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Biggest and smallest (Posted on 2015-11-24) Difficulty: 3 of 5
How many square numbers use each of the 10 digits exactly once (no leading zeros)?

Write down the smallest and the biggest of them.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution | Comment 1 of 2
There are 87, starting with 1026753849 and ending with 9814072356.

  square    sqrt
1026753849 32043
1042385796 32286
1098524736 33144
1237069584 35172
1248703569 35337
1278563049 35757
1285437609 35853
1382054976 37176
1436789025 37905
1503267984 38772
1532487609 39147
1547320896 39336
1643897025 40545
1827049536 42744
1927385604 43902
1937408256 44016
2076351489 45567
2081549376 45624
2170348569 46587
2386517904 48852
2431870596 49314
2435718609 49353
2571098436 50706
2913408576 53976
3015986724 54918
3074258916 55446
3082914576 55524
3089247561 55581
3094251876 55626
3195867024 56532
3285697041 57321
3412078569 58413
3416987025 58455
3428570916 58554
3528716409 59403
3719048256 60984
3791480625 61575
3827401956 61866
3928657041 62679
3964087521 62961
3975428601 63051
3985270641 63129
4307821956 65634
4308215769 65637
4369871025 66105
4392508176 66276
4580176329 67677
4728350169 68763
4730825961 68781
4832057169 69513
5102673489 71433
5273809641 72621
5739426081 75759
5783146209 76047
5803697124 76182
5982403716 77346
6095237184 78072
6154873209 78453
6457890321 80361
6471398025 80445
6597013284 81222
6714983025 81945
7042398561 83919
7165283904 84648
7285134609 85353
7351862049 85743
7362154809 85803
7408561329 86073
7680594321 87639
7854036129 88623
7935068241 89079
7946831025 89145
7984316025 89355
8014367529 89523
8125940736 90144
8127563409 90153
8135679204 90198
8326197504 91248
8391476025 91605
8503421796 92214
8967143025 94695
9054283716 95154
9351276804 96702
9560732841 97779
9614783025 98055
9761835204 98802
9814072356 99066

87 done

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 
 For sr = 31623 To 99999
  DoEvents
  sq$ = LTrim(Str(sr * sr))
  good = 1
  For i = 2 To 10
    If InStr(sq, Mid(sq, i, 1)) < i Then good = 0: Exit For
  Next
  If good Then
   Text1.Text = Text1.Text & sq & Str(sr) & crlf
   ct = ct + 1
  End If
 Next sr
 
 Text1.Text = Text1.Text & crlf & ct & " done"
End Sub


  Posted by Charlie on 2015-11-24 10:34:15
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