How many pairs of letters are there in the word 'BUCKET' which have as many letters between them in the word as in the alphabet?

Options

A. One
B. Two
C. Three
D. four

Explanation

To solve the problem of finding how many pairs of letters in the word "BUCKET" have as many letters between them in the word as they do in the alphabet, we can follow these steps:

### Step 1: Identify the letters and their positions
The word "BUCKET" consists of the letters: B, U, C, K, E, T. We will assign each letter its position in the alphabet:
- B = 2
- U = 21
- C = 3
- K = 11
- E = 5
- T = 20

### Step 2: List the pairs of letters
We will check all possible pairs of letters in the word "BUCKET". The pairs are:
1. (B, U)
2. (B, C)
3. (B, K)
4. (B, E)
5. (B, T)
6. (U, C)
7. (U, K)
8. (U, E)
9. (U, T)
10. (C, K)
11. (C, E)
12. (C, T)
13. (K, E)
14. (K, T)
15. (E, T)

### Step 3: Check the gaps between the letters
For each pair, we will check if the number of letters between them in the word matches the number of letters between them in the alphabet.

1. **(B, U)**: In the word: 0 letters between; In the alphabet: 19 letters between (not a pair).
2. **(B, C)**: In the word: 1 letter (U) between; In the alphabet: 1 letter (A) between (not a pair).
3. **(B, K)**: In the word: 2 letters (U, C) between; In the alphabet: 8 letters between (not a pair).
4. **(B, E)**: In the word: 3 letters (U, C, K) between; In the alphabet: 22 letters between (not a pair).
5. **(B, T)**: In the word: 4 letters (U, C, K, E) between; In the alphabet: 18 letters between (not a pair).
6. **(U, C)**: In the word: 2 letters (B, K) between; In the alphabet: 18 letters between (not a pair).
7. **(U, K)**: In the word: 1 letter (C) between; In the alphabet: 10 letters between (not a pair).
8. **(U, E)**: In the word: 2 letters (C, K) between; In the alphabet: 16 letters between (not a pair).
9. **(U, T)**: In the word: 3 letters (C, K, E) between; In the alphabet: 1 letter (S) between (not a pair).
10. **(C, K)**: In the word: 1 letter (U) between; In the alphabet: 7 letters between (not a pair).
11. **(C, E)**: In the word: 1 letter (K) between; In the alphabet: 1 letter (D) between (this is a pair).
12. **(C, T)**: In the word: 2 letters (K, E) between; In the alphabet: 16 letters between (not a pair).
13. **(K, E)**: In the word: 1 letter (C) between; In the alphabet: 6 letters between (not a pair).
14. **(K, T)**: In the word: 1 letter (E) between; In the alphabet: 9 letters between (not a pair).
15. **(E, T)**: In the word: 1 letter (K) between; In the alphabet: 15 letters between (not a pair).

### Step 4: Count the valid pairs
From the analysis above, the only valid pair is (C, E).

### Conclusion
The total number of pairs of letters in the word "BUCKET" that have the same number of letters between them in the word as in the alphabet is **1**.

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