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Splitting a Clock Face into Desired Sums

Date: 11/14/2007 at 00:07:31
From: Sujai
Subject: Breaking a clock into five pieces

Take a clock and break the clock into exactly five pieces such that
the sums of all the numbers on each piece are 8, 10, 12, 14 and 16. 

What i figured out was that the sum of nos from 1-12 is 78 and sum of
the numbers on pieces mentioned is 60. i am not able to figure out the
exact solution.



Date: 11/14/2007 at 10:32:15
From: Doctor Ian
Subject: Re: Breaking a clock into five pieces

Hi Sujai,

What occurs to me is that if you break the '12' between the 1 and the
2, you lose 

  12 - (1 + 2) = 9 

from the total.  That drops you from 78 to 69.  Similarly, if you
break the '10' between the 1 and the 0, you lose

  10 - (1 + 0) = 9 

more, dropping you to 60, which is what you want. 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
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