Some equations have been solved using a specific coding pattern. For example: 8x7x6 = 765 and 5x3x2 = 421. Using the same pattern (applied consistently to each number), what will 9x6x4 be equal to?

Introduction / Context:
This is a number coding pattern problem. The symbol x here is not multiplication; it simply separates three numbers. The output is formed by applying a consistent transformation to each of the three numbers and then writing the results together as a three-digit number.

Given Data / Assumptions:

• 8x7x6 = 765
• 5x3x2 = 421
• Find: 9x6x4 = ?
• Assume the same transformation is applied to each number individually.

Concept / Approach:
Compare each input triple with its output. A strong clue is that 8,7,6 become 7,6,5 which looks like each number is reduced by 1. Verify this rule using the second example before applying it to the target triple.

Step-by-Step Solution:
Check 8x7x6 = 765: 8 decreased by 1 gives 7 7 decreased by 1 gives 6 6 decreased by 1 gives 5 So output becomes 765. Matches. Verify with 5x3x2 = 421: 5-1 = 4, 3-1 = 2, 2-1 = 1 Output 421 matches. Now apply to 9x6x4: 9-1 = 8 6-1 = 5 4-1 = 3 So 9x6x4 = 853

Verification / Alternative check:
Since both examples match the same simple decrement-by-1 rule, using it for 9,6,4 is consistent. The output must be 8,5,3 in the same order, giving 853.

Why Other Options Are Wrong:
583: rearranges the order incorrectly. 841: uses wrong decrements or mixes digits. 481: looks like subtracting 5,2,3 randomly. 754: would correspond to 8,6,5 not to 9,6,4.

Common Pitfalls:
Treating x as multiplication, changing the order of numbers, or using different operations for each position rather than a uniform rule are frequent mistakes.

Final Answer:
853