2.3 Reversing Letter Positions in a Sequence or Pattern

 2.3 Reversing Letter Positions in a Sequence or Pattern

Below are 10 example problems for the Reversing Letter Positions in a Sequence or Pattern type of Alphabetical Reasoning questions. Each problem includes the question, the solution process, the solution, and a detailed explanation. These problems focus on reordering a sequence of letters based on their positional indices (e.g., 1st becomes last, 2nd becomes second-to-last, etc.) rather than reversing the alphabet or a word itself. The problems cover the common variants: finding the new sequence, identifying specific letters in the reversed sequence, and analyzing properties of the resulting sequence. The alphabet (A=1, B=2, ..., Z=26) is used as a reference where needed.

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Problem 1: Find the new sequence

Question: A sequence B, F, I (2nd, 6th, 9th letters of the alphabet) has its positions reversed. What is the new sequence?

Solution Process:

• Original sequence: B (1st position), F (2nd position), I (3rd position).
• Reverse the positions: 1st → 3rd, 2nd → 2nd, 3rd → 1st.
• New sequence: I (3rd position becomes 1st), F (2nd stays 2nd), B (1st becomes 3rd) → I, F, B.

Solution: I, F, B

Detailed Explanation:

• The sequence B, F, I has 3 letters, with B in position 1, F in position 2, and I in position 3.
• Reversing the positions means the 1st letter (B) moves to the 3rd position, the 2nd letter (F) stays in the 2nd position, and the 3rd letter (I) moves to the 1st position.
• Thus, the new sequence is I (1st), F (2nd), B (3rd).
• The letters B, F, I correspond to the 2nd, 6th, and 9th letters of the alphabet, but the reversal is about positional indices in the sequence, not alphabetical positions.
• This tests the ability to reorder based on sequence positions.

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Problem 2: Find the new sequence

Question: The sequence C, E, I, K (3rd, 5th, 9th, 11th letters of the alphabet) has its positions reversed. What is the new sequence?

Solution Process:

• Original sequence: C (1st), E (2nd), I (3rd), K (4th).
• Reverse the positions: 1st → 4th, 2nd → 3rd, 3rd → 2nd, 4th → 1st.
• New sequence: K (4th becomes 1st), I (3rd becomes 2nd), E (2nd becomes 3rd), C (1st becomes 4th) → K, I, E, C.

Solution: K, I, E, C

Detailed Explanation:

• The sequence C, E, I, K has 4 letters, with positions: C (1), E (2), I (3), K (4).
• Reversing the positions maps: 1st (C) to 4th, 2nd (E) to 3rd, 3rd (I) to 2nd, 4th (K) to 1st.
• The new sequence is K (1st), I (2nd), E (3rd), C (4th).
• The alphabetical positions (C=3rd, E=5th, I=9th, K=11th) are context for the sequence but do not affect the reversal, which is purely positional.
• This reinforces positional reordering for a longer sequence.

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Problem 3: Identify a specific letter in the reversed sequence

Question: In the sequence A, D, I, M (1st, 4th, 9th, 13th letters), the positions are reversed. What is the 2nd letter in the new sequence?

Solution Process:

• Original sequence: A (1st), D (2nd), I (3rd), M (4th).
• Reverse the positions: 1st → 4th, 2nd → 3rd, 3rd → 2nd, 4th → 1st.
• New sequence: M (4th becomes 1st), I (3rd becomes 2nd), D (2nd becomes 3rd), A (1st becomes 4th) → M, I, D, A.
• 2nd letter in new sequence: I.

Solution: I

Detailed Explanation:

• The sequence A, D, I, M has 4 letters: A (1), D (2), I (3), M (4).
• Reversing positions: the 1st (A) goes to 4th, 2nd (D) to 3rd, 3rd (I) to 2nd, 4th (M) to 1st, giving M, I, D, A.
• The 2nd letter in the new sequence is I.
• Alternatively, the 2nd letter in the reversed sequence corresponds to the (4-2+1)=3rd letter in the original sequence, which is I.
• This tests identifying a specific position after positional reversal.

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Problem 4: Identify a specific letter in the reversed sequence

Question: The sequence B, G, K, O (2nd, 7th, 11th, 15th letters) has its positions reversed. What is the 4th letter in the new sequence?

