Some equations are solved according to a fixed three number coding pattern: 2 x 3 x 5 = 523, 6 x 4 x 1 = 164 and 8 x 2 x 4 = 482. Using the same pattern, what is the value of 6 x 8 x 2?

Introduction / Context:
This is a three number rearrangement code similar to other coding questions. Instead of performing arithmetic operations, the three input numbers are rearranged to form a three digit output. By analyzing the provided examples, we must deduce the consistent pattern in which the positions are swapped and then apply that pattern to 6, 8 and 2.

Given Data / Assumptions:

• 2 x 3 x 5 is coded as 523.
• 6 x 4 x 1 is coded as 164.
• 8 x 2 x 4 is coded as 482.
• We must determine the code for 6 x 8 x 2.
• The symbol x represents a special pattern, not multiplication.

Concept / Approach:
Because the outputs are three digit numbers composed of the same digits as the inputs, the most likely code is a positional rearrangement. We must identify which original number becomes the hundreds digit, which becomes the tens digit and which becomes the units digit. Once a consistent mapping is established across all examples, we apply it to the new triple.

Step-by-Step Solution:
Step 1: Examine 2 x 3 x 5 = 523. The inputs are 2, 3 and 5. The output 523 uses the digits 5, 2 and 3.Step 2: This suggests the pattern (first, second, third) → (third, first, second). Here, hundreds digit is the third number, tens digit is the first number and units digit is the second number.Step 3: Confirm this with the second equation. For 6 x 4 x 1, the digits are 6, 4, 1. Using the pattern third, first, second gives 1, 6 and 4, which forms 164. This matches the given result.Step 4: Confirm again with the third equation. For 8 x 2 x 4, the digits are 8, 2, 4. Applying the same pattern yields 4, 8 and 2, which produces 482, again matching the provided value.Step 5: The mapping is now firmly established as (first, second, third) → (third, first, second).Step 6: Apply this pattern to 6 x 8 x 2, where the first number is 6, the second is 8 and the third is 2.Step 7: According to the rule, the hundreds digit is the third number (2), the tens digit is the first number (6) and the units digit is the second number (8), giving 2, 6 and 8.Step 8: Combine these digits to get the coded number 268.

Verification / Alternative check:
No other simple rearrangement such as second, third, first or first, third, second will produce all three given codes 523, 164 and 482 correctly. Testing these alternatives quickly shows mismatches. The third, first, second pattern is the only one that fits every example and therefore must be used for the target triple. Rechecking the ordering for 6, 8 and 2 confirms that 268 is correct.

Why Other Options Are Wrong:
The options 826, 286, 628 and 682 correspond to different permutations of 2, 6 and 8 that are not generated by the established mapping. They might look superficially plausible but they do not respect the rule confirmed by the earlier equations. Since the pattern is consistent across all examples, any option that does not follow it must be rejected.

Common Pitfalls:
Some candidates immediately assume multiplication because of the x symbols and spend time computing products, which leads nowhere. Others pick a rearrangement based on only one example. The correct approach is to examine all given equations to find a rule that works every time and then apply that rule without alteration.

Final Answer:
Using the same rearrangement pattern, the correct coded value of 6 x 8 x 2 is 268.