 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Pandigitals Divided by 11 (Posted on 2017-07-23) For which bases b is it possible to make a pandigital number in base b that is divisible by 11 in base b?

For example, in base 4: 1023 / 11 = 33. (In base 10 this is 75 / 5 = 15.)

 No Solution Yet Submitted by Brian Smith No Rating Comments: ( Back to comment list | You must be logged in to post comments.) computer exploration | Comment 1 of 4
dividend and quotient
in the given bases:

1023  33
10324  434
120435  10545
10234576  730416
102347586  8304326
1024375869  93125079

are such pandigitals in bases 4, 5, 6, 8, 9 and 10.

There are others in these bases, but these were the first found for each of those bases.

It doesn't tell me much. Base 7 is missing. When we go higher than base 10, execution time is too long.

DefDbl A-Z
Dim crlf\$

Form1.Visible = True

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

For b = 3 To 30
dvsr = b + 1
low = Int(b ^ (b - 1))
high = Int(b ^ b - 1)
mlt = Int(low / dvsr)
Do
found = 0
prod = dvsr * mlt
inbase\$ = base\$(prod, b)
If Len(inbase\$) = b Then
good = 1
For i = 2 To Len(inbase)
If InStr(inbase, Mid(inbase, i, 1)) < i Then good = 0: Exit For
Next
If good Then
Text1.Text = Text1.Text & inbase & "  " & base\$(mlt, b) & crlf
found = 1: Exit Do
End If
End If
mlt = mlt + 1
DoEvents
Loop Until prod > high
Next

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

End Sub

Function base\$(n, b)
v\$ = ""
n2 = n
Do
q = Int(n2 / b)
d = n2 - q * b
n2 = q
' d = n2 Mod b
' n2 = n2 \ b
v\$ = Mid("0123456789abcdefghijklmnopqrstuvwxyz", d + 1, 1) + v\$
Loop Until n2 = 0
base\$ = v\$
End Function

 Posted by Charlie on 2017-07-23 10:39:48 Please log in:

 Search: Search body:
Forums (4)