Decoding the POPULAR Code Language

This question involves deciphering a code language where words are transformed based on a specific rule. We are given two examples: 'MAINTY' is coded as 'SGOTZE', and 'GENIOUS' is coded as 'MKTOUAY'. Our task is to find the code for the word 'POPULAR' using the same logic.

Analyzing the MAINTY Code Pattern

To find the pattern, let's compare the position of each letter in the alphabet. We assign numerical values to letters based on their position (A=1, B=2, ..., Z=26).

• M (position 13) corresponds to S (position 19). The difference is $19 - 13 = 6$.
• A (position 1) corresponds to G (position 7). The difference is $7 - 1 = 6$.
• I (position 9) corresponds to O (position 15). The difference is $15 - 9 = 6$.
• N (position 14) corresponds to T (position 20). The difference is $20 - 14 = 6$.
• T (position 20) corresponds to Z (position 26). The difference is $26 - 20 = 6$.
• Y (position 25) corresponds to E (position 5). To get from Y to E, we add 6. This involves wrapping around the alphabet: $25 + 6 = 31$. Since there are 26 letters, $31 - 26 = 5$, which corresponds to the letter E.

The pattern observed is that each letter in 'MAINTY' is shifted forward by 6 positions in the alphabet to get the corresponding letter in 'SGOTZE'.

Verifying the GENIOUS Code Pattern

Let's check if this +6 shift rule applies consistently to the second example:

• G (7) + 6 = 13, which is M.
• E (5) + 6 = 11, which is K.
• N (14) + 6 = 20, which is T.
• I (9) + 6 = 15, which is O.
• O (15) + 6 = 21, which is U.
• U (21) + 6 = 27. Wrapping around ($27 - 26 = 1$), we get A.
• S (19) + 6 = 25, which is Y.

The +6 shift pattern is confirmed as it holds true for both given word pairs.

Applying the POPULAR Code Pattern

Now, we apply the identified rule (shifting each letter forward by 6 positions with wrap-around) to the word 'POPULAR':

• P (position 16): $16 + 6 = 22$. The 22^nd letter is V.
• O (position 15): $15 + 6 = 21$. The 21^st letter is U.
• P (position 16): $16 + 6 = 22$. The 22^nd letter is V.
• U (position 21): $21 + 6 = 27$. Wrapping around ($27 - 26 = 1$), the 1^st letter is A.
• L (position 12): $12 + 6 = 18$. The 18^th letter is R.
• A (position 1): $1 + 6 = 7$. The 7^th letter is G.
• R (position 18): $18 + 6 = 24$. The 24^th letter is X.

Combining these resultant letters gives us the coded word: VUVARGX.

Final Answer Summary

The coding rule identified is a consistent shift of +6 positions for each letter in the alphabet, including wrap-around from Z to A. Applying this rule to 'POPULAR' results in the code 'VUVARGX'.