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Dividing the Oxen

Published December 15, 2000
Countries: None
Age Levels: 12 and up

Three sons had a problem.  Their father who they all loved had died.  Before he died, he called them together.  "I want no fighting among you when I am gone.  I own enough land for you all to share.  It will be easy to divide it three ways.  There is enough lumber in my warehouse to build three houses - one for each of you.  I have money that I have given to a judge to be divided evenly among you."

"But, I give you one challenge. My oxen have pulled my plows.  They have hauled heavy loads.  They will help you farm your lands.  I want my oven divided among you in a special way.  My oldest son has been with me longer and helped me every day.  He shall have 1/2 of the oxen.  My second son shall have 1/3 of the oxen.  My youngest son shall have 1/9 of the oxen."  Then the old man died before he could help them solve the problem he had given them.

The sons burried their father.  They divided the land into three parts.  They helped each other build new houses, one for each son.  They went to the judge to divide their father's money.  But, the judge said, "Before you get your father's money, you must first divide the oxen."

"This would be no problem," thought the three sons.  They walked up the hill together to count their father's oxen.  There were 17 oxen.  "OH NO!"  17 cannot be evenly divided by 2 or by 3 or by 9.  "How could they dived the oxen in the way their father had wanted?"

Can you solve the problem before reading the end of the story?

The sons went back to the judge.  "Why would our father ask us to do something that cannot be done?"

"Your father wanted to let you know that sometimes you had to ask for help to solve your problems.  Now, may I help you?"  The boys already had 17 oxen.  The judge gave them one more of his own.  17 + 1 = 18.

Eighteen  could be divided in half.  So, the oldest son got nine oxen.  Eighteen could be divided evenly by three.  So the second son got six oxen.  Eighteen could be divided evenly by nine.  So the youngest son got two oxen.  There was still one problem.  9 + 6 + 2 = 17.  There was one ox left over.  But this was easy to solve.  The brothers happily gave the remaining ox back to the the judge who divided their father's money among them.