In a certain code language, the word "PEPPER" is written as "@#@@#!" and the word "AIM" is written as "^?*". Using the same symbol code, how is the word "PAMPER" written in that code language?

Introduction:
This coding question uses special characters to represent letters. We are told that "PEPPER" is written as "@#@@#!" and "AIM" is written as "^?*". We must determine the code for "PAMPER" using the same consistent mapping from letters to symbols. The task checks how well you can maintain a coherent mapping when letters appear in multiple positions and combinations.

Given Data / Assumptions:
The code for PEPPER is @#@@#!, which corresponds to the letters P, E, P, P, E, R. The code for AIM is ^?*, corresponding to A, I, M. We assume that each letter corresponds to exactly one symbol and that this mapping is consistent across all words. The target word PAMPER is composed of letters P, A, M, P, E, R, which are all present in the mapping derived from PEPPER and AIM.

Concept / Approach:
The approach is to establish a letter to symbol mapping from the given examples by pairing letters with symbols in their respective positions. Once the mapping is complete, we apply it to PAMPER by substituting each letter with its symbol in order. Because all letters of PAMPER appear in the given examples, no guesswork is needed.

Step-by-Step Solution:
Step 1: Analyze PEPPER → @#@@#!. The letters P, E, P, P, E, R align with the symbols @, #, @, @, #, !.Step 2: From this, we deduce that P = @, E = #, and R = !.Step 3: Analyze AIM → ^?*. The letters A, I, M align with the symbols ^, ?, *.Step 4: From this, we deduce A = ^, I = ?, and M = *.Step 5: Combine the mappings: P = @, E = #, R = !, A = ^, M = *.Step 6: The word PAMPER consists of letters P, A, M, P, E, R in that sequence.Step 7: Substitute each letter using the mapping: P = @, A = ^, M = *, P again = @, E = #, R = !.Step 8: Putting these symbols together gives @^*@#!.Step 9: Therefore, "PAMPER" is written as @^*@#! in the code language.

Verification / Alternative check:
To verify, we can re check PEPPER and AIM with our map. PEPPER becomes @#@@#! and AIM becomes ^?*, exactly as given. There are no contradictions, and every letter in PAMPER is mapped from established relationships, so the encoding is consistent.

Why Other Options Are Wrong:
Option b @*^@#! would assign * to A and ^ to M, which contradicts the mapping from AIM. Option c @^*#@! misplaces the # symbol and breaks the consistent positions of P and E. Option d @^*@!# swaps the positions of # and !, effectively mis encoding E and R. Option e @*^#!@ introduces an incorrect ordering of symbols that does not follow the letter sequence P, A, M, P, E, R.

Common Pitfalls:
Some learners may incorrectly assume that positions in the word influence the mapping beyond the strict one to one letter symbol relationship, leading to inconsistent symbol use for repeated letters. Others may misread the sequence of special characters, particularly when several similar symbols appear together.

Final Answer:
The word "PAMPER" is written as @^*@#! in the given code language.