Decoding the Word Transformation

The question asks us to find the coding pattern used to transform 'TEACHER' into 'RCYAFCP' and 'SCHOOL' into 'QAFMMJ', and then apply this pattern to code the word 'SUBJECT'.

Analyzing the Coding Pattern

Let's examine the transformation for 'TEACHER' to 'RCYAFCP'. We assign numerical values to letters (A=1, B=2, ..., Z=26).

• T (20) -> R (18) : Shift = 18 - 20 = -2
• E (5) -> C (3) : Shift = 3 - 5 = -2
• A (1) -> Y (25) : Shift = 25 - 1 = +24 or -2 (wrapping around, $1 - 2 = -1 \equiv 25 \pmod{26}$)
• C (3) -> A (1) : Shift = 1 - 3 = -2
• H (8) -> F (6) : Shift = 6 - 8 = -2
• E (5) -> C (3) : Shift = 3 - 5 = -2
• R (18) -> P (16) : Shift = 16 - 18 = -2

The pattern observed is a consistent shift of -2 for each letter.

Let's verify this pattern with the second example: 'SCHOOL' to 'QAFMMJ'.

• S (19) -> Q (17) : Shift = -2
• C (3) -> A (1) : Shift = -2
• H (8) -> F (6) : Shift = -2
• O (15) -> M (13) : Shift = -2
• O (15) -> M (13) : Shift = -2
• L (12) -> J (10) : Shift = -2

The pattern of shifting each letter back by 2 positions is confirmed.

Applying the Pattern to 'SUBJECT'

Now, we apply the same -2 shift pattern to the word 'SUBJECT':

• S (19) : $19 - 2 = 17$ -> Q
• U (21) : $21 - 2 = 19$ -> S
• B (2) : $2 - 2 = 0 \equiv 26 \pmod{26}$ -> Z (wrapping around from B to A to Z)
• J (10) : $10 - 2 = 8$ -> H
• E (5) : $5 - 2 = 3$ -> C
• C (3) : $3 - 2 = 1$ -> A
• T (20) : $20 - 2 = 18$ -> R

Therefore, the coded word for 'SUBJECT' is 'QSZHCAR'.