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 Four Digit Arithmetic (Posted on 2016-10-11)
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 No Rating

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 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\$

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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