Saturday, October 7, 2000
M I N D  G A M E S


Birbal makes line vanish

Birbal develops a new interest in geometry, but does not tell anyone about it. He receives a message that Akbar has called him to the court. The Sultan of Persia has sent the wisest man in his kingdom to Akbar's court and he has a puzzle for every courtier. Birbal has been summoned after everyone else has failed to solve it. "Only a magician can do it," says Raja Maan Singh after spending two hours in trying to find a solution.

"What challenge do you have for us?" Birbal asks the wise man from Persia.

"Simple! I have drawn 10 equally spaced vertical lines. Make anyone of these vanish without cutting or rubbing off any of these," says the wise man.

Birbal smiles and examines the vertical lines of equal length drawn on a sheet of paper. He draws a diagonal from the bottom of the first line to the top of the tenth line and cuts the sheet along it. He slides the lower piece of the paper downward and to the left until there are only nine lines on the paper. The tenth line just vanishes.

 


"Hail Raja Birbal, Hail Raja Birbal," say all courtiers.

The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.

— Principia Mathematica by Issac Newton

"Wonderful, bravo Birbal, bravo! We are proud of you," Akbar says.

"You Sir," Akbar addresses the Persian scholar, "never dare to challenge an Indian again." "Yes your majesty, I will remember what you have just said," the scholar says.

"However, where has the missing line gone Birbal?" says Akbar. "Mahabali, believe it or not, a part of it has became a part of each of the other lines," Birbal replies and smiles again, while the emperor and the courtiers wonder.

Just then, a poor farmer stands out of the crowd and bows before the king. "Huzoor, I have a problem as well, can Raja Birbal help me solve it?" he says. "Let all of us know what puzzle you have for Birbal; say it aloud," says Akbar.

The farmer says, "Sir, I have five pigs, but only enough material to build four enclosures or pens - 16 lengths of fence material to make four four-sided enclosures. If I put two pigs in any one pen, one pig will climb on the other pig's back and hop out of the pen. He will then open all the other pens with his snout. I cannot sell or kill the pigs because they are my daughter's pets and extremely intelligent as well. How can I get these five pigs into four pens?"

"Would any other courtier like to try it, before I order Birbal to do it?" Akbar says. Several volunteers raise their hands. Each one of them is given 16 straws representing the 16 lenghts of fence material. They have to solve the problem without putting more than one pig into any pen and without cutting any of the fences as the material is bare minimum.

When the volunteers give up, Birbal shows them the solution. He makes a central pen, each wall of which is shared by one of the other four pens. Thus, the farmer saves the four extra lengths of fence material required to build the fifth enclosure.

—Aditya Rishi