 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Squared halves (Posted on 2016-06-10) 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 No Rating Comments: ( Back to comment list | You must be logged in to post comments.) 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 Please log in:
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