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 $1 to the manager and 1/7th of the remaining to second oldest child and so on.....
 After giving the money to the seventh (youngest) child, divide the remaining money among the seven stepchildren equally.
Knowing that:
 The ages of each of the seven children are different, and:
 Each of the 15 individuals received a positive integer number of dollars
What is the minimum amount of money that Mr. Saunders had left behind?
Extra Challenge: A non computer program aided solution.
DefDbl AZ
Dim crlf$
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 eldestchild distribution to seventheldest 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

Posted by Charlie
on 20140527 15:57:58 