MATH MONDAY - Lockers in lockdown
Occasional Puzzles
Schools may be closed, but these lockers are open...or maybe closed? But that's for you to figure out!
Today's Puzzle
A high school has 1,000 students and 1,000 lockers. On the first day of school, the principal asks the first student to go down the line and open every single locker. He asks the second student to go to every second locker and close it. Then he asks the third student to go to every third locker and close it if it's open or open it if it's closed, the fourth to go to every fourth locker and so on for all 1,000 students. In the end, how many lockers are open?
Yesterday's Puzzle
You have two ropes that each burn for one hour. Given these two ropes and a way to light them, how do you measure 45 minutes? Do not assume that the two ropes are identical or that they burn evenly.
[SPOILER] Answer to Yesterday's Puzzle
Light both ends of the first rope and one end of the second rope. When the first rope burns out, light the other end of the second rope. When the second rope burns out, it will have been 45 minutes.
Explanation: The first rope will burn out after 30 minutes, since it was lit on both ends. Since the second rope was lit at the same time but only from one end, it has 30 minutes left. By lighting the other end of that rope, you cut the remaining 30 minutes down to 15. 30+15=45.