Problem 55 asks:

‘If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.

‘

‘Not all numbers produce palindromes so quickly. For example,

‘

‘349 + 943 = 1292,

‘1292 + 2921 = 4213

‘4213 + 3124 = 7337

‘

‘That is, 349 took three iterations to arrive at a palindrome.

‘

‘Although no one has proved it yet, it is thought that some numbers, like

‘196, never produce a palindrome. A number that never forms a palindrome

‘through the reverse and add process is called a Lychrel number. Due to the

‘theoretical nature of these numbers, and for the purpose of this problem,

‘we shall assume that a number is Lychrel until proven otherwise. In addition

‘you are given that for every number below ten-thousand, it will either

‘(i) become a palindrome in less than fifty iterations, or, (ii) no one, with

‘all the computing power that exists, has managed so far to map it to a

‘palindrome. In fact, 10677 is the first number to be shown to require over

‘fifty iterations before producing a palindrome:

‘4668731596684224866951378664 (53 iterations, 28-digits).

‘

‘Surprisingly, there are palindromic numbers that are themselves Lychrel

‘numbers; the first example is 4994.

‘

‘How many Lychrel numbers are there below ten-thousand?

‘

‘NOTE: Wording was modified slightly on 24 April 2007 to emphasise

‘the theoretical nature of Lychrel numbers.

‘

‘Not all numbers produce palindromes so quickly. For example,

‘

‘349 + 943 = 1292,

‘1292 + 2921 = 4213

‘4213 + 3124 = 7337

‘

‘That is, 349 took three iterations to arrive at a palindrome.

‘

‘Although no one has proved it yet, it is thought that some numbers, like

‘196, never produce a palindrome. A number that never forms a palindrome

‘through the reverse and add process is called a Lychrel number. Due to the

‘theoretical nature of these numbers, and for the purpose of this problem,

‘we shall assume that a number is Lychrel until proven otherwise. In addition

‘you are given that for every number below ten-thousand, it will either

‘(i) become a palindrome in less than fifty iterations, or, (ii) no one, with

‘all the computing power that exists, has managed so far to map it to a

‘palindrome. In fact, 10677 is the first number to be shown to require over

‘fifty iterations before producing a palindrome:

‘4668731596684224866951378664 (53 iterations, 28-digits).

‘

‘Surprisingly, there are palindromic numbers that are themselves Lychrel

‘numbers; the first example is 4994.

‘

‘How many Lychrel numbers are there below ten-thousand?

‘

‘NOTE: Wording was modified slightly on 24 April 2007 to emphasise

‘the theoretical nature of Lychrel numbers.

Euler problems should calculate under a minute. This one takes about 1.3 seconds.

Here is my code:

Option Explicit

Option Base 1

Sub Problem_055()

Dim i As Long

Dim j As Long

Dim T As Single

Dim n As String

Dim n_rev As String

Dim num As String

Dim Answer As Long

Dim Max As Long

Dim Last As Long

Dim IsTest As Boolean

Dim Series(5) As String

T = Timer ‘start timing

IsTest = True

If IsTest Then ‘to test the example cases

Max = 5

Last = 53

Series(1) = “47”

Series(2) = “196” ‘Lychrel

Series(3) = “349”

Series(4) = “4994” ‘Lychrel

Series(5) = “10677”

Else

Max = 9999 ‘ less than 10,000

Last = 50

end if

For j = 1 To Max

If IsTest Then

n = Series(j)

Else

n = CStr(j)

End If

For i = 1 To last ‘to test 10677

n_rev = StrReverse(n)

num = AddAsStrings(n, n_rev)

If num = StrReverse(num) Then ‘not a Lychrel number

Exit For

End If

n = num

If i = last Then

Answer = Answer + 1

End If

Next i

Next j

Debug.Print Answer; ” Time:”; Timer – T

End Sub

Option Base 1

Sub Problem_055()

Dim i As Long

Dim j As Long

Dim T As Single

Dim n As String

Dim n_rev As String

Dim num As String

Dim Answer As Long

Dim Max As Long

Dim Last As Long

Dim IsTest As Boolean

Dim Series(5) As String

T = Timer ‘start timing

IsTest = True

If IsTest Then ‘to test the example cases

Max = 5

Last = 53

Series(1) = “47”

Series(2) = “196” ‘Lychrel

Series(3) = “349”

Series(4) = “4994” ‘Lychrel

Series(5) = “10677”

Else

Max = 9999 ‘ less than 10,000

Last = 50

end if

For j = 1 To Max

If IsTest Then

n = Series(j)

Else

n = CStr(j)

End If

For i = 1 To last ‘to test 10677

n_rev = StrReverse(n)

num = AddAsStrings(n, n_rev)

If num = StrReverse(num) Then ‘not a Lychrel number

Exit For

End If

n = num

If i = last Then

Answer = Answer + 1

End If

Next i

Next j

Debug.Print Answer; ” Time:”; Timer – T

End Sub

It uses the AddAsStrings() function from Problem 16. It exits the loop if the addition is equal to its reverse.

Of course, the real question, is why anybody cares about Lychrel numbers, and who would make them their life’s work ;-)

…mrt

Hmmm…better set IsTest to False to prevent a correct wrong answer.

Happy New Year to all!

…mrt