In a certain system of writing three number expressions of the form a x b x c, the numbers on the left side are simply rearranged to form a three digit number on the right side. For example, 7 x 4 x 9 is written as 479, 9 x 5 x 2 is written as 592, and 6 x 9 x 5 is written as 965. Using exactly the same pattern, what number should replace the question mark in 8 x 6 x 2 = ?

Introduction / Context:
This question deals with a purely symbolic pattern where three numbers separated by x are rearranged to form a three digit number. The x symbol is not a multiplication sign in the usual sense, but a separator showing the pattern structure. The task is to observe how the positions of a, b, and c change from left to right and then apply that same ordering rule to the new triple 8, 6, and 2.

Given Data / Assumptions:

• 7 x 4 x 9 becomes 479. • 9 x 5 x 2 becomes 592. • 6 x 9 x 5 becomes 965. • We must find the result of 8 x 6 x 2. • The operation x is not real multiplication here.

Concept / Approach:
We represent the three numbers as a, b, and c, and then examine how they appear in the three digit result. By comparing the triples with their codes, we can determine the position of each of a, b, and c in the result. Once this pattern is identified, we apply it directly to the triple 8, 6, and 2. No arithmetic operations like multiplication or addition are needed, only positional rearrangement.

Step-by-Step Solution:
Step 1: For 7 x 4 x 9, write a = 7, b = 4, c = 9. Step 2: The result is 479, which has digits 4, 7, and 9. Step 3: This can be written as (b, a, c) = (4, 7, 9). Step 4: For 9 x 5 x 2, a = 9, b = 5, c = 2. The result 592 corresponds to digits (5, 9, 2). Step 5: Again this is (b, a, c). Step 6: For 6 x 9 x 5, a = 6, b = 9, c = 5, and the result 965 equals (9, 6, 5), which is once more (b, a, c). Step 7: So the rule is consistent: the code is always b, then a, then c. Step 8: Now apply this to 8 x 6 x 2, where a = 8, b = 6, c = 2. Step 9: The code is (b, a, c) = (6, 8, 2), giving 682.

Verification / Alternative check:
Check that there is no other simple ordering rule that fits all examples. For instance, (a, b, c) would yield 749, 952, and 695, which do not match. (b, c, a) would give 4, 9, 7 as 497, and so on, also failing to align with all given codes. Only (b, a, c) consistently produces the results 479, 592, and 965, confirming that 682 is the correct continuation of the pattern.

Why Other Options Are Wrong:
Option 286 corresponds to (a, c, b) and does not match the pattern used in the examples. Option 628 corresponds roughly to (c, a, b) and is inconsistent with the established rule. Option 268 corresponds to (c, b, a) and fails to reproduce the sample codes. Option 826 corresponds to (a, b, c), which is clearly not the rearrangement used in the examples.

Common Pitfalls:
Learners sometimes assume x means multiplication and start computing numeric products, which is not supported by the right hand side format. Another mistake is to look only at one of the examples and infer an ordering that does not work for the others. It is essential to verify that the proposed pattern matches all given cases before applying it to the new triple.

Final Answer:
Following the consistent rearrangement rule (b, a, c), the expression 8 x 6 x 2 is written as 682.