perplexus.info :: Numbers : Pandigital concatenations

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

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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

Private Sub Form_Load()

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

If good Then Text1.Text = Text1.Text & Str(n) & " " & n2$ & " " & n3$ & crlf$: Form1.Visible = True: DoEvents

End If

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

If ct = 10 Then Text1.Text = Text1.Text & Str(n) & " " & n2$ & " " & n3$ & crlf$: Form1.Visible = True: DoEvents

End Sub

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

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