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 AABBCCDD and Perfect Square (Posted on 2016-05-16)
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 No Rating

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 computer solutions | Comment 2 of 3 |
`   N      sqrt(N+1)11336688   336722886655   478444009955   6634`

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

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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