In a certain numerical code, the symbol "@" denotes a special operation between two numbers. It is known that 17 @ 1 = 8, 9 @ 1 = 4 and 6 @ 4 = 1. Using the same rule, what is the value of 8 @ 2?

Introduction:
This question introduces another custom numeric operator, written as "@". Several example equations involving pairs of numbers and small integer results are given. We must identify the rule that connects each pair to its result and then apply that rule to the pair 8 and 2. This type of problem is common in reasoning tests to check comfort with basic arithmetic patterns.

Given Data / Assumptions:
The relationships are:
1) 17 @ 1 = 8
2) 9 @ 1 = 4
3) 6 @ 4 = 1
We must find 8 @ 2. We assume:
1) The operator @ is defined consistently for all input pairs.
2) The results are derived through a simple arithmetic expression, likely involving differences, sums, or averages of the two numbers.

Concept / Approach:
Because the results 8, 4, and 1 are noticeably smaller than the first numbers in each pair, it is natural to examine the difference between the two numbers. A convenient pattern to test is whether the result equals half of the difference between the first and second numbers. If this pattern works for all three examples, we can reasonably apply it to 8 and 2.

Step-by-Step Solution:
Step 1: For 17 @ 1, compute the difference 17 - 1 = 16.Step 2: Half of this difference is 16 / 2 = 8, which matches the given result.Step 3: For 9 @ 1, compute 9 - 1 = 8, and half of this is 8 / 2 = 4, again matching the given result.Step 4: For 6 @ 4, compute 6 - 4 = 2, and half is 2 / 2 = 1, which also matches the given result.Step 5: Since in each case the result equals half of the difference between the first and second numbers, we define a @ b = (a - b) / 2.Step 6: Apply this rule to 8 @ 2: compute (8 - 2) / 2.Step 7: The difference is 6, and 6 / 2 = 3.Step 8: Therefore, 8 @ 2 equals 3.

Verification / Alternative check:
We can rule out alternative simple patterns. The sum based rule (a + b) or (a + b) / 2 does not produce the results 8, 4, and 1. Products or ratios get even further from these small integers. The half difference rule is the only simple arithmetic expression that matches all three sample equations precisely.

Why Other Options Are Wrong:
The values 26, 23, and 47 are far larger than expected from a rule that generates 8, 4, and 1 for reasonably small inputs. The value 5 would require a different operation or an added constant. None of these alternative values are consistent with the pattern confirmed by all three examples, so they cannot be correct for 8 @ 2.

Common Pitfalls:
Some learners try to force a sum based or product based rule because those are more familiar, but these do not fit all the data. Another mistake is to test a rule on a single example and then apply it without checking the others, which can lead to incorrect generalisation. Always verify a hypothesised rule with every example provided.

Final Answer:
Under the defined pattern, the value of 8 @ 2 is 3.