# JavaScript - Count all the numbers with unique digits in a range

## JavaScript Math: Exercise-109 with Solution

Write a JavaScript program that accepts a number (n) and counts all numbers with unique digits of length p within a specified range.

Range: 0 <= p < 10^{n}

Example:

When n = 1, numbers with unique digits (10) between 0 and 9 are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

When n = 2, numbers with unique digits (91) between 0 and 100 are 0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15 …..99 except 11, 22, 33, 44, 55, 66, 77, 88 and 99.

**Test Data:**

(1) -> 10

(2) -> 91

**Sample Solution:**

**JavaScript Code:**

```
/**
* Function to calculate the count of numbers with unique digits in a given range.
* @param {number} n - The upper limit of the range (from 0 to n).
* @returns {number} - The count of numbers with unique digits in the specified range.
*/
function test(n) {
// If n is 0, there's one number with a unique digit: 0 itself
if(n===0){
return 1;
}
// Initialize result to 10, as numbers from 0 to 9 all have unique digits
var result = 10;
// Initialize temp to 9, representing the number of choices for the first digit (1 to 9)
var temp = 9;
// Loop through the range starting from 1 (since we've already considered the case when n=0)
for(var i=1; i<n; i++){
// Update temp by multiplying with the number of remaining choices
temp *= 10 - i;
// Add temp to result, representing the count of numbers with unique digits at each iteration
result += temp;
}
// Return the final count of numbers with unique digits in the range
return result;
}
// Test cases
n = 1;
console.log("Range: " + n + " to 10");
console.log("Numbers with unique digits in the said range: " + test(n));
n = 2;
console.log("Range: " + n + " to 10");
console.log("Numbers with unique digits in the said range: " + test(n));
```

Output:

Range: 1 to 10 Numbers with unique digits in the said range: 10 Range: 2 to 10 Numbers with unique digits in the said range: 91

**Flowchart: **

**Live Demo: **

See the Pen javascript-math-exercise-109 by w3resource (@w3resource) on CodePen.

**Improve this sample solution and post your code through Disqus.**

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