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Squared halves (Posted on 2016-06-10) Difficulty: 4 of 5
8833 = 88^2 + 33^2
As you see, the above number is equal to the sum of the squares of its two halves.

Provide all numbers below 1,000,000 possessing this feature.

Bonus question: As above, but the numbers should be equal to the sum of the cubes of their thirds, i.e. ABCDEF= (AB)^3+(CD)^3+(EF)^3

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution (spoiler) Comment 1 of 1
Squared halves

1233
8833
990100

Cubed thirds

153
370
371
407
165033
221859
336700
336701
340067
341067
407000
407001
444664
487215
982827
983221
166500333
296584415
333667000
333667001
334000667
710656413
828538472


BTW, a little tweak to the below program also finds for the squared halves portion 94122353 = 9412^2 + 2353^2.


from

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 ulimplus1 = 10
 For digs = 1 To 3
   lowlim = ulimplus1 / 10
   upplim = ulimplus1 - 1
   For a = lowlim To upplim
     For b = 0 To upplim
       DoEvents
       a2 = a * a
       b2 = b * b
       n = a * ulimplus1 + b
       If n = Val(a2 + b2) Then
         Text1.Text = Text1.Text & n & crlf
       End If
     Next
   Next
   ulimplus1 = ulimplus1 * 10
 Next
 
 
 ulimplus1 = 10
 For digs = 1 To 3
   lowlim = ulimplus1 / 10
   upplim = ulimplus1 - 1
   For a = lowlim To upplim
     For b = 0 To upplim
      For c = 0 To upplim
       DoEvents
       a3 = a * a * a
       b3 = b * b * b
       c3 = c * c * c
       n = a * ulimplus1 * ulimplus1 + b * ulimplus1 + c
       If n = Val(a3 + b3 + c3) Then
         Text1.Text = Text1.Text & n & crlf
       End If
      Next
     Next
   Next
   ulimplus1 = ulimplus1 * 10
 Next
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2016-06-10 15:02:02
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