How many such pairs of letters are there in the word HEALTH which has as many…
2023
How many such pairs of letters are there in the word HEALTH which has as many letters between them (from both the sides) as in the alphabets from A to Z?
- A.
3
- B.
2
- C.
1
- D.
None
Attempted by 146 students.
Show answer & explanation
Correct answer: D
Answer: None (0 pairs).
Reasoning:
Map each letter to its position in the alphabet: H = 8, E = 5, A = 1, L = 12, T = 20, H = 8.
The required condition: the number of letters between two letters in the word equals the number of letters between them in the alphabet. Equivalently, if the letters occur at word indices i and j (j > i) with alphabet positions p_i and p_j, then j - i = |p_j - p_i|.
Check pairs: no pair satisfies j - i = |p_j - p_i|. Examples: H (index 1, p=8) and E (index 2, p=5) give 1 ≠ 3; the two H's (indices 1 and 6, p=8 and 8) give 5 ≠ 0.
Therefore there are 0 pairs of letters in the word that satisfy the condition.