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AABBCCDD and Perfect Square (Posted on 2016-05-16) Difficulty: 3 of 5
By adding 1 to the non leading zeros number N= AABBCCDD, we get a perfect square. Find N.
(A, B, C and D are different base ten digits.)

*** AABBCCDD denotes the concatenation of the digits and not their product .

Note: For an extra challenge, solve this puzzle without using a computer program aided method.

No Solution Yet Submitted by K Sengupta    
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Solution computer solutions | Comment 2 of 3 |
   N      sqrt(N+1)
11336688   3367
22886655   4784
44009955   6634

DefDbl A-Z
Dim crlf$, used(9)


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For a = 1 To 9
   used(a) = 1
 For b = 0 To 9
   If used(b) = 0 Then
     used(b) = 1
 For c = 0 To 9
   If used(c) = 0 Then
     used(c) = 1
 For d = 0 To 9
   If used(d) = 0 Then
     used(d) = 1
   aabbccddplus = 11000000 * a + 110000 * b + 1100 * c + 11 * d + 1
   sr = Int(Sqr(aabbccddplus) + 0.5)
   If sr * sr = aabbccddplus Then
     Text1.Text = Text1.Text & aabbccddplus - 1 & "   " & sr & crlf
   End If
      used(d) = 0
   End If
 Next
     used(c) = 0
   End If
 Next
     used(b) = 0
   End If
 Next
   used(a) = 1
 Next
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2016-05-16 16:23:10
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