Anjuli has written all the letters (or characters) of English alphabets (i.e., A,B,C,D,……Y,Z) horizontally in a single line. She started counting as `A - 1, B- 2, C- 3, D - 4, ….Y - 25, Z - 26` and reversed back as `Y - 27, X - 28, W - 29, V - 30,…..B-50, A - 51` and further reversed back as `B - 52, C - 53, D - 54,..` etc. She continued counting till she reached the 777th character. At which letter or character she stopped counting ?

Options

A. Y
B. B
C. R
D. none of these

Answer

To solve the problem step by step, we need to understand how Anjuli counts the letters of the English alphabet and how they repeat.

### Step 1: Understand the counting pattern
Anjuli counts the letters of the English alphabet as follows:
- A = 1, B = 2, C = 3, ..., Z = 26
- After Z, she continues counting in reverse: Y = 27, X = 28, ..., A = 51
- Then she starts again: B = 52, C = 53, ..., Z = 76
- And continues in reverse again: Y = 77, X = 78, ..., A = 101
- This pattern continues indefinitely.

### Step 2: Identify the cycle of counting
The pattern repeats every 52 counts:
- From A to Z (1 to 26)
- From Y to A (27 to 51)
- From B to Z (52 to 76)
- From Y to A (77 to 101)

Thus, we can summarize the counting pattern:
- A appears at positions: 1, 51, 101, 151, ..., which can be expressed as \( 50n + 1 \) where \( n \) is a non-negative integer.
- B appears at positions: 2, 52, 102, 152, ..., which can be expressed as \( 50n + 2 \).
- C appears at positions: 3, 53, 103, 153, ..., which can be expressed as \( 50n + 3 \).
- And so on up to Z.

### Step 3: Determine the position of the 777th character
To find the letter at the 777th position, we need to find which letter corresponds to this position using the formula \( 50n + k \), where \( k \) is the position of the letter in the alphabet (1 for A, 2 for B, etc.).

1. First, we find \( n \) such that \( 50n + k \) is close to 777.
2. We can start by calculating \( n \):
- If \( n = 15 \):
\[ 50 \times 15 = 750 \]
- This means \( 750 + k = 777 \) implies \( k = 777 - 750 = 27 \).

### Step 4: Identify the letter for \( k = 27 \)
Now we need to determine which letter corresponds to \( k = 27 \):
- Since \( k = 27 \) corresponds to Y in the reverse counting (Y = 27).

### Conclusion
Thus, the letter Anjuli stops counting at the 777th character is **Y**.