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Four Digit Arithmetic (Posted on 2016-10-11) Difficulty: 3 of 5
Each of A, B and C is a positive integer in arithmetic sequence, with A < B < C such that the last four digits in the base ten expansion of A*B*C is 2016.

Determine the three smallest values of A+B+C

No Solution Yet Submitted by K Sengupta    
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Solution computer solution | Comment 1 of 2
The three smallest values are 96, 456 and 468.

Those with A + B + C under 1000:

     A+B+C      A*B*C    A    B    C
       96         2016    1   32   63
      456      3482016  138  152  166
      468      3032016   86  156  226
      486      4142016  136  162  188
      543      1002016   16  181  346
      543      4622016   96  181  266
      546      6022016  176  182  188
      693       632016    6  231  456
      693      5252016   56  231  406
      693     12182016  206  231  256
      696      2642016   26  232  438
      756     11342016  116  252  388
      816     16892016  163  272  381
      831     15902016  138  277  416
      843     19652016  186  281  376
      876     17972016  138  292  446
      918     28622016  296  306  316
      
      
DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For b = 10 To 334
   For a = 1 To b - 1
      c = 2 * b - a
      prod = a * b * c
      q = Int(prod / 10000)
      r = prod - q * 10000
      If r = 2016 Then
        Text1.Text = Text1.Text & mform(a + b + c, "#########")
        Text1.Text = Text1.Text & mform(a * b * c, "#############")
        Text1.Text = Text1.Text & mform(a, "#####")
        Text1.Text = Text1.Text & mform(b, "#####")
        Text1.Text = Text1.Text & mform(c, "#####") & crlf
      End If
      DoEvents
   Next
 Next
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub

Function mform$(x, t$)
  a$ = Format$(x, t$)
  If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
  mform$ = a$
End Function
      

  Posted by Charlie on 2016-10-11 09:52:41
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