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?

FOR GROWNUPS

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

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SOLUTIONS TO PROBLEMS ON 09/21/06

FOR CHILDREN

PROBLEM # 1
One chicken lays two eggs in three days. How many eggs do three chickens lay in seven days?

SOLUTION
12 eggs assuming they can't lay fractions of an egg, 14 otherwise. 

FOR GROWNUPS

PROBLEM # 2
You walk upwards on an escalator, with a speed of 1 step per second. After 50 steps you are at the end. You turn around and run downwards with a speed of 5 steps per second. After 125 steps you are back at the beginning of the escalator. How many steps do you need if the escalator stands still?

SOLUTION
100 steps.

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