Mr. Saunders has recently passed away.
In his will, he has divided his money among his 7 children, 7 stepchildren and a manager.
Mr. Sanders’ will stipulated:
- First give $1 to manager, and 1/7th of the remaining to the eldest child.
- Now give $1 to the manager and 1/7th of the remaining to second oldest child and so on.....
- After giving the money to the seventh (youngest) child, divide the remaining money among the seven stepchildren equally.
Knowing that:
- The ages of each of the seven children are different, and:
- Each of the 15 individuals received a positive integer number of dollars
What is the minimum amount of money that Mr. Saunders had left behind?
Extra Challenge: A non computer program aided solution.
DefDbl A-Z
Dim crlf$
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents
st = 100
For amt0 = st To 2000000
amt = amt0
good = 1
For kid = 1 To 7
mgr = 1: kidgets = (amt - mgr) / 7
If kidgets <> Int(kidgets) Then good = 0: Exit For
amt = amt - mgr - kidgets
' Text1.Text = Text1.Text & Str(mgr) & Str(kidgets) & Str(amt) & crlf
Next kid
If good Then
If amt Mod 7 = 0 Then
Text1.Text = Text1.Text & Str(amt0) & Str(amt / 7) & crlf
asave = amt0
End If
End If
Next
amt = asave
good = 1
For kid = 1 To 7
mgr = 1: kidgets = (amt - mgr) / 7
If kidgets <> Int(kidgets) Then good = 0: Exit For
amt = amt - mgr - kidgets
Text1.Text = Text1.Text & Str(mgr) & Str(kidgets) & Str(amt) & crlf
Next kid
If good Then
If amt Mod 7 = 0 Then
Text1.Text = Text1.Text & Str(amt / 7) & crlf
asave = amt0
End If
End If
End Sub
finds
823537 as the initial total amount, and 39990 as the amount that each stepchild will receive.
Details given, from eldest-child distribution to seventh-eldest child, showing manager's cut, child's cut and what's left after each distribution:
mgr child what's left
1 117648 705888
1 100841 605046
1 86435 518610
1 74087 444522
1 63503 381018
1 54431 326586
1 46655 279930
that last remainder being divided into seven amounts of
39990 each
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Posted by Charlie
on 2014-05-27 15:57:58 |
computer solution
