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Puzzle 6.8 illustrates the well-know egg-drop experiment.
Suppose you wish to know which floors in a 36-story building are safe to drop eggs from and which will cause the eggs to break on landing (using a special container for the eggs). We eliminate chance and possible differences between different eggs (e.g. one egg breaks when dropped from the 7th floor and another egg survives a drop from the 20th floor) by making a few (reasonable!) assumptions:
- An egg that survives a drop can be used again (no harm is done and the egg is not weaker).
- A broken egg can not be used again for any experiment.
- The effect of a fall is the same for all eggs.
- If an egg breaks when dropped from some floor, it would break also if dropped from a higher floor.
- If an egg survives a fall when dropped from some floor, it would survive also if dropped from a lower floor.
- There are no pre-existing assumptions concerning when the egg will break. It is possible that a drop from the first floor in the special container would break an egg. It is also possible that a drop from the 36th floor in the special container would not break an egg.
Now, if only one egg is available for experimentation, we have no choice. To obtain the required result, we have to start by dropping the egg from the first floor. If it breaks, we know the answer. If it survives, we drop it from the second floor and continue upward until the egg breaks. The worst-case scenario would require 36 drops to determine the egg-breaking floor.
Now, suppose we have two eggs. What is the least number of egg drops required to determine the egg-breaking floor? Note that the method should work in all cases.
The software would allow you to change the number of floors and the number of eggs available, so you can experiment with many scenarios. Note that every time you start a new game, the software generates a new (random) egg-breaking floor …