Solving the Letter Series Completion Problem

The problem asks us to find the missing letters in a given letter series. We are provided with the series and four options, each containing a sequence of letters that can fill the blanks in order.

The given letter series is: a_ca_bab_ad_abc_db

Let's count the total number of characters in the series, including the blanks:

a (1) _ (2) c (3) a (4) _ (5) b (6) a (7) b (8) _ (9) a (10) d (11) _ (12) a (13) b (14) c (15) _ (16) d (17) b (18)

The series has a total of 18 positions, with blanks at positions 2, 5, 9, 12, 16, and 18. There are 6 blanks in total.

However, the options provided contain only 5 letters. This indicates a potential discrepancy, but we will proceed by testing the options by filling the first 5 blanks (at positions 2, 5, 9, 12, 16) and observing the resulting pattern, keeping in mind the last character at position 18 is 'b'.

Let's test Option 1: bdcba. We will place these letters into the blanks at positions 2, 5, 9, 12, and 16:

• Blank at position 2 gets 'b'. Series becomes: abca_bab_ad_abc_db
• Blank at position 5 gets 'd'. Series becomes: abcadbab_ad_abc_db
• Blank at position 9 gets 'c'. Series becomes: abcadbabcad_abc_db
• Blank at position 12 gets 'b'. Series becomes: abcadbabcadbabc_db
• Blank at position 16 gets 'a'. Series becomes: abcadbabcadbabacdb

The series after filling the first 5 blanks with bdcba is: abcadbabcadbacadb

Let's re-check the filling process carefully with the original series structure:

Original series: a _ c a _ b a b _ a d _ a b c _ d b

Fill blanks 2, 5, 9, 12, 16 with b, d, c, b, a:

• Position 1: a
• Position 2 (blank 1): b
• Position 3: c
• Position 4: a
• Position 5 (blank 2): d
• Position 6: b
• Position 7: a
• Position 8: b
• Position 9 (blank 3): c
• Position 10: a
• Position 11: d
• Position 12 (blank 4): b
• Position 13: a
• Position 14: b
• Position 15: c
• Position 16 (blank 5): a
• Position 17: d
• Position 18: b

The resulting filled series is: abcadbabcadbabcadb

Now, let's look for a repeating pattern in abcadbabcadbabcadb. We can try dividing it into equal parts. Since the total length is 18, possible block lengths are 2, 3, 6, 9, 18.

• If we divide into blocks of 6: abcadb | abcadb | abcadb

We observe that the series consists of the block abcadb repeated three times consecutively.

Let's check if this pattern matches the original series with the filled letters:

Original series structure with blanks at 2, 5, 9, 12, 16, 18:

a_ca_b a b_a d_a b c_d b

Comparing with the pattern abcadb:

• Block 1 (pos 1-6): a_ca_b needs 'b' at pos 2 and 'd' at pos 5 to become abcadb. The letters needed are 'b', 'd'.
• Block 2 (pos 7-12): ab_ad_ needs 'c' at pos 9 and 'b' at pos 12 to become abcadb. The letters needed are 'c', 'b'.
• Block 3 (pos 13-18): abc_db needs 'a' at pos 16 and 'b' at pos 18 to become abcadb. The letters needed are 'a', 'b'.

The letters required to fill the blanks at positions 2, 5, 9, 12, 16, 18 according to the abcadb pattern would be b, d, c, b, a, b. The option providing the filling letters is bdcba, which matches the required letters for the first five blanks (positions 2, 5, 9, 12, 16).

Thus, filling the first five blanks with bdcba reveals the repeating pattern abcadb, where the last character of the series 'b' (at position 18) completes the third repetition of the pattern.

Let's quickly consider why other options wouldn't work. If we fill the blanks at positions 2, 5, 9, 12, 16 with any other option (bcdba, bdcab, or bddac), the resulting sequence does not form a simple, clear repeating block pattern like abcadb.

Therefore, Option 1 provides the correct sequence of letters to fill the blanks and complete the series with a repeating pattern.

Revision Table: Analyzing Options

Additional Information on Letter Series

Letter series completion is a common type of question in logical reasoning. These questions present a sequence of letters that follow a specific rule or pattern. The pattern can be based on various principles, including:

• Repeating Blocks: A specific sequence of letters repeats throughout the series. This was the pattern found in the problem above.
• Alphabetical Progression: Letters advance or recede by a fixed number of steps in the alphabet (e.g., A, C, E, G...).
• Skipping Letters: Letters are skipped in a specific order (e.g., AbC dE FgH...).
• Combination of Patterns: The series might involve a combination of letter progressions, skips, or repeating elements within a block.
• Position-Based Patterns: The pattern might relate to the position of the letter in the sequence or the position in the alphabet.

To solve letter series problems, one should look for:

• The total number of elements (including blanks).
• Possible repeating blocks by dividing the total length by small integers.
• Relationships between consecutive letters or groups of letters.
• The letters provided in the options to see which sequence creates a recognizable pattern.

Practice with different types of letter series helps improve pattern recognition skills necessary for solving these problems.