Solution Process:

• Original sequence: B (1st), G (2nd), K (3rd), O (4th).
• Reverse the positions: 1st → 4th, 2nd → 3rd, 3rd → 2nd, 4th → 1st.
• New sequence: O (4th becomes 1st), K (3rd becomes 2nd), G (2nd becomes 3rd), B (1st becomes 4th) → O, K, G, B.
• 4th letter in new sequence: B.

Solution: B

Detailed Explanation:

• The sequence B, G, K, O has 4 letters: B (1), G (2), K (3), O (4).
• Reversing positions: 1st (B) to 4th, 2nd (G) to 3rd, 3rd (K) to 2nd, 4th (O) to 1st, resulting in O, K, G, B.
• The 4th letter in the new sequence is B.
• Alternatively, the 4th letter in the reversed sequence is the (4-4+1)=1st letter in the original sequence, which is B.
• This further tests positional mapping for a specific index.

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Problem 5: Analyze properties of the resulting sequence

Question: In the sequence A, E, I (1st, 5th, 9th letters), the positions are reversed. How many vowels are in the new sequence? (Vowels: A, E, I, O, U)

Solution Process:

• Original sequence: A (1st), E (2nd), I (3rd).
• Reverse the positions: 1st → 3rd, 2nd → 2nd, 3rd → 1st.
• New sequence: I (3rd becomes 1st), E (2nd stays 2nd), A (1st becomes 3rd) → I, E, A.
• Check for vowels: I (vowel), E (vowel), A (vowel).
• Number of vowels: 3.

Solution: 3 vowels

Detailed Explanation:

• The sequence A, E, I has 3 letters: A (1), E (2), I (3), all of which are vowels.
• Reversing positions: 1st (A) to 3rd, 2nd (E) to 2nd, 3rd (I) to 1st, giving I, E, A.
• The new sequence I, E, A contains I, E, and A, all vowels, so there are 3 vowels.
• The number of vowels remains the same as in the original sequence because the letters are unchanged, only reordered.
• This tests property analysis (vowels) after positional reversal.

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Problem 6: Find the new sequence

Question: The sequence D, I, M, P, S (4th, 9th, 13th, 16th, 19th letters) has its positions reversed. What is the new sequence?

Solution Process:

• Original sequence: D (1st), I (2nd), M (3rd), P (4th), S (5th).
• Reverse the positions: 1st → 5th, 2nd → 4th, 3rd → 3rd, 4th → 2nd, 5th → 1st.
• New sequence: S (5th becomes 1st), P (4th becomes 2nd), M (3rd stays 3rd), I (2nd becomes 4th), D (1st becomes 5th) → S, P, M, I, D.

Solution: S, P, M, I, D

Detailed Explanation:

• The sequence D, I, M, P, S has 5 letters: D (1), I (2), M (3), P (4), S (5).
• Reversing positions: 1st (D) to 5th, 2nd (I) to 4th, 3rd (M) to 3rd, 4th (P) to 2nd, 5th (S) to 1st.
• The new sequence is S, P, M, I, D.
• The alphabetical positions (4th, 9th, 13th, 16th, 19th) provide context but do not affect the positional reversal.
• This tests reordering for a longer sequence.

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Problem 7: Identify a specific letter in the reversed sequence

Question: In the sequence C, G, K (3rd, 7th, 11th letters), the positions are reversed. What is the 1st letter in the new sequence?

Solution Process:

• Original sequence: C (1st), G (2nd), K (3rd).
• Reverse the positions: 1st → 3rd, 2nd → 2nd, 3rd → 1st.
• New sequence: K (3rd becomes 1st), G (2nd stays 2nd), C (1st becomes 3rd) → K, G, C.
• 1st letter in new sequence: K.

Solution: K

Detailed Explanation:

• The sequence C, G, K has 3 letters: C (1), G (2), K (3).
• Reversing positions: 1st (C) to 3rd, 2nd (G) to 2nd, 3rd (K) to 1st, giving K, G, C.
• The 1st letter in the new sequence is K.
• Alternatively, the 1st letter in the reversed sequence is the (3-1+1)=3rd letter in the original sequence, which is K.
• This is a simpler positional mapping task.

