This particular blog entry is somewhat special to me. None of this post’s content is my creation. This is about one of the mathematical puzzles I struggled to solve as a kid. It’s about fair division & how various players perceive the value of their contribution. And how the pie is actually divided by an expert. Read on!
Here is the actual puzzle (Names are Americanized to make your life easier):
One very hot day two people Joe & Sam were getting ready to eat their lunch. Joe had 3 pieces of flatbread & Sam had 5 pieces flatbread. As they were about to begin their meal, a young nobleman came by.The nobleman looked hungry and tired, so Joe and Sam invited him to eat with them.
After some discussion about how to divide the food, they decided to stack all the 8 flatbreads (Joe’s 3 + Sam’s 5) on top of each other and then cut the stack into 3 equal parts. So did they divide and all three of them had a great meal. The nobleman happily paid 8 gold coins as a token of gratitude & left!
Now Joe & Sam were arguing about how to divide the pie (8 gold coins). Joe thinks they should get 4 gold coins each. Sam thinks he should get 5 out of 8 coins as he contributed 5 flatbreads compared to Joe’s 3. Finally they decided to go to a judge.
The Judge thought for a while and said “The fair way to divide these gold coins is to give seven coins to Sam and one coin to Joe."
What!!?? Exclaimed both Joe & Sam. Then, the judge explained how his division is FAIR & both the players left convinced.
This is was the puzzle. Now, can YOU tell why judge ruled the way he did? What is his logic behind giving 7 gold coins for Sam (who contributed 5 flatbreads)&(1 gold coin to Joe who contributed 3 flatbreads)?? Solve it if you can!!
SPOILER ALERT: Here is the solution:
As Joe’s contribution towards guest is only 1/8th& Sam’s contribution is 7/8th – the Judge ordered Joe to have only 1 gold coin & give 7 coins to Sam!! Fair division. huhh!
NOTE: If you want to read the classic Indian version of this tale/puzzle here it is (no solution given though!): http://www.edb.utexas.edu/empson/wp-content/fairsharefolktale2.jpg
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