Book pages

Question

The problem description is here: http://www.mcs.vuw.ac.nz/~david/acm/P2_Pages.pdf
The code I have outputs the correct number of pages for most small digits, but when I get to 1999999998, it outputs a negative number and nowhere in the code can I find out why. Was wondering if anyone had a better solution.
import java.lang.*;
public class Test {
static int count = 0;
static int count2 = 1;
static int num_pages = 0;
static int argument;
public static int getDigits(int n) // returns the number of digits in n
{  ++count;
  return (n / 10) < 1 ? count : getDigits(n / 10);
public static void compute(int digits)
{ double i = 0.0; double j = 1.0;
boolean h = true;
    while (h) {
double low = Math.pow(10.0, i++);
double high = Math.pow(10.0, j++);
int x = (int) (high - low);
int total_digits = x * count2;
if (argument <= total_digits && (argument % count2 == 0)) { num_pages += argument / count2;
h = false;}
else if (argument <= total_digits && (argument % count2 != 0)) { System.out.println("Impossible");
h = false;}
else { argument -= total_digits; num_pages += x; }
   ++count2; }
public static void main(String[] args) {
int p = Integer.parseInt(args[0]);
argument = p;
int c = getDigits(p);
compute(c);
System.out.println("For " + p + " digits " + "there are " + num_pages + " pages");
          }

Answer 1

I'm sure there is a mathematical expression whereby it just takes one line to solve this, but I can't quite see that. What I can see is that you're complicating things far too much.
    private static int compute(int digits) {
        int length = 0;
        int page = 0;
        int numDigits = 1;
        int increaseAt = 10;
        while(true) {
            page++;
            if(page >= increaseAt) { numDigits++; increaseAt*=10; }
            length += numDigits;
            if(length == digits) return page;
            if(length > digits) return -1; // Impossible!
    }