Dividing a Clock into Three Equal Parts

Date: 10/27/2002 at 12:36:09
From: Peter Hage
Subject: Logic

If you could help me with this fourth-grade problem I would be very 
grateful.

They give you a picture of a clock with numbers 1-12 and ask, "Can you 
divide this clock into three parts using two lines and making all of 
the parts add up to the same number?"

Here is my logic. I figured out that if you add up all the numbers of 
the clock, they add up to 78. Since 78 divided by 3 is 26, all the 
parts have to equal 26.

My teacher suggested using toothpicks instead of erasing all of the 
pencil lines. I took her advice but it didn't help very much.

Thank you in advance!

- Peter

Date: 10/27/2002 at 13:13:09
From: Doctor Sarah
Subject: Re: Logic

Hi Peter - thanks for writing to Dr. Math.

Your thinking about the sums of the numbers in the three different 
parts being 26 is excellent!

Sometimes we get stuck on a problem like this because we think the 
lines have to start and end exactly where the numbers are.  For this 
problem, we need to think about lines that start and end _between_ the 
numbers.  

You can see a start on this problem here:

   

See if you can finish!

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

Date: 10/28/2002 at 18:33:40
From: Peter Hage
Subject: Thank you (Logic)

Thank you for your advice. It was very helpful and I have answered the 
question. I bet you will hear from me again in the future.

- Peter