In this coding puzzle, three digit numbers are transformed according to a fixed pattern: 462 is written as 551 and 398 is written as 487. On the same basis, what should 856 be written as?

Introduction / Context:
This is a simple number coding question where each three digit number is converted into another three digit number using a consistent rule. You are given two examples, 462 = 551 and 398 = 487, and must apply the same rule to the number 856. Questions like this test your ability to identify an underlying arithmetic relationship between input and output values and to generalise that pattern to a new case.

Given Data / Assumptions:

• 462 maps to 551 under the coding rule.
• 398 maps to 487 under the same rule.
• The rule is uniform for all numbers in this question.
• We must find the coded form of 856.
• The transformation is numerical, not a rearrangement of digits.

Concept / Approach:
The easiest approach is to consider whether the output is obtained by adding or subtracting a fixed number from the input. You can compute the difference between the given pairs and see whether it is constant. If the difference is the same for both examples, then the code is simply adding that constant. This is a very common pattern in such three digit number puzzles and is quick to apply once detected.

Step-by-Step Solution:
Step 1: Compute the difference between 462 and 551. 551 - 462 = 89. Step 2: Compute the difference between 398 and 487. 487 - 398 = 89. Step 3: The difference is the same in both cases, suggesting that the coding rule is "add 89 to the original number". Step 4: Now apply this rule to 856. 856 + 89 = 945.

Verification / Alternative check:
To verify, you can check whether any plausible alternative pattern, such as manipulating digits separately, would produce the given outputs and also match 856. For instance, reversing digits or adding digit sums does not produce 551 from 462 or 487 from 398. The clean and consistent explanation is that each number is simply increased by 89. Because 462 + 89 = 551 and 398 + 89 = 487 both hold, and 856 + 89 gives 945, the pattern appears stable and unambiguous.

Why Other Options Are Wrong:
Options 745, 773, 743 and 851 do not equal 856 + 89 and therefore cannot match the discovered rule. If you attempted to fit a different rule to produce one of those values, it would not simultaneously work for both 462 and 398 without becoming contrived. Since the question explicitly tells you that the same basis must be used for each transformation, only the output that preserves the constant difference of 89 is acceptable, which is 945.

Common Pitfalls:
A common mistake is to immediately manipulate digits separately (for example, adding or subtracting tens and units) without first checking the simple possibility of adding a fixed number. Another pitfall is to find a rule that works for the first example but not verify it with the second, leading to a mismatched pattern. Always test any hypothesised transformation on all given examples before applying it to the unknown case.

Final Answer:
On the same basis as the given examples, 856 should be written as 945.