Finding the Missing Number in the Sequence

The problem presents a sequence of digits written together with a question mark: 46753?414558. We need to find the digit that replaces the question mark from the given options.

Let's interpret the sequence as a series of individual digits lined up:

4, 6, 7, 5, 3, ?, 4, 1, 4, 5, 5, 8

The question mark is at the sixth position in this sequence of digits. We need to discover the pattern that connects these digits.

Analyzing the Sequence Pattern

Let's look at the digits around the missing number:

• The digit immediately before the question mark is 3.
• The digit immediately after the question mark is 4.

We are given options for the missing number: 12, 9, 51, and 3. Since the question mark is placed within a sequence of single digits, it is highly probable that the missing number is also a single digit from the options (9 or 3). The options 12 and 51 are less likely in this format unless the structure implies something else, but the layout strongly suggests a single missing character.

Let's consider the single-digit options. If the missing number is 3, the sequence becomes:

4, 6, 7, 5, 3, 3, 4, 1, 4, 5, 5, 8

Upon inserting 3, we notice that the digit immediately preceding the missing position is 3, and the inserted digit is also 3. This suggests a potential pattern:

• The missing digit is the same as the digit that comes directly before it in the sequence.

Step-by-Step Solution Process

Let's apply this observed pattern to find the missing number:

1. Locate the position of the question mark (?) in the sequence 4, 6, 7, 5, 3, ?, 4, 1, 4, 5, 5, 8.
2. Identify the digit that comes immediately before the question mark. This digit is 3.
3. Based on the pattern where the missing digit is the same as the preceding digit, the missing number is 3.

Verification of the Pattern

If we place 3 in the missing position, the sequence is 4, 6, 7, 5, 3, 3, 4, 1, 4, 5, 5, 8. The digit before the second 3 is indeed 3, which confirms our pattern for this specific position in the sequence.

The calculated missing number, 3, is present in the given options.

Revision Table: Sequence Pattern Analysis

Additional Information: Tips for Solving Number Sequences

Number sequence problems can have many different types of patterns. Some common approaches include:

• Looking for a constant difference or ratio between consecutive terms.
• Examining the differences between consecutive terms for a pattern.
• Checking for patterns in alternate terms or groups of terms.
• Considering mathematical operations like squares, cubes, or prime numbers.
• Looking for patterns related to the digits themselves (sum of digits, number of digits, etc.).
• Sometimes, the pattern might be position-based or involve repetition or visual cues, as likely seen in this problem.

It's often helpful to write the sequence clearly and systematically test potential patterns. Comparing your result with the given options can also guide your search for the correct pattern.