letter is S.

Combining these letters gives the coded word: UBKUS.