Using the reference sequence ABC$+#DEF&=?GHI!2*@, find the missing term in the analogy: ABC : @*2 :: $#E : ____

Introduction / Context:
This is a coded analogy question where a long mixed string of letters, digits, and symbols acts as a reference. We are told that ABC corresponds to @*2 under a certain pattern derived from the reference sequence. We must apply the same pattern to $#E to determine the missing term. Such questions test the ability to interpret hidden mapping rules in a complex sequence.

Given Data / Assumptions:

• The reference sequence is ABC$+#DEF&=?GHI!2*@.
• We know that ABC maps to @*2.
• We need to find what $#E maps to using the same pattern.
• Positions in the reference string are fixed; mapping is positional rather than alphabetical.

Concept / Approach:
We analyse how ABC is transformed into @*2 using the positions of these characters within the reference sequence. If a consistent index based rule can be identified, we then apply it to the characters $, #, and E. The rule turns out to be a reflection across the ends of the sequence, pairing characters from the front with characters from the back.

Step-by-Step Solution:
Step 1: Number the characters in the reference sequence from left to right. ABC$+#DEF&=?GHI!2*@ has 19 characters, indexed from 0 to 18. Step 2: A, B, C are at indices 0, 1, and 2 respectively. The mapped term @*2 has characters at indices 18 (@), 17 (*), and 16 (2). Step 3: Notice that 18 is 18 minus 0, 17 is 18 minus 1, and 16 is 18 minus 2. So each character at index i maps to the character at index 18 minus i. This is a reflection rule. Step 4: Now identify the indices of $, #, and E. From the sequence, $ is at index 3, # is at index 5, and E is at index 7. Step 5: Apply the reflection rule. For $, use index 18 minus 3 equals 15. The character at index 15 is !. Step 6: For #, use index 18 minus 5 equals 13. The character at index 13 is H. Step 7: For E, use index 18 minus 7 equals 11. The character at index 11 is ?. Step 8: Thus $#E maps to !H? under the same transformation as ABC to @*2.

Verification / Alternative check:
We can verify by checking that each pair of mapped positions sums to 18. A (0) and @ (18), B (1) and * (17), C (2) and 2 (16) all satisfy the rule. Similarly, $ (3) with ! (15), # (5) with H (13), and E (7) with ? (11) each satisfy index original plus index mapped equals 18. Therefore, the reflection mapping is consistent and correct.

Why Other Options Are Wrong:
HH!, !HG, and ?H! are all made from similar looking characters but do not correspond to the correct reflected indices. For example, ?H! would mean using characters at indices 11, 13, and 15 in a different order than that defined by the rule. Only !H? preserves the precise index mapping from left to right, ensuring that each character in $#E is reflected correctly.

Common Pitfalls:
Some candidates try to find a direct alphabetical or symbolic relation between ABC and @*2 without considering the larger reference string. Others may reverse the order incorrectly or miscount indices. Starting by indexing every character and identifying the pattern of index reversal avoids these errors and reveals the correct rule.

Final Answer:
The missing term that completes the analogy is !H?.