It would appear that you earthlings win again.
The only lockers that remain open are perfect squares (1, 4, 9, 16, etc) because they are the only numbers divisible by an odd number of whole numbers; every factor other than the number's square root is paired up with another. Thus, these lockers will be "changed" an odd number of times, which means they will be left open. All the other numbers are divisible by an even number of factors and will consequently end up closed.
So the number of open lockers is the number of perfect squares less than or equal to one thousand. These numbers are one squared, two squared, three squared, four squared, and so on, up to thirty one squared. (Thirty two squared is greater than one thousand, and therefore out of range.) So the answer is thirty one.
Fast Adrian the used car sales representative sold a well-used car for a 30% profit.
The poor soul who bought the car was happy with the vehicle until it started breaking down a week later. The customer who bought the car went back to Fast Adrian and demanded he receive his money back.
Adrian countered that the car had been used for a week, thus, no refund. However, Fast Adrian offered to buy the car back for 20% less than the customer paid.
The customer agreed. Fast Adrian was then able to unload the car for the same amount that he initially paid for it.
What percentage of profit did Adrian make on the whole deal
Riddle
There is a barrel with no lid and some wine in it. "This barrel of wine is more than half full," said Frank. "No it's not," says Adrian. "It's less than half full."
Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct.