My first attempt was to permute the ten digits to find a perfect square whose square root was tested for being strobogrammatic.  It failed as I had a bug in my test for strobogrammaticity. It's the same test I used in the successful program, below, but this time I successfully debugged it. (When looking for ix2, in the set of valid digits is was taking all the digits from i onward, rather than the single digit pointed at by i.)  I thought that I'd need pandigitals larger than 10 digits long (with repeated digits).

Doing the check for strobogrammaticity first made it easier to debug, as the check was missing a lot of valid numbers.

strobo     square

99066   9814072356      This is the one desired.

961196   923897750416

1910161   3648715045921

1968961   3876807419521

2061902   4251439857604

2281822   5206711639684

2528252   6392058175504

2668992   7123518296064

2698692   7282938510864

2892682   8367609153124

2920262   8527930148644

5612195   31496732718025

5625295   31643943837025

5811185   33769871104225

6210129   38565702196641

6212129   38590546712641

6581859   43320867895881

6651599   44243769256801

6808089   46350075831921

8105018   65691316780324

8161918   66616905438724

8268928   68375170269184

8508058   72387050931364

8511158   72439810500964

8521258   72611837902564

8558558   73248915039364

8682898   75392717678404

8888888   79012329876544

8891688   79062115489344

9150516   83731943066256

9152516   83768549130256

9528256   90787662401536

9608096   92315508745216

9611196   92375088550416

9910166   98211390147556

9921266   98431519042756

9965966   99320478313156

9990666   99813407123556

DefDbl A-Z

Dim crlf$

Private Sub Form_Load()

 Form1.Visible = True

 

 

 Text1.Text = ""

 crlf = Chr$(13) + Chr$(10)

 

 For stroboNum = 31992 To 9999999

       pandig = stroboNum * stroboNum

       good = 1

       strobo$ = LTrim(Str(stroboNum))

       For i = 1 To (Len(strobo) + 1) / 2

         ix = InStr("1256890", Mid(strobo, i, 1))

         If ix > 0 Then

           ix2 = InStr("1259860", Mid(strobo, Len(strobo) + 1 - i, 1))

           If ix2 <> ix Then good = 0: Exit For

         Else

           good = 0: Exit For

         End If

       Next

       If good Then

        pan$ = LTrim(Str(pandig))

        ReDim had(9)

        For i = 1 To Len(pan)

          had(Val(Mid(pan, i, 1))) = 1

        Next

        For i = 0 To 9

          If had(i) = 0 Then good = 0: Exit For

        Next

        If good Then

         Text1.Text = Text1.Text & strobo & "   " & pandig & crlf

        End If

       End If

       DoEvents

 Next stroboNum

 

  

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

  

End Sub