Euler Problem 19

Euler Problem 19 asks:

‘You are given the following information, but you may prefer to do some
‘research for yourself.

‘    * 1 Jan 1900 was a Monday.
‘    * Thirty days has September,
‘      April, June and November.
‘      All the rest have thirty-one,
‘      Saving February alone,
‘      Which has twenty-eight, rain or shine.
‘      And on leap years, twenty-nine.
‘    * A leap year occurs on any year evenly divisible by 4, but not on a
‘century unless it is divisible by 400.

‘How many Sundays fell on the first of the month during the twentieth
‘century (1 Jan 1901 to 31 Dec 2000)?

Wow. First thought: Euler actually got the century right. Math-minded indeed. Second thought: I need a day counter, a week counter, a month counter, a leap year checker. That’s a lot of conditionals. No wonder this is here. Third thought: I’m doing this in Excel. Piece of cake. This may be the only one aimed right at us, if not intentionally. Here’s my code. Ran in under a second.

Sub Problem_019()  
   Dim Start   As Date
   Dim Answer  As Long
   Dim T       As Single
   T = Timer
   Start = DateSerial(1901, 1, 1)
   Do While Start <  DateSerial(2001, 1, 1)
      If Weekday(Start) = vbSunday And Day(Start) = vbSunday Then
         Answer = Answer + 1
      End If
      Start = Start + 1
   Debug.Print Answer; ”  Time:”, Timer – T
End Sub

Coded it up. It ran the first time, and I checked in with the right answer. I was feeling so good until I saw the pencil and paper approach of those who’d solved it …100 years with 12 months per year over 7 days


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5 thoughts on “Euler Problem 19

  1. The code as written is examining an awful lot of irrelevant dates, since we only want the first of each month. Changing the loop to

    If Weekday(Start) = vbSunday Then
    Answer = Answer + 1
    End If
    Start = DateSerial(Year(Start), Month(Start) + 1, 1)

    is about 20 times faster on my machine (0.001875 vs 0.035625). Not 30-odd, I imagine, because the DateSerial business is more expensive than incrementing.

  2. Tushar –

    Do you have a link on your website to your large arithmetic functions?

    Happy New Year!


  3. What about:

    For j = 0 To 1200
      If Format(DateAdd(“m”, j, “01-01-1900”), “w”) = 1 Then x = x + 1

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