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Problem 8: Analyze properties of the resulting sequence

Question: The sequence B, D, F, I (2nd, 4th, 6th, 9th letters) has its positions reversed. How many consonants are in the new sequence? (Consonants: all letters except A, E, I, O, U)

Solution Process:

• Original sequence: B (1st), D (2nd), F (3rd), I (4th).
• Reverse the positions: 1st → 4th, 2nd → 3rd, 3rd → 2nd, 4th → 1st.
• New sequence: I (4th becomes 1st), F (3rd becomes 2nd), D (2nd becomes 3rd), B (1st becomes 4th) → I, F, D, B.
• Check for consonants: I (vowel), F (consonant), D (consonant), B (consonant).
• Number of consonants: 3.

Solution: 3 consonants

Detailed Explanation:

• The sequence B, D, F, I has 4 letters: B (1), D (2), F (3), I (4).
• Reversing positions: 1st (B) to 4th, 2nd (D) to 3rd, 3rd (F) to 2nd, 4th (I) to 1st, giving I, F, D, B.
• Analyzing the new sequence: I is a vowel, while F, D, and B are consonants, so there are 3 consonants.
• The original sequence had 3 consonants (B, D, F) and 1 vowel (I), and the reversed sequence maintains the same letters, so the consonant count is unchanged.
• This tests property analysis after reversal.

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Problem 9: Find the new sequence with a pattern

Question: The sequence A, C, I, M (1st, 3rd, 9th, 13th letters) follows a pattern. Reverse the positions of the sequence. What is the new sequence?

Solution Process:

• Original sequence: A (1st), C (2nd), I (3rd), M (4th).
• Reverse the positions: 1st → 4th, 2nd → 3rd, 3rd → 2nd, 4th → 1st.
• New sequence: M (4th becomes 1st), I (3rd becomes 2nd), C (2nd becomes 3rd), A (1st becomes 4th) → M, I, C, A.

Solution: M, I, C, A

Detailed Explanation:

• The sequence A, C, I, M has 4 letters: A (1), C (2), I (3), M (4).
• The alphabetical positions (1st, 3rd, 9th, 13th) suggest a pattern, but the task is to reverse the sequence positions, not the alphabetical indices.
• Reversing positions: 1st (A) to 4th, 2nd (C) to 3rd, 3rd (I) to 2nd, 4th (M) to 1st, giving M, I, C, A.
• The pattern in the original sequence (possibly increasing alphabetical positions) does not affect the reversal, which is purely positional.
• This tests sequence reordering with a pattern context.

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Problem 10: Analyze properties with combined operations

Question: The sequence B, F, I, K (2nd, 6th, 9th, 11th letters) has its positions reversed. After reversal, shift each letter forward by 1 in the alphabet (e.g., A→B, Z→A). What is the new sequence?

Solution Process:

• Original sequence: B (1st), F (2nd), I (3rd), K (4th).
• Reverse the positions: 1st → 4th, 2nd → 3rd, 3rd → 2nd, 4th → 1st.
• New sequence after reversal: K (4th becomes 1st), I (3rd becomes 2nd), F (2nd becomes 3rd), B (1st becomes 4th) → K, I, F, B.
• Shift each letter forward by 1:
  • K (11th) → L (12th).
  • I (9th) → J (10th).
  • F (6th) → G (7th).
  • B (2nd) → C (3rd).
• New sequence: L, J, G, C.

Solution: L, J, G, C

Detailed Explanation:

• The sequence B, F, I, K has 4 letters: B (1), F (2), I (3), K (4).
• Reversing positions: 1st (B) to 4th, 2nd (F) to 3rd, 3rd (I) to 2nd, 4th (K) to 1st, giving K, I, F, B.
• The additional operation shifts each letter forward by 1 in the alphabet:
  • K (11th letter) becomes L (12th).
  • I (9th) becomes J (10th).
  • F (6th) becomes G (7th).
  • B (2nd) becomes C (3rd).
• The final sequence is L, J, G, C.
• This tests both positional reversal and an additional alphabetical transformation, combining sequence manipulation with letter shifting.

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Summary of Problems

• Problems 1, 2, 6, 9: Find the new sequence after reversing positions.
• Problems 3, 4, 7: Identify a specific letter at a given position in the reversed sequence.
• Problems 5, 8: Analyze properties (vowels or consonants) of the reversed sequence.
• Problem 10: Combine positional reversal with an additional operation (alphabetical shift).
• Each problem emphasizes reordering based on positional indices, with variations in sequence length, pattern context, and property analysis.

If you need more examples, specific variants, or further explanations for any problem, let me know!