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Ingy döt Net
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Option Strict On
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Option Explicit On
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Imports System.IO
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''' <summary>
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''' Finds n digit numbers N such that the sum of the nth powers of
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''' their digits = N
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''' </summary>
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Module OwnDigitsPowerSum
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Public Sub Main
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' counts of used digits, check is a copy used to check the number is an own digit power sum
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Dim used(9) As Integer
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Dim check(9) As Integer
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Dim power(9, 9) As Long
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For i As Integer = 0 To 9
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check(i) = 0
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Next i
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For i As Integer = 1 To 9
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power(1, i) = i
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Next i
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For j As Integer = 2 To 9
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For i As Integer = 1 To 9
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power(j, i) = power(j - 1, i) * i
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Next i
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Next j
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' find the lowest possible first digit for each digit combination
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' this is the roughly the low3est n where P*n^p > 10^p
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Dim lowestDigit(9) As Integer
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lowestDigit(1) = -1
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lowestDigit(2) = -1
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Dim p10 As Long = 100
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For i As Integer = 3 To 9
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For p As Integer = 2 To 9
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Dim np As Long = power(i, p) * i
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If Not ( np < p10) Then Exit For
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lowestDigit(i) = p
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Next p
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p10 *= 10
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Next i
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' find the maximum number of zeros possible for each width and max digit
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Dim maxZeros(9, 9) As Integer
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For i As Integer = 1 To 9
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For j As Integer = 1 To 9
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maxZeros(i, j) = 0
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Next j
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Next i
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p10 = 1000
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For w As Integer = 3 To 9
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For d As Integer = lowestDigit(w) To 9
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Dim nz As Integer = 9
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Do
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If nz < 0 Then
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Exit Do
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Else
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Dim np As Long = power(w, d) * nz
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IF Not ( np > p10) Then Exit Do
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End If
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nz -= 1
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Loop
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maxZeros(w, d) = If(nz > w, 0, w - nz)
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Next d
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p10 *= 10
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Next w
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' find the numbers, works backeards through the possible combinations of
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' digits, starting from all 9s
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Dim numbers(100) As Long ' will hold the own digit power sum numbers
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Dim nCount As Integer = 0 ' count of the own digit power sums
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Dim tryCount As Integer = 0 ' count of digit combinations tried
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Dim digits(9) As Integer ' the latest digit combination to try
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For d As Integer = 1 To 9
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digits(d) = 9
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Next d
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For d As Integer = 0 To 8
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used(d) = 0
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Next d
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used(9) = 9
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Dim width As Integer = 9 ' number of digits
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Dim last As Integer = width ' final digit position
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p10 = 100000000 ' min value for a width digit power sum
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Do While width > 2
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tryCount += 1
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Dim dps As Long = 0 ' construct the digit power sum
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check(0) = used(0)
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For i As Integer = 1 To 9
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check(i) = used(i)
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If used(i) <> 0 Then
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dps += used(i) * power(width, i)
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End If
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Next i
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' reduce the count of each digit by the number of times it appear in the digit power sum
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Dim n As Long = dps
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Do
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check(CInt(n Mod 10)) -= 1 ' reduce the count of this digit
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n \= 10
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Loop Until n <= 0
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Dim reduceWidth As Boolean = dps <= p10
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If Not reduceWidth Then
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' dps is not less than the minimum possible width number
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' check there are no non-zero check counts left and so result is
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' equal to its digit power sum
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Dim zCount As Integer = 0
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For i As Integer = 0 To 9
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If check(i) <> 0 Then Exit For
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zCount+= 1
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Next i
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If zCount = 10 Then
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nCount += 1
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numbers(nCount) = dps
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End If
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' prepare the next digit combination: reduce the last digit
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used(digits(last)) -= 1
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digits(last) -= 1
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If digits(last) = 0 Then
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' the last digit is now zero - check this number of zeros is possible
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If used(0) >= maxZeros(width, digits(1)) Then
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' have exceeded the maximum number of zeros for the first digit in this width
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digits(last) = -1
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End If
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End If
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If digits(last) >= 0 Then
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' still processing the last digit
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used(digits(last)) += 1
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Else
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' last digit is now -1, start processing the previous digit
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Dim prev As Integer = last
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Do
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prev -= 1
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If prev < 1 Then
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Exit Do
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Else
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used(digits(prev)) -= 1
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digits(prev) -= 1
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IF digits(prev) >= 0 Then Exit Do
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End If
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Loop
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If prev > 0 Then
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' still some digits to process
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If prev = 1 Then
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If digits(1) <= lowestDigit(width) Then
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' just finished the lowest possible maximum digit for this width
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prev = 0
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End If
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End If
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If prev <> 0 Then
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' OK to try a lower digit
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used(digits(prev)) += 1
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For i As Integer = prev + 1 To width
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digits(i) = digits(prev)
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used(digits(prev)) += 1
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Next i
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End If
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End If
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If prev <= 0 Then
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' processed all the digits for this width
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reduceWidth = True
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End If
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End If
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End If
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If reduceWidth Then
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' reduce the number of digits
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last -= 1
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width = last
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If last > 0 Then
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' iniialise for fewer digits
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For d As Integer = 1 To last
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digits(d) = 9
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Next d
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For d As Integer = last + 1 To 9
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digits(d) = -1
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Next d
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For d As Integer = 0 To 8
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used(d) = 0
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Next d
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used(9) = last
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p10 \= 10
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End If
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End If
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Loop
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' show the own digit power sums
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Console.Out.WriteLine("Own digits power sums for N = 3 to 9 inclusive:")
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For i As Integer = nCount To 1 Step -1
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Console.Out.WriteLine(numbers(i))
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Next i
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Console.Out.WriteLine("Considered " & tryCount & " digit combinations")
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End Sub
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End Module
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