1. How many of them contain at least one '1'?
2. If I wrote them out in one long line, how many 1 digits would there be?

Sorry for the silly subject line -- it's Mick Jagger's birthday...

There are 612,579,512 numbers from 1 to a 1,000,000,000 with at least one 1, and there are 900,000,001 total 1's if they are all strung together.  

That is.... IF the following Visual Basic program, which ran in less than a second elapsed time, is correct....

Imports System
Imports System.IO
Imports System.Text
Imports System.Runtime.InteropServices
Imports System.Math
Module Module1
    Sub Main()
        Randomize()
        Dim strstarttime As String
        Dim strendtime As String
        Dim strend As String
        Dim dblstart As Double
        Dim dblnums As Double
        Dim dbltots As Double
        strstarttime = TimeOfDay
        Console.WriteLine("Start of execution: " & strstarttime)
        dblstart = 1
        dblnums = 1
        dbltots = 1
        While dblstart < 100000000
            dblstart *= 10
            dblnums += dblstart + (8 * dblnums)
            dbltots += dblstart + (9 * dbltots)
        End While
        dblnums += 1
        dbltots += 1
        Console.WriteLine("There are " & Str(dblnums) & _
        " numbers with at least one 1")
        Console.WriteLine("There are " & Str(dbltots) & _
        " total 1s")
        Console.WriteLine(" ")
        Console.WriteLine("Start of execution was: " & strstarttime)
        strendtime = TimeOfDay
        Console.WriteLine( _
        Str(1000000000))
        Console.WriteLine("End of execution: " & strendtime)
        strend = "?"
        Console.WriteLine(" ")
        While strend <> "X"
            Console.WriteLine("Please enter X to exit program...")
            strend = UCase(Console.ReadLine())
        End While
    End Sub
End Module 

Edited on July 26, 2004, 10:11 am

Posted by Penny on 2004-07-26 10:10:26