In a certain code language, the word "CONDITION" is written as "@#^$*!*#^" by assigning special symbols to letters. Using the same one to one mapping, how is the word "NOTION" written in that code language?

Introduction / Context:
This coding and decoding problem uses a substitution of letters with special symbols such as @, #, ^, $ and so on. The example "CONDITION" to "@#^$*!*#^" defines a fixed mapping between particular letters and specific symbols. The candidate must read off that mapping and apply it to the new word "NOTION".

Given Data / Assumptions:

• CONDITION is coded as @#^$*!*#^.
• Each letter is replaced by exactly one symbol, and the same letter always receives the same symbol.
• We must find the coded form of NOTION.
• The word CONDITION contains the letters C, O, N, D, I and T, which appear multiple times and define the mapping for all letters that also appear in NOTION.

Concept / Approach:
The idea is to match each letter of CONDITION to its corresponding symbol in the given code. Once we know how C, O, N, D, I and T are encoded, we can encode any word made only from those letters. The word NOTION uses letters N, O, T and I, all of which already appear in CONDITION, so no new mapping is needed. Then we simply write the symbols in the correct order.

Step-by-Step Solution:
Step 1: Write CONDITION above its code @#^$*!*#^ and match each letter. Step 2: From the first positions we see C maps to @, O maps to # and N maps to ^. Step 3: The fourth letter D maps to $, the fifth letter I maps to * and the sixth letter T maps to !. Step 4: Check repeated letters: the seventh letter I is again coded as *, the eighth O as # and the ninth N as ^. This confirms a consistent mapping. Step 5: Now encode the word NOTION, which consists of N, O, T, I, O and N. Step 6: Using the mapping, N becomes ^, O becomes #, T becomes !, I becomes * and again O becomes # and N becomes ^. Step 7: So NOTION is written as ^ # ! * # ^, that is ^#!*#^.

Verification / Alternative check:
We can quickly verify by reversing the mapping on the candidate code ^#!*#^. Mapping ^ back to N, # back to O, ! back to T and * back to I reconstructs N O T I O N in order. This confirms that our encoding and decoding are consistent and that no letters have been mismapped.

Why Other Options Are Wrong:
The other options reorder the symbols or insert an incorrect symbol at one position, which corresponds to swapping letters or changing one letter in NOTION. However, there is no justification for such changes because the mapping from CONDITION is fixed and unambiguous. Only ^#!*#^ respects the exact letter to symbol relationship in the correct order of the target word.

Common Pitfalls:
A common mistake is to assume that similar looking symbols such as # and ^ might be interchangeable or to misalign letters when reading the mapping from CONDITION. Another error is to try to derive a numerical rule for the symbols, which is not needed. Carefully pairing each letter with its symbol exactly as shown in the example avoids these complications.

Final Answer:
By applying the same symbol substitution used for CONDITION, the word "NOTION" is coded as ^#!*#^.