<html><head><style type="text/css"></style></head><body><div style="font-family:times new roman, new york, times, serif;font-size:12pt"><div style="font-family: times new roman,new york,times,serif; font-size: 12pt;"><div style="font-size: 12pt; font-family: times new roman,new york,times,serif;">My solution to Euler #12 runs in less than 1 minute. </div> Let us list the factors of the first eight triangle numbers: <blockquote style="font-size: 12pt; font-family: courier new;">  1: 1  3: 1,3  6: 1,2,3,6 10: 1,2,5,10 15: 1,3,5,15 21: 1,3,7,21 28: 1,2,4,7,14,28 36: 1,2,3,4,6,8,9,12,18,36</blockquote> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;">Note the numbers that are underlined in each sequence. This is the half way point. </div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;">a)  If you divide the triangle number by the first number that is underlined the result will be greater than the divisor.</div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;">b)  On the other hand if you divide the triangle number by the second number that is underlined the result will be less than the divisor.</div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;">c)  The triangle number 36 has only one number at the centre of the sequence, because that centre number is the square root of the triangle number 36.</div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;"> </div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;">In cases a) and b) if you wanted to know the total number of divisors, you look for the position of the number underlined as described in b), then subtract 1 from it, then multiply it by 2. For example, for triangle number 28, value 7 is in position 4. So (4-1) * 2 = 6</div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;"> </div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;">In cases c) if you wanted to know the total number of divisors, you look for the position of the center number underlined, then multiply it by 2. For example, for triangle number 36, value 6 is in position 5. </div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;">So 5 * 2 = 10</div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;"> Here is the program. </div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;"> </div> <div style="font-size: 12pt; font-family: times new roman,new york,times,serif;"> Dim triagNo As Integer              ' Triangle number Dim counter As Integer              ' for calculating the next triangle number Dim varValue As Integer            ' Incremented in search for a Divisor Dim NoDivisors As Integer        ' number of Divisors found Dim Divisor As Integer              ' Value of found Divisor   Do    counter += 1    triagNo = triagNo + counter    varValue = 0    Divisor = 0    NoDivisors = 0         Do          varValue += 1         If triagNo Mod varValue = 0 Then                    ' is varValue a Divisor          Divisor = varValue         NoDivisors += 1         End If      Loop Until (triagNo / Divisor) <= Divisor               ' Find when you reach the second centre value        If (triagNo / Divisor) = Divisor Then         NoDivisors = (NoDivisors - 1) * 2 + 1                  ' cases a) and b)     Else         NoDivisors = (NoDivisors - 1) * 2                        ' case c)     End If   Loop Until (NoDivisors > 500)   TextBox1.Text = triagNo Z. Mwangi </div> <div style="font-family: times new roman,new york,times,serif; font-size: 12pt;">----- Original Message ---- From: Andrew Mathenge <mathenge@gmail.com> To: ubuntu Kenya <ubuntu-ke@lists.ubuntu.com> Sent: Friday, July 11, 2008 3:24:23 AM Subject: Re: Euler Problems This email is from a ubuntu-ke subscriber to other subscribers inluding you:) I've been working on #12 and the performance is simply not acceptable. Has anyone been able to get this running as fast as some of the posts on the site claim? Andrew. On Tue, Jul 8, 2008 at 12:40 PM, kinuthiA muchanE <<a ymailto="mailto:muchanek@gmail.com" href="mailto:muchanek@gmail.com">muchanek@gmail.com</a>> wrote: > Andrew, > For #10, if you do not use a sieve to find the primes, it will run > forever! > There is one called the Sieve of Erastothenes. Check it out on > <a target="_blank" href="http://www.wikipedia.org/">Wikipedia</a>. > > Good luck :-) > Kinuthia... > On Tue, 2008-07-08 at 10:47 -0400, Andrew Mathenge wrote: >> I'm still trying them. I started at #1 after the one you proposed >> (#26) and I'm at #10 now. This one should be very simple but I don't >> know why it's taking so long to run. >> >> Andrew. >> >> On Tue, Jul 8, 2008 at 6:52 AM, kinuthiA muchanE <<a ymailto="mailto:muchanek@gmail.com" href="mailto:muchanek@gmail.com">muchanek@gmail.com</a>> wrote: >> > Habari, >> > Anybody still trying these problems, you are all so, so silent... >> > >> > Kinuthia... >> > >> > > > -- Ubuntu-ke mailing list <a ymailto="mailto:Ubuntu-ke@lists.ubuntu.com" href="mailto:Ubuntu-ke@lists.ubuntu.com">Ubuntu-ke@lists.ubuntu.com</a> <a href="https://lists.ubuntu.com/mailman/listinfo/ubuntu-ke" target="_blank">https://lists.ubuntu.com/mailman/listinfo/ubuntu-ke</a> </div></div></div> </body></html>