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 Squares built from leftovers (Posted on 2018-04-05)
Let N1=123456789
Erase n digits and shrink the remnants of N1 into one continuous chain creating a new number N1'.

What is the minimum number of digits to be erased so that N1' will be a square number?

Same question for N2=987654321 and N2'.

 See The Solution Submitted by Ady TZIDON No Rating

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 computer solution | Comment 1 of 4
N1
`leftover  square root     9        3     4        2    49        7    36        6   289       17    25        5   256       16     1        1    16        4   169       13  1369       37 13689      117134689      367  minimum number of digits erased: 3 13456      116 N2leftover  square root     1        1     4        2    64        8    81        9   841       29  minimum number of digits erased: 6       9        3   961       31  minimum number of digits erased: 6`

DefDbl A-Z
Dim crlf\$, nx\$, leftovers\$

Form1.Visible = True
Text1.Text = ""
crlf = Chr(13) & Chr(10)

nx\$ = "123456789"
leftovers = ""

buildon 1

nx\$ = "987654321"
leftovers = ""

buildon 1

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

End Sub

Sub buildon(wh)
For i = 0 To 1
DoEvents
sve\$ = leftovers
If i Then leftovers = leftovers + Mid(nx, wh, 1)
If wh = 9 Then
sq = Val(leftovers)
sr = Int(Sqr(sq) + 0.5)
If sr * sr = sq Then
Text1.Text = Text1.Text & mform(sq, "#####0") & "   " & mform(sr, "#####0") & crlf
End If
Else
buildon (wh + 1)
End If
leftovers = sve
Next
End Sub

Function mform\$(x, t\$)
a\$ = Format\$(x, t\$)
If Len(a\$) < Len(t\$) Then a\$ = Space\$(Len(t\$) - Len(a\$)) & a\$
mform\$ = a\$
End Function

 Posted by Charlie on 2018-04-05 12:27:33

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