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Breaking the Billiard Ball

Braingle.com on

Published in Brain Teasers

It is your task to determine how high you can drop a billiard ball without it breaking. There is a 100 story building and you must determine which is the highest floor you can drop a ball from without it breaking. You have only two billiard balls to use as test objects. If both of them break before you determine the answer then you have failed at your task. What is the order of floors that you should drop the balls from to minimize the number of droppings that you will have to make to determine the answer?

Assume that if a ball doesn't break you can reuse it without worrying about it being weakened.


Solution:

If the proper order is chosen, you can determine the breaking point with a maximum of 14 drops. Here's how to do it:

First drop the first ball from the 14th floor. If it breaks you can determine the exact breaking point with the other ball in at most 13 more droppings, starting at the bottom and going up one floor at a time.

If the first ball survives the 14 floor drop then drop it again from the 27th (14+13) floor. If it breaks you can determine the exact breaking point with at most 12 more droppings.

If the first ball survives the 27 floor drop then drop it again from the 39th (14+13+12) floor. If it breaks you can determine the exact breaking point with at most 11 more droppings.

 

Keep repeating this process always going up one less floor than the last dropping until the first ball breaks. If it breaks on the xth dropping you will only need at most 14-x more droppings with the second ball to find the breaking point. By the 11th dropping of the first ball, if you get that far, you will have reached the 99th floor.

Today's brain teaser courtesy of Braingle.com.

 

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