Consider the following sequence of letters, digits and symbols: K$23DBE8HM4@5JF4%K1+WR#AA*415. How many such symbols are there which are not immediately preceded by a letter but are immediately followed by a number?

Introduction / Context:
This problem involves scanning a mixed sequence of letters, digits and special symbols to count symbols that satisfy a specific positional condition. It tests the ability to distinguish character types (letter, digit, symbol) and to apply a local condition involving the immediate neighbours of each symbol in the sequence.

Given Data / Assumptions:

• The sequence is: K$23DBE8HM4@5JF4%K1+WR#AA*415.
• We consider a character to be a symbol if it is neither a letter nor a digit (for example @, %, +, #, *, $).
• We must count those symbols that are not immediately preceded by a letter but are immediately followed by a digit.
• Positions are checked only with respect to immediate left and immediate right neighbours.

Concept / Approach:
The approach is to scan the sequence from left to right, identify each symbol, and then check two conditions: the character on its immediate left must either be a digit, another symbol or not exist (at the very start), and the character on its immediate right must be a digit. Only symbols that satisfy both conditions are counted. Careful classification of each character as letter, digit or symbol is necessary.

Step-by-Step Solution:
Step 1: List the sequence with each character clearly: K $ 2 3 D B E 8 H M 4 @ 5 J F 4 % K 1 + W R # A A * 4 1 5. Step 2: Identify symbols in the sequence: $, @, %, +, #, *. Step 3: Check each symbol one by one. For $: previous character is K (a letter) and next character is 2 (a digit). It is immediately followed by a digit but it is immediately preceded by a letter, so it does not satisfy the given condition. For @: previous character is 4 (a digit) and next character is 5 (a digit). It is not immediately preceded by a letter and is immediately followed by a digit, so it satisfies the condition. For %: previous character is 4 (a digit) and next character is K (a letter). It is not preceded by a letter but is not followed by a digit, so it fails the condition. For +: previous character is 1 (a digit) and next character is W (a letter). It is not followed by a digit, so it fails. For #: previous character is R (a letter), so it fails immediately. For *: previous character is A (a letter), so it also fails. Step 4: Only the symbol @ satisfies both parts of the condition. Step 5: Therefore, there is exactly 1 such symbol.

Verification / Alternative check:
We can quickly recheck by highlighting each symbol in the sequence and marking L for letter, D for digit and S for symbol around it. Only the pattern D S D with S as the symbol and the left neighbour not a letter, appears once at 4 @ 5. This reconfirms that the count is one.

Why Other Options Are Wrong:
Counts of 2 or 3 would require other symbols to meet both conditions, but careful examination shows that none of $, %, +, # or * qualify. A count of 0 contradicts the valid @ case that clearly fits both conditions.

Common Pitfalls:
A frequent mistake is to misclassify digits as letters or vice versa or to read the condition only partially, for example checking only that the symbol is followed by a number but ignoring whether it is preceded by a letter. Another pitfall is to overlook one of the symbols when scanning a long mixed sequence. A methodical left to right scan helps prevent such errors.

Final Answer:
There is exactly 1 such symbol in the given sequence.