A nine digit number has the property where the first digit equals the number of zeros and ones used in the number, the second digit equals the number of ones and twos used in the number, the third digit equals the number of twos and threes used in the number, etc. through the ninth digit equals the number of eights and nines used in the number. What could the number be?
A ten digit number has a similar property to the nine digit number. The first digit equals the number of zeros and ones used in the number, the second digit equals the number of ones and twos used in the number, etc. through the ninth digit. And also, the tenth digit equals the number of zeros and nines used in the number. What could this number be?
Three 9 digit numbers:
533211000
542121000
740110110
One 10 digit number
4224400004
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The following "short" VB program found both numbers in 12 seconds.
Option Strict On
Imports System
Imports System.IO
Imports System.Text
Imports System.Runtime.InteropServices
Imports System.Math
Module Module1
Dim number(10) As Integer
Sub Main()
Randomize()
Dim interval As Double = 0
Dim quit As String
Console.WriteLine( _
"Start: " & TimeOfDay)
For index0 As Integer = 0 To 9
For index1 As Integer = 0 To 9
If index0 _
+ index1 <= 20 Then
For index2 As Integer = 0 To 9
If index0 _
+ index1 _
+ index2 <= 20 Then
For index3 As Integer = 0 To 9
If index0 _
+ index1 _
+ index2 _
+ index3 <= 20 Then
For index4 As Integer = 0 To 9
If index0 _
+ index1 _
+ index2 _
+ index3 _
+ index4 <= 20 Then
For index5 As Integer = 0 To 9
If index0 _
+ index1 _
+ index2 _
+ index3 _
+ index4 _
+ index5 <= 20 Then
For index6 As Integer = 0 To 9
If index0 _
+ index1 _
+ index2 _
+ index3 _
+ index4 _
+ index5 _
+ index6 <= 20 Then
For index7 As Integer = 0 To 9
If index0 _
+ index1 _
+ index2 _
+ index3 _
+ index4 _
+ index5 _
+ index6 _
+ index7 <= 20 Then
For index8 As Integer = 0 To 9
number(0) = index0
number(1) = index1
number(2) = index2
number(3) = index3
number(4) = index4
number(5) = index5
number(6) = index6
number(7) = index7
number(8) = index8
number(9) = 0
check_number9()
If index0 _
+ index1 _
+ index2 _
+ index3 _
+ index4 _
+ index5 _
+ index6 _
+ index7 _
+ index8 <= 20 Then
For index9 As Integer = 0 To 9
If index0 _
+ index1 _
+ index2 _
+ index3 _
+ index4 _
+ index5 _
+ index6 _
+ index7 _
+ index8 _
+ index9 = 20 Then
number(9) = index9
check_number10()
End If
Next
End If
Next
End If
Next
End If
Next
End If
Next
End If
Next
End If
Next
End If
Next
End If
Next
Next
Console.WriteLine( _
"End: " & TimeOfDay)
quit = "?"
While quit <> "x"
Console.WriteLine("Enter x to exit")
quit = LCase(Console.ReadLine())
End While
End Sub
Sub check_number10()
Dim count10(10) As Integer
Dim sub1 As Integer
Dim string0 As String
For index1 As Integer = 0 To 9
count10(index1) = 0
Next
For index1 As Integer = 0 To 9
count10(number(index1)) += 1
Next
For index1 As Integer = 0 To 8
If number(index1) <> _
count10(index1) + count10(index1 + 1) Then
Exit Sub
End If
Next
If number(9) <> count10(9) + count10(0) Then
Exit Sub
End If
Console.WriteLine("Answer for 10 digit number:")
string0 = ""
For index1 As Integer = 0 To 9
string0 &= Str(number(index1))
Next
Console.WriteLine(string0)
End Sub
Sub check_number9()
Dim count9(10) As Integer
Dim sub1 As Integer
Dim string0 As String
For index1 As Integer = 0 To 9
count9(index1) = 0
Next
For index1 As Integer = 0 To 8
count9(number(index1)) += 1
Next
For index1 As Integer = 0 To 8
If number(index1) <> _
count9(index1) + count9(index1 + 1) Then
Exit Sub
End If
Next
Console.WriteLine("Answer for 9 digit number:")
string0 = ""
For index1 As Integer = 0 To 8
string0 &= Str(number(index1))
Next
Console.WriteLine(string0)
End Sub
End Module
Edited on September 24, 2005, 11:35 am
|
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Posted by Penny
on 2005-09-23 19:36:29 |
Computer program solution
