Decoding the Cipher Logic

The problem requires identifying a coding pattern from the example UNSURE coded as ELGEHU and applying it to find the word coded as YNYHM.

Deriving the Coding Rule

The coding pattern involves two steps:

• Step 1: Reverse Alphabet Mapping (Atbash Cipher): Each letter is replaced by its opposite letter in the alphabet (e.g., $A \leftrightarrow Z$, $B \leftrightarrow Y$).
• Step 2: Positional Shift: The resulting letters are then shifted back by 1 position (e.g., $B \rightarrow A$, $C \rightarrow B$).

Verification using the example UNSURE $\rightarrow$ ELGEHU:

• Original Word: UNSURE
• Step 1 (Reverse Mapping): $U \rightarrow F$, $N \rightarrow M$, $S \rightarrow H$, $U \rightarrow F$, $R \rightarrow I$, $E \rightarrow V$. Intermediate result: FMHFI V.
• Step 2 (Shift -1): $F \rightarrow E$, $M \rightarrow L$, $H \rightarrow G$, $F \rightarrow E$, $I \rightarrow H$, $V \rightarrow U$. Final result: ELGEHU.

The established coding rule is: $Code(Letter) = Shift(-1, Rev(Letter))$.

Finding the Original Word for YNYHM

To find the word that codes to YNYHM, we reverse the coding process by applying the inverse operations in reverse order:

• Step 1: Inverse Shift (+1): Apply a shift of +1 to the coded word YNYHM.
  • $Y + 1 \rightarrow Z$
  • $N + 1 \rightarrow O$
  • $Y + 1 \rightarrow Z$
  • $H + 1 \rightarrow I$
  • $M + 1 \rightarrow N$
  The result after the inverse shift is ZOZIN.
• Step 2: Inverse Reverse Mapping: Find the reverse alphabet mapping (Atbash) for ZOZIN.
  • $Rev(Z) \rightarrow A$
  • $Rev(O) \rightarrow L$
  • $Rev(Z) \rightarrow A$
  • $Rev(I) \rightarrow R$
  • $Rev(N) \rightarrow M$
  The final result is ALARM.

Conclusion

Following the derived coding logic, the word that is written as YNYHM is ALARM.