In this number pattern puzzle, if 9 = 63, 8 = 48 and 7 = 35, then according to the same rule what should 4 be equal to?

Introduction / Context:
This question presents an apparent sequence of equalities such as 9 = 63, 8 = 48 and 7 = 35, and then asks what number 4 should correspond to under the same hidden rule. Problems like this are classic number pattern puzzles that test your ability to detect relationships rather than perform complicated calculations. The key is to look for a simple arithmetic operation that consistently turns the left hand number into the right hand number for all given examples.

Given Data / Assumptions:

• The pattern shows: 9 corresponds to 63, 8 corresponds to 48, and 7 corresponds to 35.
• The question asks for the value that 4 should correspond to under the same rule.
• We assume standard arithmetic operations like addition, subtraction, multiplication and division.
• The same rule must work for all given pairs, not just one of them.

Concept / Approach:
A good strategy for these puzzles is to check simple expressions such as n * (n - 1), n * (n - 2) or 2 * n^2 and see if any match all entries. For 9 = 63, the product 9 * 7 equals 63, and 7 is 9 - 2. For 8 = 48, the product 8 * 6 equals 48, and 6 is 8 - 2. For 7 = 35, the product 7 * 5 equals 35, and 5 is 7 - 2. This reveals the pattern: each number n is being multiplied by (n - 2). Once we identify this rule, we can apply it to 4 to find the missing value.

Step-by-Step Solution:
Step 1: Consider the first pair: 9 and 63. Compute 9 * (9 - 2) = 9 * 7 = 63. Step 2: Check the second pair using the same rule: 8 * (8 - 2) = 8 * 6 = 48, which matches the given value. Step 3: Check the third pair: 7 * (7 - 2) = 7 * 5 = 35, again matching the given value. Step 4: Conclude that the rule is "multiply the number by two less than itself" or n * (n - 2). Step 5: Apply the rule to 4: compute 4 * (4 - 2) = 4 * 2 = 8. Step 6: Compare 8 with the answer options and select the matching choice.

Verification / Alternative check:
To verify, we can test whether any alternative rule might produce the same sequence without contradicting the data. For example, n^2 - 2n also gives n * (n - 2), so it is essentially the same method and not a new rule. No simple linear rule like 7n or 5n + something fits all three given pairs at once. Because the pattern n * (n - 2) correctly reproduces every example and gives a clear value for 4, we can be confident that it is the intended logic of the puzzle. Therefore, the answer 8 is unique and consistent.

Why Other Options Are Wrong:
4: This would require a rule that shrinks the number instead of multiplying it by a positive factor, which does not match the earlier pairs.
12: 4 * 3 equals 12, but that would imply multiplying n by n - 1, which fails for 9 and 8 because 9 * 8 is not 63 and 8 * 7 is not 48.
16: 4 * 4 equals 16, which suggests squaring the number, but 9^2 is 81, not 63, and 8^2 is 64, not 48.
None of these: This is incorrect because 8 fits perfectly with the established pattern n * (n - 2).

Common Pitfalls:
Many learners try complicated formulas too early, such as combining squares, cubes or multiple operations, when a simple multiplication pattern is enough. Another common mistake is to find a rule that fits only one or two of the given examples and then stop checking. A valid pattern must apply to all provided pairs. Some students also guess based on the size of the numbers instead of verifying calculations. To avoid these issues, always test your rule against every example in the puzzle and confirm that it works consistently before applying it to the missing case.

Final Answer:
Using the rule n * (n - 2), the value corresponding to 4 is 8.