# C Exercises: Find the n^{th} digit of number 1 to n

## C Programming Mathematics: Exercise-17 with Solution

Write a C program to find the nth digit of the number 1 to n?

Infinite integer sequence: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 .. where n is a positive integer.

Example:

Input:

7

Output:

7

Input:

12

Output:

1

The 12th digit of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... is 1, which is part of the number 11.

**Visual Presentation:**

**Sample Solution:**

**C Code:**

```
#include <stdio.h>
// Function to find the Nth digit in a sequence
int find_Nth_Digit(int n) {
unsigned int i, j, k;
i = j = 1;
// Loop to find the appropriate position of the digit in the sequence
while (n > 9 * i * j) {
n -= 9 * i * j; // Decrement n based on the sequence length
j *= 10; // Increase j to move to the next digit length
i++; // Increment i to keep track of digit length
}
k = j + (n - 1) / i; // Calculate the position of the digit in the sequence
// Loop to extract the desired digit
for (j = (n - 1) % i; j < i - 1; j++) {
k = k / 10; // Move to the specific digit position
}
return k % 10; // Return the Nth digit
}
// Main function to test the find_Nth_Digit function
int main(void) {
int n = 7;
printf("\n%d digit of the sequence is %d", n, find_Nth_Digit(n));
n = 12;
printf("\n%d digit of the sequence is %d", n, find_Nth_Digit(n));
return 0;
}
```

Sample Output:

7 digit of the sequence is 7 12 digit of the sequence is 1

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