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Perhaps it would be best, to save time, to estimate whereabouts you think the egg will break, for example if you estimated that it would break on the sixth floor, if you dropped it on that floor and it didn't break, you could go up a few floors and try again. If it did break on the sixth floor, you could then go down a few floors instead, and keep doing the same thing.
This method would be time efficient because it would mean you would be dropping eggs on less floors, therefore you are also saving the company money because you are using less of their eggs. There is no 'solution' to this puzzle as such, because there are many different ways of doing this, and because we are not actually doing this experiment, it is impossible to test all these different methods out. This is just one of the many conclusions people can come to.