Mathematics Problem Of the Week

Spring 2003

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POW #12

Ball Breakers

 

We would like to determine how far a billiard ball can be dropped before it breaks.  We can test balls by dropping them from any of the floors of a fifty-story building, but we are only allowed to use two balls for the entire test.  Of course, we could just test from floors 1, 2, 3, ... in succession until a ball breaks to find the answer, but that could require up to 50 trips up the elevator to determine the breaking floor. What is the minimum number of trips required to be sure to find the lowest height (floor) at which billiard balls will first break? 

 

Describe a plan for carrying out this test that will guarantee success within that minimum number of trips.  You may assume that a ball will always break at the “breaking” floor or higher and will never break at a lower floor. 

 

 

 

 

Due Friday, May 2nd at Noon.