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Smallest Multiple of 99 (Posted on 2016-07-19) Difficulty: 3 of 5
Determine the minimum positive integer multiple of 99, such that
The sum of the digits is 99, and
The multiple begins and ends with 97.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Seems to be | Comment 2 of 3 |
The multiplier for 99 must end ...03 in order that the product end in ...97.  The multiplier must begin 979... or 98... in order for the product to begin 97....

The multiple must have at least 13 digits, and so be 99 times a number between 9888888888 and

 pt1 = 98000000003# * 99
 midpart1 = 9900
 endpt = 9900# * 10101011#
 For n = pt1 To endpt + pt1 Step midpart1
  DoEvents
   If sod(n) = 99 Then
     Text1.Text = Text1.Text & n & crlf
   End If
 Next

gives

9731999999997


while 

 pt1 = 97900000003# * 99
 midpart1 = 9900
 endpt = 9900# * 10101011#
 For n = pt1 To endpt + pt1 Step midpart1
  DoEvents
  If n > 9699999999999# Then
   If sod(n) = 99 Then
     Text1.Text = Text1.Text & n & crlf
     Exit Sub
   End If
  End If
 Next
 
increments up to that same answer.

BTW the sod function is

Function sod(n)
  s$ = LTrim(Str(n))
  tot = 0
  For i = 1 To Len(s$)
   tot = tot + Val(Mid(s$, i, 1))
  Next
  sod = tot
End Function


  Posted by Charlie on 2016-07-19 14:51:57
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