'Getting the count of digits from n numbers , timeout error (How many pages in a book? from codewars)

Problem: Given the summary, find the number of pages n the book has.

Example If the input is summary=25, then the output must be n=17: The numbers 1 to 17 have 25 digits in total: 1234567891011121314151617.

All inputs will be valid.

My current solution

function amountOfPages(summary){


    let n=1;   let arrKc=[1]
        
        while((arrKc.join('').toString().length)!=summary){
         
           arrKc.push( n.toString())
         
            n++
        }
        
   return n
  
}

All the tests passes but i get a timeout error as shown below

enter image description here

javascriptarraysstringalgorithmwhile-loop


Solution 1:[1]

Here is my code,

I see a pattern here to find the digits count

9 + 9 * 10 power 1 * 2 + 9 * 10 power 2 * 3 + ...+ 9 * 10 power n-1 * n My solution is based on the above pattern

function initialLoad() {
      document.getElementById("outcome").innerHTML = "Answer: "+  amountOfPages(25);
}

function amountOfPages(summary) {
        var n = summary;
        var totalNumbersSoFar = 0;
        var pagesSoFar = 0;
        var ninthDigit = "9";
        while (parseInt(ninthDigit) < (n / ninthDigit.length)) {
                var numbersInRange = Math.pow(10, ninthDigit.length - 1) * 9;
                pagesSoFar += numbersInRange * ninthDigit.length;
                n -= numbersInRange;
                totalNumbersSoFar += numbersInRange;
                ninthDigit += "9";
        };
        return ((summary - pagesSoFar) / ninthDigit.length) + totalNumbersSoFar;
    };
 <HTML>
        <HEAD>
        </HEAD>
        <BODY id="outcome" onload="initialLoad()">
            <h1>

        </h1>
        </BODY>
    </HTML>

Sources

This article follows the attribution requirements of Stack Overflow and is licensed under CC BY-SA 3.0.

Source: Stack Overflow

Solution Source
Solution 1 HariHaravelan

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