Decoding the Code Language Pattern

This problem involves deciphering a specific code language where words are transformed based on a consistent pattern. We are given two examples: 'FAITH' becomes 'JDMWL', and 'GLASS' becomes 'KOEVW'. Our task is to apply the same logic to find the coded form of 'HEART'.

Analyzing the FAITH to JDMWL Transformation

Let's examine the relationship between the letters in 'FAITH' and 'JDMWL'. We can represent the letters by their position in the alphabet (A=1, B=2, ..., Z=26).

• F is the 6th letter, J is the 10th letter. The difference is $10 - 6 = 4$.
• A is the 1st letter, D is the 4th letter. The difference is $4 - 1 = 3$.
• I is the 9th letter, M is the 13th letter. The difference is $13 - 9 = 4$.
• T is the 20th letter, W is the 23rd letter. The difference is $23 - 20 = 3$.
• H is the 8th letter, L is the 12th letter. The difference is $12 - 8 = 4$.

The pattern observed is adding 4, then 3, then 4, then 3, then 4 to the position of each letter:

• F (position $6$) $+ 4$ gives $10$, which corresponds to J.
• A (position $1$) $+ 3$ gives $4$, which corresponds to D.
• I (position $9$) $+ 4$ gives $13$, which corresponds to M.
• T (position $20$) $+ 3$ gives $23$, which corresponds to W.
• H (position $8$) $+ 4$ gives $12$, which corresponds to L.

This confirms the coding sequence is $+4, +3, +4, +3, +4$.

Verifying the Pattern with GLASS to KOEVW

Let's check if this same $+4, +3, +4, +3, +4$ pattern applies to the second example, 'GLASS' becoming 'KOEVW'.

• G (position $7$) $+ 4$ gives $11$ (K).
• L (position $12$) $+ 3$ gives $15$ (O).
• A (position $1$) $+ 4$ gives $5$ (E).
• S (position $19$) $+ 3$ gives $22$ (V).
• S (position $19$) $+ 4$ gives $23$ (W).

The pattern holds true for 'GLASS' as well, reinforcing our understanding of the coding logic.

Applying the Code to HEART

Now, we apply the established pattern ($+4, +3, +4, +3, +4$) to the word 'HEART':

1. H: The 8th letter. Apply $+4$. $8 + 4 = 12$. The 12th letter is L.
2. E: The 5th letter. Apply $+3$. $5 + 3 = 8$. The 8th letter is H.
3. A: The 1st letter. Apply $+4$. $1 + 4 = 5$. The 5th letter is E.
4. R: The 18th letter. Apply $+3$. $18 + 3 = 21$. The 21st letter is U.
5. T: The 20th letter. Apply $+4$. $20 + 4 = 24$. The 24th letter is X.

Combining these results, we form the coded word: LHEUX.

Final Coded Word

Therefore, in this specific code language, 'HEART' is written as 'LHEUX'.