All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Money Division Muse (Posted on 2014-05-27) Difficulty: 4 of 5
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.)
Solution computer solution | Comment 1 of 4
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

  Posted by Charlie on 2014-05-27 15:57:58
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information