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 Pandigital and divisible (Posted on 2017-12-29)
List all the numbers like 2,438,195,760
i.e.
- being pandigital (10 distinct digits)
and
- divisible by each of the integers below 23,
19
excluded.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer solution (spoiler) | Comment 1 of 3
To be divisible by each of the integers below 23 save for 19, it is necessary and sufficient to be divisible by each integer below 19, as 20 is covered by 5 and 4, 21 is covered by 3 and 7 and 22 by 2 and 11.

The LCM of the first 18 whole numbers is 12,252,240 (2^4 * 3^2 * 5 * 7 * 11 * 13 * 17) so we need only check multiples of that number and find any that are 10-digit pandigital.  There are four of them:

2438195760
3785942160
4753869120
4876391520

from the program where we check all 10-digit multiples for being pandigital, and stop the search as soon as 10 digits are exceeded.

DefDbl A-Z
Dim crlf\$

Private Sub Form_Load()
Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

unit = 12252240
n = 10 * unit
Do
n = n + unit
ns\$ = LTrim(Str(n))
If Len(ns) = 10 Then
good = 1
For i = 1 To 10
If InStr(ns, Mid("0123456789", i, 1)) = 0 Then good = 0: Exit For
Next
If good Then
Text1.Text = Text1.Text & n & crlf
End If
End If
DoEvents
Loop Until Len(ns) > 10

Text1.Text = Text1.Text & crlf & " done"

End Sub

 Posted by Charlie on 2017-12-29 11:15:53
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