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 Money Division Muse (Posted on 2014-05-27)
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:
1. First give \$1 to manager, and 1/7th of the remaining to the eldest child.
2. Now give \$1 to the manager and 1/7th of the remaining to second oldest child and so on.....
3. 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.

 No Solution Yet Submitted by K Sengupta Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 1 of 4
DefDbl A-Z
Dim crlf\$

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

 Posted by Charlie on 2014-05-27 15:57:58

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