FOR CHILDREN

PROBLEM # 1
From a book, a number of consecutive pages are missing. The sum of the page numbers of these pages is 9808.

The Question: Which pages are missing?

FOR GROWNUPS

PROBLEM # 2
Long ago, a young prince wanted to marry a King's daughter. The King decided to test the prince. He gave the prince two empty, porcelain vases, 100 white pearls, and 100 black pearls. "You must put all the pearls in the vases", he told the prince. "After this, I will call my daughter from the room next door. She will take a random pearl from one of the two vases. If this pearl is a black one, you are allowed to marry my daughter."

The Question: What was the best way in which the prince could divide the pearls over the vases?

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SOLUTIONS TO PROBLEMS ON 10/05/06

FOR CHILDREN

PROBLEM # 1
What is the largest radius of the circle that can fit in the empty space in between four circles of radius 1, which touch each other and the centers lie on the corners of  a square?

SOLUTION
0.41. 

FOR GROWNUPS

PROBLEM # 2
What is the largest volume of a cone that can fit in a sphere of radius 1?

SOLUTION 
1.24.

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