Euler Problem 55

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.

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”
      Max = 9999    ‘ less than 10,000
     Last = 50
  end if
 For j = 1 To Max
      If IsTest Then
         n = Series(j)
         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 ;-)


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