Three horses are standing in a triangular field, which is exactly 100 yards on each side. One horse stands at each corner; and simultaneously all three set off running. Each horse runs after the horse in the adjacent corner on his left, thus following a curved course, which terminates in the middle of the field, all three horses arriving there together. The horses obviously ran at the same speed, but just how far did they run?

Find a number ABCDEFGHIJ such that A is the count of how many 0's are in the number, B is the number of 1's, and so on.

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?