All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Pandigital concatenations (Posted on 2014-05-10)
What is the smallest integer n such that a concatenation of n2 and n3 contains each of the ten decimal digits exactly once?

What is the smallest integer m, m>n such that a concatenation of m2 and m3 contains each of the ten decimal digits once and some of them more than once?

Please provide few additional(i.e. not smallest) samples for both cases.

 See The Solution Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solutions Comment 1 of 1
There is only one value for n, shown below, above the row of hyphens, together with n^2 and n^3.

For m, all values below 1000 are shown (just ignore the first line where m = n, contrary to the specific rule) below the row of hyphens.

69     4761  328509  Smallest and only value for n
---------------
69     4761  328509
128     16384  2097152  Smallest value for m
203     41209  8365427
302     91204  27543608
327     106929  34965783
366     133956  49027896
398     158404  63044792
467     218089  101847563
542     293764  159220088
591     349281  206425071
593     351649  208527857
598     357604  213847192
633     400689  253636137
643     413449  265847707
669     447561  299418309
690     476100  328509000
747     558009  416832723
759     576081  437245479
903     815409  736314327
923     851929  786330467
943     889249  838561807

DefDbl A-Z

Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
For n = 9 To 999
n2\$ = LTrim(Str(n * n))
n3\$ = LTrim(Str(n * n * n))
combo\$ = n2\$ + n3\$
If Len(combo\$) = 10 Then
good = 1
For i = 1 To Len(combo\$)
If InStr(Mid(combo\$, i + 1), Mid(combo\$, i, 1)) > 0 Then good = 0: Exit For
Next
If good Then Text1.Text = Text1.Text & Str(n) & "     " & n2\$ & "  " & n3\$ & crlf\$: Form1.Visible = True: DoEvents
End If
Next

Text1.Text = Text1.Text & "---------------" & crlf\$

For n = 9 To 999
n2\$ = LTrim(Str(n * n))
n3\$ = LTrim(Str(n * n * n))
combo\$ = n2\$ + n3\$
ct = 0
For i = 1 To Len(combo\$)
If InStr(combo\$, Mid(combo\$, i, 1)) = i Then ct = ct + 1
Next
If ct = 10 Then Text1.Text = Text1.Text & Str(n) & "     " & n2\$ & "  " & n3\$ & crlf\$: Form1.Visible = True: DoEvents
Next
End Sub

 Posted by Charlie on 2014-05-10 15:55:51

 Search: Search body:
Forums (0)