English Alphabet Rearrangement: Finding the Thirteenth Letter

This question asks us to find the thirteenth letter from the left in the English alphabet after applying a specific rearrangement rule. The rule involves swapping letters based on their initial positions.

The standard English alphabet in order from left to right is:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

There are 26 letters in total. The rule states that we interchange the first and third letters, the second and fourth letters, and so on.

Let's look at the original positions and the letters:

Original Positions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Original Letters: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The rearrangement rule means:

• The letter at original position 1 swaps with the letter at original position 3.
• The letter at original position 2 swaps with the letter at original position 4.
• The letter at original position 5 swaps with the letter at original position 7.
• The letter at original position 6 swaps with the letter at original position 8.
• This pattern continues, swapping letter at original position \(n\) with letter at original position \(n+2\).

Applying this rule, we can determine which letter will occupy each position in the new sequence:

The new arrangement of the alphabet from left to right is:

C D A B G H E F K L I J O P M N S T Q R W X U V Y Z

We are asked to find the thirteenth letter from the left in this new arrangement.

Counting the letters from the left in the new sequence:

1st: C, 2nd: D, 3rd: A, 4th: B, 5th: G, 6th: H, 7th: E, 8th: F, 9th: K, 10th: L, 11th: I, 12th: J, 13th: O

Therefore, the thirteenth letter from the left in the rearranged alphabet is O.

English Alphabet Rearrangement Revision Table

Let's summarize the swapping pattern for the first few letters:

• Positions 1 & 3 swap: A ↔ C. New order starts C A... but position 1 gets C, position 3 gets A.
• Positions 2 & 4 swap: B ↔ D. New order at pos 2 gets D, pos 4 gets B.
• Combined first four: C D A B
• Positions 5 & 7 swap: E ↔ G. New order at pos 5 gets G, pos 7 gets E.
• Positions 6 & 8 swap: F ↔ H. New order at pos 6 gets H, pos 8 gets F.
• Combined next four: G H E F

This pattern \(n \leftrightarrow n+2\) continues. For the 13th position, its original letter is M. This position swaps with position \(13+2 = 15\), which originally held the letter O. So, the letter O moves to the 13th position in the new arrangement.

Additional Information on Letter Arrangement Puzzles

Letter arrangement or alphabet rearrangement puzzles are common in reasoning sections of competitive exams. They test your ability to follow instructions and track changes in sequence or position. Key concepts include:

• Positional Value: Knowing the standard position of each letter (A=1, B=2, ... Z=26).
• Following Rules Precisely: Carefully applying the given interchanging or shifting rules.
• Tracking Changes: Keeping track of which letter ends up in which new position.
• Left and Right Ends: Understanding that 'from the left' means starting from A's side, and 'from the right' means starting from Z's side.

Practice with different types of rules (like shifting, reversing, interchanging) helps improve speed and accuracy in solving such problems.